The correct answers for the fluid mechanics problems are:
(c) Shear stress and the shear strain rate.
(a) 4000 kg/cm².
(b) Fluid pressure is zero.
(c) Pascal's law.
(a) Remains horizontal.
(b) Archimedes's principle.
b) has zero viscosity
(c) N/m².
∇·p = g
(b) F = pg[tex]h_{p}[/tex]A
How to interpret Fluid mechanics?8) Newton's law for the shear stress states that the shear stress is directly proportional to the velocity gradient.
Thus, Newton's law for the shear stress is a relationship between c) Shear stress and the shear strain rate .
9) Formula for Bulk modulus here is:
Bulk modulus =∆p/(∆v/v)
Thus:
∆p = 150 - 50 = 100 kg/m²
∆v = 0.040 - 0.039 = 0.001
Bulk modulus = 100/(0.001/0.040)
= 4000kg/cm²
10) In a static fluid, it means no motion as it is at rest and as such the fluid pressure is zero.
11) Pascal's law says that pressure applied to an enclosed fluid will be transmitted without a change in magnitude to every point of the fluid and to the walls of the container.
12) When an open tank containing liquid moves with an acceleration in the horizontal direction, then the free surface of the liquid a) Remains horizontal
13) When a body is immersed wholly or partially in a liquid, it is lifted up by a force equal to the weight of liquid displaced by the body. This statement is called b) Archimedes's principle
14) An ideal fluid is a fluid that is incompressible and no internal resistance to flow (zero viscosity)
15) Surface tension is also called Pressure or Force over the area. Thus:
The unit of surface tension is c) N/m²
16) The correct formula for Euler's equation of hydrostatics is:
∇p = ρg
17) The force acting on inclined submerged area is:
F = pg[tex]h_{p}[/tex]A
Read more about Fluid Mechanics at: https://brainly.com/question/31174575
#SPJ4
5. (14 points) Steam expands isentropically in a piston-cylinder arrangement from a pressure of P1=2MPa and a temperature of T1=500 K to a saturated vapor at State2. a. Draw this process on a T-S diagram. b. Calculate the mass-specific entropy at State 1 . c. What is the mass-specific entropy at State 2? d. Calculate the pressure and temperature at State 2.
The pressure and temperature at State 2 are P2 = 1.889 MPa and T2 = 228.49°C.
a) The isentropic expansion process from state 1 to state 2 is shown on the T-S diagram below:b) The mass-specific entropy at State 1 (s1) can be determined using the following expression:s1 = c_v ln(T) - R ln(P)where, c_v is the specific heat at constant volume, R is the specific gas constant for steam.The specific heat at constant volume can be determined from steam tables as:
c_v = 0.718 kJ/kg.K
Substituting the given values in the equation above, we get:s1 = 0.718 ln(500) - 0.287 ln(2) = 1.920 kJ/kg.Kc) State 2 is a saturated vapor state, hence, the mass-specific entropy at State 2 (s2) can be determined by using the following equation:
s2 = s_f + x * (s_g - s_f)where, s_f and s_g are the mass-specific entropy values at the saturated liquid and saturated vapor states, respectively. x is the quality of the vapor state.Substituting the given values in the equation above, we get:s2 = 1.294 + 0.831 * (7.170 - 1.294) = 6.099 kJ/kg.Kd) Using steam tables, the pressure and temperature at State 2 can be determined by using the following steps:Step 1: Determine the quality of the vapor state using the following expression:x = (h - h_f) / (h_g - h_f)where, h_f and h_g are the specific enthalpies at the saturated liquid and saturated vapor states, respectively.
Substituting the given values, we get:x = (3270.4 - 191.81) / (2675.5 - 191.81) = 0.831Step 2: Using the quality determined in Step 1, determine the specific enthalpy at State 2 using the following expression:h = h_f + x * (h_g - h_f)Substituting the given values, we get:h = 191.81 + 0.831 * (2675.5 - 191.81) = 3270.4 kJ/kgStep 3: Using the specific enthalpy determined in Step 2, determine the pressure and temperature at State 2 from steam tables.Pressure at state 2:P2 = 1.889 MPaTemperature at state 2:T2 = 228.49°C
Therefore, the pressure and temperature at State 2 are P2 = 1.889 MPa and T2 = 228.49°C.
Learn more about pressure :
https://brainly.com/question/30638002
#SPJ11
Considering the above scenario, the engineer should make a report/presentation explaining the process of design on different component and its manufacturing; finally, an integration as a complete system. (Process of VR design (constraints and criteria), components of manufacturing a fountain including audio system and lights display and any other auxiliary (fire-works display, multiple screen and advertising screens)
For the process of VR design, the engineer should start by considering the constraints and criteria. The engineer should first consider the specific requirements of the client in terms of the design of the fountain. The constraints may include the size of the fountain, the materials that will be used, and the budget that the client has allocated for the project.
After considering the constraints and criteria, the engineer should start designing the fountain using virtual reality technology. Virtual reality technology allows engineers to design complex systems such as fountains with great accuracy and attention to detail. The engineer should be able to create a virtual model of the fountain that incorporates all the components that will be used in its manufacture, including the audio system and the lights display.
Once the design is complete, the engineer should then proceed to manufacture the fountain. The manufacturing process will depend on the materials that have been chosen for the fountain. The engineer should ensure that all the components are of high quality and meet the specifications of the client.
Finally, the engineer should integrate all the components to create a complete system. This will involve connecting the audio system, the lights display, and any other auxiliary components such as fireworks displays and multiple screens. The engineer should also ensure that the fountain meets all safety and regulatory requirements.
In conclusion, the engineer should prepare a report or presentation that explains the process of designing and manufacturing the fountain, including all the components and the integration process. The report should also highlight any challenges that were encountered during the project and how they were overcome. The engineer should also provide recommendations for future improvements to the design and manufacturing process.
To know more about engineer visit:
https://brainly.com/question/33162700
#SPJ11
A contractor manufacturing company purchased a production equipment for $450,000 to meet the specific needs of a customer that had awarded a 4-year contract with the possibility of extending the contract for another 4 years. The company plans to use the MACRS depreciation method for this equipment as a 7-year property for tax purposes. The combined income tax rate for the company is 24%, and it expects to have an after-tax rate of return of 8% for all its investments. The equipment generated a yearly revenue of $90,000 for the first 4 years. The customer decided not to renew the contract after 4 years. Consequently, the company decided to sell the equipment for $220,000 at the end of 4 years. Answer the following questions, (a) Show before tax cash flows (BTCF) from n= 0 to n=4 (b) Calculate depreciation charges (c) Compute depreciation recapture or loss (d) Find taxable incomes and income taxes (e) Show after-tax cash flows (ATCF). (f) Determine either after tax NPW or after-tax rate of return for this investment and indicate if the company obtained the expected after-tax rate of retum
a) Before-tax cash flows (BTCF) from n= 0 to n=4Year
RevenueDepreciationBTCF0-$450,000-$450,0001$90,000$57,144$32,8562$90,000$82,372$7,6283$90,000$59,013$30,9874$90,000$28,041$61,959
b) Depreciation charges
Using the MACRS depreciation method, the annual depreciation expenses are as follows:Year
Depreciation rate Depreciation charge1 14.29% $64,215.002 24.49% $110,208.753 17.49% $78,705.754 12.49% $56,216.28Therefore, the total depreciation charge over 4 years is $309,345.75.
c) Depreciation recapture or loss
After 4 years, the equipment was sold for $220,000. The adjusted basis of the equipment is the initial cost minus the accumulated depreciation, which is:$450,000 - $309,345.75 = $140,654.25Therefore, the depreciation recapture or loss is:$220,000 - $140,654.25 = $79,345.75The depreciation recapture is positive and hence, the company must report this as ordinary income in the current tax year.
d) Taxable incomes and income taxesYearRevenueDepreciationBTCFTaxable IncomeTax1$90,000$64,215.00$25,785.00$6,187.60(24% x $25,785.00)2$90,000$110,208.75-$20,208.75-$4,850.10(24% x -$20,208.75)3$90,000$78,705.75$11,294.25$2,710.22(24% x $11,294.25)4$90,000$56,216.28$33,783.72$8,107.69(24% x $33,783.72)
The total income taxes paid over 4 years is $21,855.61.e) After-tax cash flows (ATCF)YearBTCFTaxIncome TaxATCF0-$450,000-$450,0001$32,856$6,188$26,6692$7,628$4,850$2,7793$30,987$2,710$28,2774$61,959$8,108$53,851The total ATCF over 4 years is $110,576.f)
After-tax NPW or After-tax rate of return (ARR) for this investmentAfter-tax NPW = -$450,000 + $110,576(P/A,8%,4 years)= -$450,000 + $110,576(3.3121)= -$28,128.04Since the NPW is negative, the company did not obtain the expected after-tax rate of return.
Learn more about Before-tax cash flows (BTCF) here:
brainly.com/question/16005797
#SPJ11
please answer asap and correctly! must show detailed steps.
Find the Laplace transform of each of the following time
functions. Your final answers must be in rational form.
Unfortunately, there is no time function mentioned in the question.
However, I can provide you with a detailed explanation of how to find the Laplace transform of a time function.
Step 1: Take the time function f(t) and multiply it by e^(-st). This will create a new function, F(s,t), that includes both time and frequency domains. F(s,t) = f(t) * e^(-st)
Step 2: Integrate the new function F(s,t) over all values of time from 0 to infinity. ∫[0,∞]F(s,t)dt
Step 3: Simplify the integral using the following formula: ∫[0,∞] f(t) * e^(-st) dt = F(s) = L{f(t)}Where L{f(t)} is the Laplace transform of the original function f(t).
Step 4: Check if the Laplace transform exists for the given function. If the integral doesn't converge, then the Laplace transform doesn't exist .Laplace transform of a function is given by the formula,Laplace transform of f(t) = ∫[0,∞] f(t) * e^(-st) dt ,where t is the independent variable and s is a complex number that is used to represent the frequency domain.
Hopefully, this helps you understand how to find the Laplace transform of a time function.
To know more about function visit :
https://brainly.com/question/31062578
#SPJ11
The average flow speed in a constant-diameter section of the pipeline is 2.5 m/s. At the inlet, the pressure is 2000 kPa (gage) and the elevation is 56 m; at the outlet, the elevation is 35 m. Calculate the pressure at the outlet (kPa, gage) if the head loss = 2 m. The specific weight of the flowing fluid is 10000N/m³. Patm = 100 kPa.
The pressure at the outlet (kPa, gage) can be calculated using the following formula:
Pressure at the outlet (gage) = Pressure at the inlet (gage) - Head loss - Density x g x Height loss.
The specific weight (γ) of the flowing fluid is given as 10000N/m³.The height difference between the inlet and outlet is 56 m - 35 m = 21 m.
The head loss is given as 2 m.Given that the average flow speed in a constant-diameter section of the pipeline is 2.5 m/s.Given that Patm = 100 kPa.At the inlet, the pressure is 2000 kPa (gage).
Using Bernoulli's equation, we can find the pressure at the outlet, which is given as:P = pressure at outlet (gage), ρ = specific weight of the fluid, h = head loss, g = acceleration due to gravity, and z = elevation of outlet - elevation of inlet.
Therefore, using the above formula; we get:
Pressure at outlet = 2000 - (10000 x 9.81 x 2) - (10000 x 9.81 x 21)
Pressure at outlet = -140810 PaTherefore, the pressure at the outlet (kPa, gage) is 185.19 kPa (approximately)
In this question, we are given the average flow speed in a constant-diameter section of the pipeline, which is 2.5 m/s. The pressure and elevation are given at the inlet and outlet. We are supposed to find the pressure at the outlet (kPa, gage) if the head loss = 2 m.
The specific weight of the flowing fluid is 10000N/m³, and
Patm = 100 kPa.
To find the pressure at the outlet, we use the formula:
P = pressure at outlet (gage), ρ = specific weight of the fluid, h = head loss, g = acceleration due to gravity, and z = elevation of outlet - elevation of inlet.
The specific weight (γ) of the flowing fluid is given as 10000N/m³.
The height difference between the inlet and outlet is 56 m - 35 m = 21 m.
The head loss is given as 2 m
.Using the above formula; we get:
Pressure at outlet = 2000 - (10000 x 9.81 x 2) - (10000 x 9.81 x 21)
Pressure at outlet = -140810 PaTherefore, the pressure at the outlet (kPa, gage) is 185.19 kPa (approximately).
The pressure at the outlet (kPa, gage) is found to be 185.19 kPa (approximately) if the head loss = 2 m. The specific weight of the flowing fluid is 10000N/m³, and Patm = 100 kPa.
Learn more about head loss here:
brainly.com/question/33310879
#SPJ11
What is the type number of the following system: G(s) = (s +2) /s^2(s +8) (A) 0 (B) 1 (C) 2 (D) 3
To determine the type number of a system, we need to count the number of integrators in the open-loop transfer function. The system has a total of 2 integrators.
Given the transfer function G(s) = (s + 2) / (s^2 * (s + 8)), we can see that there are two integrators in the denominator (s^2 and s). The numerator (s + 2) does not contribute to the type number.
Therefore, the system has a total of 2 integrators.
The type number of a system is defined as the number of integrators in the open-loop transfer function plus one. In this case, the type number is 2 + 1 = 3.
The correct answer is (D) 3.
Learn more about integrators here
https://brainly.com/question/28992365
#SPJ11
a) With the aid of a diagram, briefly explain how electricity is generated by a solar cell and state the types of solar cells. b) What type of connections are used in solar cells and panels? State the rationale for these connections.
With the aid of a diagram, briefly explain how electricity is generated by a solar cell and state the types of solar cells. Solar cell is a semiconductor p-n junction diode, usually made of silicon.
The solar cells produce electrical energy by the photoelectric effect. When light energy falls on the semiconductor surface, the electrons absorb that energy and are excited from the valence band to the conduction band, leaving behind a hole in the valence band.
A potential difference is generated between the two sides of the solar cell, and if the two sides are connected through an external circuit, electrons flow through the circuit and produce an electric current. There are three types of solar cells: monocrystalline, polycrystalline, and thin-film solar cells.
To know more about silicon visit:
https://brainly.com/question/15412188
#SPJ11
Design a circuit which counts seconds, minutes and hours and displays them on the 7-segement display in 24 hour format. The clock frequency available is 36 KHz. Assume that Binary to BCD converter and BCD to 7-Segement display is already available for the design.
The 24-hour clock has two digits for hours, two digits for minutes, and two digits for seconds. Binary Coded Decimal (BCD) is a technique for representing decimal numbers using four digits in which each decimal digit is represented by a 4-bit binary number.
A 7-segment display is used to display the digits from 0 to 9.
Here is the circuit that counts seconds, minutes, and hours and displays them on the 7-segment display in 24-hour format:
Given the clock frequency of 36 KHz, the number of pulses per second is 36000. The seconds counter requires 6 digits, or 24 bits, to count up to 59. The minutes counter requires 6 digits, or 24 bits, to count up to 59. The hours counter requires 5 digits, or 20 bits, to count up to 23.The clock signal is fed into a frequency divider that produces a 1 Hz signal. The 1 Hz signal is then fed into a seconds counter, minutes counter, and hours counter. The counters are reset to zero when they reach their maximum value.
When the seconds counter reaches 59, it generates a carry signal that increments the minutes counter. Similarly, when the minutes counter reaches 59, it generates a carry signal that increments the hours counter.
The outputs of the seconds, minutes, and hours counters are then converted to BCD format using a binary to BCD converter. Finally, the BCD digits are fed into a BCD to 7-segment display decoder to produce the display on the 7-segment display.Here's a block diagram of the circuit: Block diagram of the circuit
To know more about frequency visit:
https://brainly.com/question/29739263
#SPJ11
A 320-kg space vehicle traveling with a velocity v₀ = ( 365 m/s)i passes through the origin O at t= 0. Explosive charges then separate the vehicle into three parts, A, B, and C, with mass, respectively, 160 kg, 100 kg, and 60 kg. Knowing that at t = 4 s, the positions of parts A and B are observed to be A (1170 m, -290 m, -585 m) and B (1975 m, 365 m, 800 m), determine the corresponding position of part C. Neglect the effect of gravity. The position of part Cis rc=( m)i + ( m)j + ( m)k.
The corresponding position of Part C is `rc = (837.5 m)i + (0 m)j + (0 m)k`. Hence, the answer is `(837.5 m)i + (0 m)j + (0 m)k`.
Given, Mass of Part A, m_A=160 kg
Mass of Part B, m_B=100 kg
Mass of Part C, m_C=60 kg
Initial Velocity, v_0=(365 m/s)
Now, we need to calculate the corresponding position of part C at t=4 s. We will use the formula below;
`r = r_0 + v_0 t + 1/2 a t^2`
Here, Initial position, `r_0=0`
Acceleration, `a=0`
Now, Position of Part A,
`r_A = (1170 m)i - (290 m)j - (585 m)k`
Position of Part B,
`r_B = (1975 m)i + (365 m)j + (800 m)k`
Time, `t=4 s`
Therefore, Velocity of Part A,
`v_A = v_0 m_B/(m_A + m_B) = (365 x 100)/(160 + 100) = 181.25 m/s
`Velocity of Part B,`v_B = v_0 m_A/(m_A + m_B) = (365 x 160)/(160 + 100) = 183.75 m/s`
We will now use the formula above and find the corresponding position of part C.
Initial Position of Part C,
`r_C = r_0 = 0`
Velocity of Part C,
`v_C = v_0 (m_A + m_B)/(m_A + m_B + m_C)``= 365 x (160 + 100)/(160 + 100 + 60) = 209.375 m/s`
Now,`r_C = r_0 + v_0 t + 1/2 a t^2``=> r_C = v_C t``=> r_C = (209.375 m/s) x (4 s)``=> r_C = 837.5 m`
Therefore, the corresponding position of Part C is `rc = (837.5 m)i + (0 m)j + (0 m)k`.Hence, the answer is `(837.5 m)i + (0 m)j + (0 m)k`.
Learn more about Mass visit:
brainly.com/question/11954533
#SPJ11
12. 2 points Capacitive susceptance decreases as frequency increases O a. True O b. False 13. 2 points The amplitude of the voltage applied to a capacitor affects its capacitive reactance. O a. True O b. False 14. 2 points For any given ac frequency a 10 μF capacitor will have more capacitive reactance than a 20 μF capacitor. O a. True
O b. False 15. 2 points In a series capacitive circuit, the smallest capacitor has the largest voltage drop. O a. True O b. False 16. 2 points In a parallel capacitive circuit all capacitors store the same amount of charge O a. True O b. False
12. False 13. False 14. FALSE 15. true 16. true are the answers
12. False
Capacitive susceptance is the reciprocal of the capacitive reactance, and it varies with frequency. The higher the frequency of the AC, the lower the capacitive reactance.
13. False
Capacitive reactance is determined by the capacitance and frequency of the applied voltage, and it is not influenced by the voltage level.
14. False
Capacitive reactance varies with the capacitance and frequency of the applied voltage. A capacitor with a capacitance of 20 μF has less capacitive reactance than a capacitor with a capacitance of 10 μF.
15. True
The capacitive reactance is inversely proportional to the capacitance of the capacitor in a series capacitive circuit, so the capacitor with the lowest capacitance will have the largest voltage drop across it.
16. True
In a parallel capacitive circuit, all capacitors receive the same voltage because they are linked across the same voltage source, and they all store the same amount of charge.
Q = CV is the equation used to calculate the amount of charge stored in a capacitor,
where Q is the charge stored in coulombs, C is the capacitance in farads, and V is the voltage across the capacitor in volts.
Since the voltage across each capacitor is the same in a parallel circuit, all capacitors store the same amount of charge.
to know more about capacitors visit:
https://brainly.com/question/31627158
#SPJ11
Efficiency of home furnace can be improved by preheating combustion air using hot flue gas. The flue gas has temperature of Tg = 1000°C, specific heat of c = 1.1 kJ/kg°C and is available at the rate of 12 kg/sec. The combustion air needs to be delivered at the rate of 15 kg/sec, its specific heat is ca 1.01 kJ/kg°C and its temperature is equal to the room temperature, i.e. Tair,in = 20°C. The overall heat transfer coefficient for the heat exchanger is estimated to be U = 80 W/m2°C. (i) Determine size of the heat exchanger (heat transfer surface area A) required to heat the air to Tair,out 600°C assuming that a single pass, cross-flow, unmixed heat exchanger is used. (ii) Determine temperature of flue gases leaving heat exchanger under these conditions. (iii) Will a parallel flow heat exchanger deliver the required performance and if yes, will it reduce/increase its size, i.e. reduce/increase the heat transfer area A? (iv) Will use of a counterflow heat exchanger deliver the required performance and, if yes, will it reduce/increase its size, i.e. reduce/increase the heat transfer area A?
i) The size of the heat exchanger required is approximately 13.5 m².
ii) The temperature of the flue gases leaving the heat exchanger T_flue,out ≈ 311.36°C.
iii) To achieve the desired outlet temperature of 600°C for the combustion air, a counterflow heat exchanger is needed.
iv) The required surface area A remains the same for a counterflow heat exchanger, so the size of the heat exchanger does not change.
To solve this problem, we can use the energy balance equation for the heat exchanger.
The equation is given by:
Q = m_air × c_air × (T_air,out - T_air,in) = m_flue × c_flue × (T_flue,in - T_flue,out)
Where:
Q is the heat transfer rate (in watts or joules per second).
m_air is the mass flow rate of combustion air (in kg/s).
c_air is the specific heat of combustion air (in kJ/kg°C).
T_air,in is the inlet temperature of combustion air (in °C).
T_air,out is the desired outlet temperature of combustion air (in °C).
m_flue is the mass flow rate of flue gas (in kg/s).
c_flue is the specific heat of flue gas (in kJ/kg°C).
T_flue,in is the inlet temperature of flue gas (in °C).
T_flue,out is the outlet temperature of flue gas (in °C).
Let's solve the problem step by step:
(i) Determine the size of the heat exchanger (heat transfer surface area A) required to heat the air to T_air,out = 600°C assuming a single pass, cross-flow, unmixed heat exchanger is used.
We can rearrange the energy balance equation to solve for A:
A = Q / (U × ΔT_lm)
Where ΔT_lm is the logarithmic mean temperature difference given by:
ΔT_lm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
ΔT1 = T_flue,in - T_air,out
ΔT2 = T_flue,out - T_air,in
Plugging in the values:
ΔT1 = 1000°C - 600°C = 400°C
ΔT2 = T_flue,out - 20°C (unknown)
We need to solve for ΔT2 by substituting the values into the energy balance equation:
Q = m_air × c_air × (T_air,out - T_air,in) = m_flue × c_flue × (T_flue,in - T_flue,out)
15 kg/s × 1.01 kJ/kg°C × (600°C - 20°C) = 12 kg/s × 1.1 kJ/kg°C × (1000°C - T_flue,out)
Simplifying:
9090 kJ/s = 13200 kJ/s - 13.2 kJ/s * T_flue,out
13.2 kJ/s × T_flue,out = 4110 kJ/s
T_flue,out = 311.36°C
Now we can calculate ΔT2:
ΔT2 = T_flue,out - 20°C
ΔT2 = 311.36°C - 20°C
ΔT2 = 291.36°C
Now we can calculate ΔT_lm:
ΔT_lm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
ΔT_lm = (400°C - 291.36°C) / ln(400°C / 291.36°C)
ΔT_lm ≈ 84.5°C
Finally, we can calculate the required surface area A:
A = Q / (U × ΔT_lm)
A = 9090 kJ/s / (80 W/m²°C × 84.5°C)
A ≈ 13.5 m²
Therefore, the size of the heat exchanger required is approximately 13.5 m².
(ii) Determine the temperature of flue gases leaving the heat exchanger under these conditions.
We already determined the temperature of the flue gases leaving the heat exchanger in part (i): T_flue,out ≈ 311.36°C.
(iii) In a parallel flow heat exchanger, the hot and cold fluids flow in the same direction. The temperature difference between the two fluids decreases along the length of the heat exchanger. In this case, a parallel flow heat exchanger will not deliver the required performance because the outlet temperature of the flue gases is significantly higher than the desired outlet temperature of the combustion air.
To achieve the desired outlet temperature of 600°C for the combustion air, a counterflow heat exchanger is needed.
(iv) In a counterflow heat exchanger, the hot and cold fluids flow in opposite directions. This arrangement allows for better heat transfer and can achieve a higher temperature difference between the two fluids. A counterflow heat exchanger can deliver the required performance in this case.
To determine if the size of the heat exchanger will be reduced or increased, we need to recalculate the required surface area A using the new ΔT1 and ΔT2 values for a counterflow heat exchanger.
ΔT1 = 1000°C - 600°C = 400°C
ΔT2 = T_flue,out - T_air,in = 311.36°C - 20°C = 291.36°C
ΔT_lm = (ΔT1 - ΔT2) / ln(ΔT1 / ΔT2)
ΔT_lm = (400°C - 291.36°C) / ln(400°C / 291.36°C)
ΔT_lm ≈ 84.5°C
A = Q / (U × ΔT_lm)
A = 9090 kJ/s / (80 W/m²°C * 84.5°C)
A ≈ 13.5 m²
The required surface area A remains the same for a counterflow heat exchanger, so the size of the heat exchanger does not change.
Learn more about combustion click;
https://brainly.com/question/31123826
#SPJ4
7.4 A six-pulse rectifier supplies 8.8 kW to a resistive load. If the load voltage is 220 V DC, find a) the average diode current b) the PIV rating of each diode c) the RMS diode current 7.5 A three-pulse rectifier supplies a resistive load of 10 2 from a 220 V source. Find
a) the average load voltage b) the average load current c) the maximum load current d) the PIV rating of the diode e) the maximum diode current f) the average load power 7.6 Repeat problem 7.5 after adding a large inductance in series with the load resistance. 7.7 A three-pulse rectifier is connected to a 220 V source. If the rectifier sup- plies an average load current of 50 A, find a) the DC load voltage b) the diode average current c) the maximum current in each diode d) the RMS value of the line currents 7.8 The six-pulse rectifier in Figure 7.6 is connected to a 220 V source. If the rectifier supplies an average load current of 50 A, find a) the DC load voltage b) the diode average current c) the maximum current in each diode d) the RMS value of the line current
7.4 Given:Power, P = 8.8 kWLoad Voltage, VL
= 220 V DCNumber of pulses, n
= 6Load, RLoad current, I
= VL / RThe average voltage of the rectifier is given by;Vdc
= (2 / π) VL ≈ 0.9 VL The power input to the rectifier is the output power.
Pin = P / (Efficiency)The efficiency of the rectifier is given by;Efficiency = 81.2% = 0.812 = 81.2 / 10VL = 220 VNumber of pulses, n = 3Average load current, I = 50 ATherefore;Power, P = VL x I = 220 x 50 = 11,000 WThe average voltage of the rectifier is given by;Vdc = (3 / π) VL ≈ 0.95 VLPower input to the rectifier;Pin = P / (Efficiency)The efficiency of the rectifier is given by;
Efficiency = 81.2% = 0.812
= 81.2 / 100Therefore,P / Pin
= 0.812Average diode current, I
= P / Vdc
= 11,000 / 209
= 52.63 AMax. diode current, I
= I / n
= 52.63 / 3
= 17.54 ARMS value of the current in each diode;Irms =
I / √2 = 12.42 ALoad resistance, Rload = VL / I
= 220 / 50
= 4.4 Ω7.8Given:Load Voltage, VL
= 220 VNumber of pulses, n
= 6Average load current, I
= 50 ATherefore;Power, P
= VL x I = 220 x 50
= 11,000 WThe average voltage of the rectifier is given by;Vdc
= (2 / π) VL ≈ 0.9 VLPower input to the rectifier;Pin
= P / (Efficiency)The efficiency of the rectifier is given by;Efficiency = 81.2%
= 0.812
= 81.2 / 100Therefore,P / Pin
= 0.812Average diode current, I
= P / Vdc
= 11,000 / 198
= 55.55 AMax. diode current, I
= I / n = 55.55 / 6
= 9.26 ARMS value of the current in each diode;Irms
= I / √2
= 3.29 ALoad resistance, Rload
= VL / I
= 220 / 50
= 4.4 Ω.
To know more about Power visit:
https://brainly.com/question/29575208
#SPJ11
Methane gas at 120 atm and −18°C is stored in a 20−m³ tank. Determine the mass of methane contained in the tank, in kg, using the
(a) ideal gas equation of state. (b) van der Waals equation. (c) Benedict-Webb-Rubin equation.
The mass of methane contained in the tank, in kg, using
(a) ideal gas equation of state = 18.38 kg
(b) van der Waals equation = 18.23 kg
(c) Benedict-Webb-Rubin equation = 18.21 kg.
(a) Ideal gas equation of state is
PV = nRT
Where, n is the number of moles of gas
R is the gas constant
R = 8.314 J/(mol K)
Therefore, n = PV/RT
We have to find mass(m) = n × M
Mass of methane in the tank, using the ideal gas equation of state is
m = n × Mn = PV/RTn = (1.2159 × 10⁷ Pa × 20 m³) / (8.314 J/(mol K) × 255 K)n = 1145.45 molm = n × Mm = 1145.45 mol × 0.016043 kg/molm = 18.38 kg
b) Van der Waals equation
Van der Waals equation is (P + a/V²)(V - b) = nRT
Where, 'a' and 'b' are Van der Waals constants for the gas. For methane, the values of 'a' and 'b' are 2.25 atm L²/mol² and 0.0428 L/mol respectively.
Therefore, we can write it as(P + 2.25 aP²/RT²)(V - b) = nRT
At given conditions, we have
P = 120 atm = 121.59 × 10⁴ Pa
T = 255 K
V = 20 m³
n = (P + 2.25 aP²/RT²)(V - b)/RTn = (121.59 × 10⁴ Pa + 2.25 × (121.59 × 10⁴ Pa)²/(8.314 J/(mol K) × 255 K) × (20 m³ - 0.0428 L/mol))/(8.314 J/(mol K) × 255 K)n = 1138.15 molm = n × Mm = 1138.15 mol × 0.016043 kg/molm = 18.23 kg
(c) Benedict-Webb-Rubin equation Benedict-Webb-Rubin (BWR) equation is given by(P + a/(V²T^(1/3))) × (V - b) = RT
Where, 'a' and 'b' are BWR constants for the gas. For methane, the values of 'a' and 'b' are 2.2538 L² kPa/(mol² K^(5/2)) and 0.0387 L/mol respectively.
Therefore, we can write it as(P + 2.2538 aP²/(V²T^(1/3)))(V - b) = RT
At given conditions, we haveP = 120 atm = 121.59 × 10⁴ PaT = 255 KV = 20 m³n = (P + 2.2538 aP²/(V²T^(1/3)))(V - b)/RTn = (121.59 × 10⁴ Pa + 2.2538 × (121.59 × 10⁴ Pa)²/(20 m³)² × (255 K)^(1/3) × (20 m³ - 0.0387 L/mol))/(8.314 J/(mol K) × 255 K)n = 1135.84 molm = n × Mm = 1135.84 mol × 0.016043 kg/molm = 18.21 kg
Learn more about ideal gas equation at
https://brainly.com/question/15046679
#SPJ11
Create summarize of roles of phonon in specific heat of
a solid crystal ! (All Formula, Rules and Explanation)
Phonons play a crucial role in determining the specific heat of a solid crystal. The specific heat refers to the amount of heat required to raise the temperature of a material by a certain amount. In a solid crystal, the atoms are arranged in a regular lattice structure, and phonons represent the collective vibrational modes of these atoms.
1. Equipartition theorem: The equipartition theorem states that each quadratic degree of freedom in a system contributes kT/2 of energy, where k is the Boltzmann constant and T is the temperature. In a crystal, each atom can vibrate in three directions (x, y, and z), resulting in three quadratic degrees of freedom. Therefore, each phonon mode contributes kT/2 of energy.
2. Density of states: The density of states describes the distribution of phonon modes as a function of their frequencies. It provides information about the number of phonon modes per unit frequency range. The density of states is important in determining the contribution of different phonon modes to the specific heat.
3. Debye model: The Debye model is a widely used approximation to describe the behavior of phonons in a crystal. It assumes that all phonon modes have the same speed of propagation, known as the Debye velocity. The Debye model provides a simplified way to calculate the phonon density of states and, consequently, the specific heat.
4. Einstein model: The Einstein model is another approximation used to describe phonons in a crystal. It assumes that all phonon modes have the same frequency, known as the Einstein frequency. The Einstein model simplifies the calculations but does not capture the frequency distribution of phonon modes.
5. Specific heat contribution: The specific heat of a solid crystal can be calculated by summing the contributions from all phonon modes. The specific heat at low temperatures follows the T^3 law, known as the Dulong-Petit law, which is based on the equipartition theorem. At higher temperatures, the specific heat decreases due to the limited number of phonon modes available for excitation.
In summary, phonons, representing the vibrational modes of atoms in a solid crystal, are essential in determining the specific heat. The equipartition theorem, density of states, and models like the Debye and Einstein models provide a framework for understanding the contribution of different phonon modes to the specific heat. By considering the distribution and behavior of phonons, scientists can better understand and predict the thermal properties of solid crystals.
Learn more about Equipartition theorem here:
https://brainly.com/question/30907512
#SPJ11
Equation: y=5-x^x
Numerical Differentiation 3. Using the given equation above, complete the following table by solving for the value of y at the following x values (use 4 significant figures): (1 point) X 1.00 1.01 1.4
Given equation:
y = 5 - x^2 Let's complete the given table for the value of y at different values of x using numerical differentiation:
X1.001.011.4y = 5 - x²3.00004.980100000000014.04000000000001y
= 3.9900 y
= 3.9798y
= 0.8400h
= 0.01h
= 0.01h
= 0.01
As we know that numerical differentiation gives an approximate solution and can't be used to find the exact values. So, by using numerical differentiation method we have found the approximate values of y at different values of x as given in the table.
To know more about complete visit:
https://brainly.com/question/29843117
#SPJ11
MatLab Question, I have most of the lines already just need help with the last part and getting the four plots that are needed. The file is transient.m and the case is for Bi = 0.1 and Bi = 10 for N = 1 and N = 20.
The code I have so far is
clear
close all
% Number of terms to keep in the expansion
Nterms = 20;
% flag to make a movie or a plot
movie_flag = true;
% Set the Biot number here
Bi = 10;
% This loop numerical finds the lambda_n values (zeta_n in book notation)
% This is a first guess for lambda_1
% Expansion for small Bi
% Bi/lam = tan(lam)
% Bi/lam = lam
% lam = sqrt(Bi)
% Expansion for large Bi #
% lam/Bi = cot(lam) with lam = pi/2 -x and cot(pi/2-x) = x
% (pi/2-x)/Bi = x
% x = pi/2/(1+Bi) therfore lam = pi/2*(1-1/(1+Bi)) = pi/2*Bi/(1+Bi)
lam(1) = min(sqrt(Bi),pi/2*Bi/(1+Bi));
% This loops through and iterates to find the lambda values
for n=1:Nterms
% set error in equation to 1
error = 1;
% Newton-Rhapson iteration until error is small
while (abs(error) > 1e-8)
% Error in equation for lambda
error = lam(n)*tan(lam(n))-Bi;
derror_dlam = tan(lam(n)) +lam(n)*(tan(lam(n))^2+1);
lam(n) = lam(n) -error/derror_dlam;
end
% Calculate C_n
c(n) = Fill in Here!!!
% Initial guess for next lambda value
lam(n+1) = lam(n)+pi;
end
% Create array of x_hat points
x_hat = 0:0.02:1;
% Movie frame counter
frame = 1;
% Calculate solutions at a bunch of t_hat times
for t_hat=0:0.01:1.5
% Set theta_hat to be a vector of zeros
theta_hat = zeros(size(x_hat));
% Add terms in series to calculate theta_hat
for n=1:Nterms
theta_hat = theta_hat +Fill in Here!!!
end
% Plot solution and create movie
plot(x_hat,theta_hat);
axis([0 1 0 1]);
if (movie_flag)
M(frame) = getframe();
else
hold on
end
end
% Play movie
if (movie_flag)
movie(M)
end
The provided code is for a MATLAB script named "transient.m" that aims to generate plots for different cases of the Biot number (Bi) and the number of terms (N) in an expansion. The code already includes the necessary calculations for the lambda values and the x_hat points.
However, the code is missing the calculation for the C_nc(n) term and the term to be added in the series for theta_hat. Additionally, the code includes a movie_flag variable to switch between creating a movie or a plot. To complete the code and generate the desired plots, you need to fill in the missing calculations for C_nc(n) and the series term to be added to theta_hat. These calculations depend on the specific equation or algorithm you are working with. Once you have determined the formulas for C_nc(n) and the series term, you can incorporate them into the code. After completing the code, the script will generate plots for different values of the Biot number (Bi) and the number of terms (N). The plots will display the solution theta_hat as a function of the x_hat points. The axis limits of the plot are set to [0, 1] for both x and theta_hat. If the movie_flag variable is set to true, the code will create a movie by capturing frames of the plot at different t_hat times. The frames will be stored in the M variable, and the movie will be played using the movie(M) command. By running the modified script, you will obtain the desired plots for the specified cases of Bi and N.
Learn more about algorithm here:
https://brainly.com/question/21172316
#SPJ11
A fluid in a fire hose with a 46.5 mm radius, has a velocity of 0.56 m/s. Solve for the power, hp, available in the jet at the nozzle attached at the end of the hose if its diameter is 15.73 mm. Express your answer in 4 decimal places.
Given data: Radius of hose
r = 46.5m
m = 0.0465m
Velocity of fluid `v = 0.56 m/s`
Diameter of the nozzle attached `d = 15.73 mm = 0.01573m`We are supposed to calculate the power, hp available in the jet at the nozzle attached to the hose.
Power is defined as the rate at which work is done or energy is transferred, that is, P = E/t, where E is the energy (J) and t is the time (s).Now, Energy E transferred by the fluid is given by the formula E = 1/2mv² where m is the mass of the fluid and v is its velocity.We can write m = (ρV) where ρ is the density of the fluid and V is the volume of the fluid. Volume of the fluid is given by `V = (πr²l)`, where l is the length of the hose through which fluid is coming out, which can be assumed to be equal to the diameter of the nozzle or `l=d/2`.
Thus, `V = (πr²d)/2`.Energy transferred E by the fluid can be expressed as Putting the value of V in the above equation, we get .Now, the power of the fluid P, can be written as `P = E/t`, where t is the time taken by the fluid to come out from the nozzle.`Putting the given values of r, d, and v, we get Thus, the power available in the jet at the nozzle attached to the hose is 0.3011 hp.
To know more about Radius visit :
https://brainly.com/question/13449316
#SPJ11
An acrylonitrile-butadiene-styrene copolymer (ABS) bar, with a width of 10 mm, a thickness of 4 mm and an internal transverse flaw size of 0.2 mm, is subjected to tension-compression cyclic loading between ±200 N. The crack growth rate, da/dN, in the ABS follows Equation Q2.2: da/dN = 1.8 x 10⁻⁷ ΔK^3.5 Equation Q2.2 where ΔK is the range of cyclic stress intensity factor in MPa m^0.5 Assuming the geometric factor Y = 1.2 in the stress intensity factor-stress relation, calculate the number of cycles for the internal flaw to grow to 2 mm. Under these cycles of loading, the bar will not fail.
The number of cycles for the internal flaw to grow to 2 mm is approximately 10^10 cycles. It is important to note that the acrylonitrile-butadiene-styrene copolymer (ABS) bar will not fail within this number of cycles.
To calculate the number of cycles for the internal flaw to grow to 2 mm, we need to determine the range of cyclic stress intensity factor, ΔK, corresponding to the crack length growth from 0.2 mm to 2 mm.
The stress intensity factor, K, is related to the applied stress and crack size by the equation:
K = Y * σ * (π * a)^0.5
Given:
- Width of the bar (b) = 10 mm
- Thickness of the bar (h) = 4 mm
- Internal flaw size at the start (a0) = 0.2 mm
- Internal flaw size at the end (a) = 2 mm
- Range of cyclic stress, σ = ±200 N (assuming the cross-sectional area is constant)
First, let's calculate the stress intensity factor at the start and the end of crack growth.
At the start:
K0 = Y * σ * (π * a0)^0.5
= 1.2 * 200 * (π * 0.2)^0.5
≈ 76.92 MPa m^0.5
At the end:
K = Y * σ * (π * a)^0.5
= 1.2 * 200 * (π * 2)^0.5
≈ 766.51 MPa m^0.5
The range of cyclic stress intensity factor is ΔK = K - K0
= 766.51 - 76.92
≈ 689.59 MPa m^0.5
Now, we can use the crack growth rate equation to calculate the number of cycles (N) required for the crack to grow from 0.2 mm to 2 mm.
da/dN = 1.8 x 10^-7 ΔK^3.5
Substituting the values:
2 - 0.2 = (1.8 x 10^-7) * (689.59)^3.5 * N
Solving for N:
N ≈ (2 - 0.2) / [(1.8 x 10^-7) * (689.59)^3.5]
≈ 1.481 x 10^10 cycles
The number of cycles for the internal flaw to grow from 0.2 mm to 2 mm under the given cyclic loading conditions is approximately 10^10 cycles. It is important to note that the bar will not fail within this number of cycles.
To know more about acrylonitrile-butadiene-styrene copolymer, visit:-
https://brainly.com/question/28875917
#SPJ11
What are the possible legal consequences of
mechatronics engineering solutions? Give three (3)
different examples and explain.
Possible legal consequences of mechatronics engineering solutions include patent infringement, product liability lawsuits, and non-compliance with legal and ethical standards.
Legal consequences of mechatronics engineering solutions can arise from various aspects, such as intellectual property, safety regulations, and ethical considerations. Here are three examples of possible legal consequences:
1. Patent Infringement:
Mechatronics engineers may develop innovative technologies, systems, or components that are eligible for patent protection. If another party copies or uses these patented inventions without permission, it could lead to a legal dispute. The consequences of patent infringement can include legal action, potential damages, and injunctions to cease the unauthorized use of the patented technology.
2. Product Liability:
Mechatronics engineers are involved in designing and developing complex machinery, robotic systems, or automated devices. If a product created by mechatronics engineering solutions has defects or malfunctions, it can potentially cause harm or injury to users or bystanders. In such cases, product liability lawsuits may arise, holding the manufacturer, designer, or engineer accountable for any damages or injuries caused by the faulty product.
3. Ethical and Legal Compliance:
Mechatronics engineering solutions often involve the integration of software, hardware, and control systems. Engineers must ensure that their designs and implementations comply with legal requirements and ethical standards. Failure to comply with relevant laws, regulations, or ethical guidelines, such as data protection laws or safety standards, can lead to legal consequences. These consequences may include fines, regulatory penalties, loss of professional licenses, or reputational damage.
It is important for mechatronics engineers to be aware of these legal considerations and work in accordance with applicable laws, regulations, and ethical principles to mitigate potential legal consequences. Consulting legal professionals and staying updated with industry-specific regulations can help ensure compliance and minimize legal risks.
Learn more about mechatronics
brainly.com/question/32753655
#SPJ11
A small aircraft has a wing area of 50 m², a lift coefficient of 0.45 at take-off settings, and a total mass of 5,000 kg. Determine the following: a. Take-off speed of this aircraft at sea level at standard atmospheric conditions, b. Wing loading and c. Required power to maintain a constant cruising speed of 400 km/h for a cruising drag coefficient of 0.04.
a. The take-off speed of the aircraft is approximately 79.2 m/s.
b. The wing loading is approximately 100 kg/m².
c. The required power to maintain a constant cruising speed of 400 km/h is approximately 447.2 kW.
a. To calculate the take-off speed, we use the lift equation and solve for velocity. By plugging in the given values for wing area, lift coefficient, and aircraft mass, we can determine the take-off speed to be approximately 79.2 m/s. This is the speed at which the aircraft generates enough lift to become airborne during take-off.
b. Wing loading is the ratio of the aircraft's weight to its wing area. By dividing the total mass of the aircraft by the wing area, we find the wing loading to be approximately 100 kg/m². Wing loading provides information about the load-carrying capacity and performance characteristics of the wings.
c. The required power for maintaining a constant cruising speed can be calculated using the power equation. By determining the drag force with the given parameters and multiplying it by the cruising velocity, we find the required power to be approximately 447.2 kW. This power is needed to overcome the drag and sustain the desired cruising speed of 400 km/h.
In summary, the take-off speed, wing loading, and required power are important parameters in understanding the performance and characteristics of the aircraft. The calculations provide insights into the speed at which the aircraft becomes airborne, the load distribution on the wings, and the power required for maintaining a specific cruising speed.
Learn more about Aircraft
brainly.com/question/32264555
#SPJ11
(a) A solid conical wooden cone (s=0.92), can just float upright with apex down. Denote the dimensions of the cone as R for its radius and H for its height. Determine the apex angle in degrees so that it can just float upright in water. (b) A solid right circular cylinder (s=0.82) is placed in oil(s=0.90). Can it float upright? Show calculations. The radius is R and the height is H. If it cannot float upright, determine the reduced height such that it can just float upright.
Given Data:S = 0.82 (Density of Solid)S₀ = 0.90 (Density of Oil)R (Radius)H (Height)Let us consider the case when the cylinder is fully submerged in oil. Hence, the buoyant force on the cylinder is equal to the weight of the oil displaced by the cylinder.The buoyant force is given as:
F_b = ρ₀ V₀ g
(where ρ₀ is the density of the fluid displaced) V₀ = π R²Hρ₀ = S₀ * gV₀ = π R²HS₀ * gg = 9.8 m/s²
Therefore, the buoyant force is F_b = S₀ π R²H * 9.8
The weight of the cylinder isW = S π R²H * 9.8
For the cylinder to float upright,F_b ≥ W.
Therefore, we get,S₀ π R²H * 9.8 ≥ S π R²H * 9.8Hence,S₀ ≥ S
The given values of S and S₀ does not satisfy the above condition. Hence, the cylinder will not float upright.Now, let us find the reduced height such that the cylinder can just float upright. Let the reduced height be h.
We have,S₀ π R²h * 9.8
= S π R²H * 9.8h
= H * S/S₀h
= 1.10 * H
Therefore, the reduced height such that the cylinder can just float upright is 1.10H.
To know more about buoyant force visit:
brainly.com/question/20165763
#SPJ4
True/fase
4. Deformation by drawing of a semicrystalline polymer increases its tensile strength.
5.Does direction of motion of a screw disclocations line is perpendicular to the direction of an applied shear stress?
6.How cold-working effects on 0.2% offself yield strength?
4. False. Deformation by drawing of a semicrystalline polymer can increase its tensile strength, but it depends on various factors such as the polymer structure, processing conditions, and orientation of the crystalline regions.
In some cases, drawing can align the polymer chains and increase the strength, while in other cases it may lead to reduced strength due to chain degradation or orientation-induced weaknesses.
5. True. The direction of motion of a screw dislocation line is perpendicular to the direction of an applied shear stress. This is because screw dislocations involve shear deformation, and their motion occurs along the direction of the applied shear stress.
6. Cold working generally increases the 0.2% offset yield strength of a material. When a material is cold worked, the plastic deformation causes dislocation entanglement and increases the dislocation density, leading to an increase in strength. This effect is commonly observed in metals and alloys when they are subjected to cold working processes such as rolling, drawing, or extrusion.
To learn more about DEFORMATION click here;
/brainly.com/question/13039704
#SPJ11
Practice Service Call 8 Application: Residential conditioned air system Type of Equipment: Residential split system heat pump (See Figure 15.45.) Complaint: System heats when set to cool. Symptoms: 1. System heats adequately. 2. With thermostat fan switch on, the fan operates properly. 3. Outdoor fan motor is operating. 4. Compressor is operating. 5. System charge is correct. 6. R to O on thermostat is closed. 7. 24 volts are being supplied to reversing valve solenoid.
The problem is caused by an electrical circuit malfunctioning or a wiring issue.
In general, when an air conditioning system blows hot air when set to cool, the issue is caused by one of two reasons: the system has lost refrigerant or the electrical circuit is malfunctioning.
The following are the most likely reasons:
1. The thermostat isn't working properly.
2. The reversing valve is malfunctioning.
3. The defrost thermostat is malfunctioning.
4. The reversing valve's solenoid is malfunctioning.
5. There's a wiring issue.
6. The unit's compressor isn't functioning correctly.
7. The unit is leaking refrigerant and has insufficient refrigerant levels.
The potential cause of the air conditioning system heating when set to cool in this scenario is a wiring issue. The system is heating when it's set to cool, and the symptoms are as follows:
the system heats well, the fan operates correctly when the thermostat fan switch is turned on, the outdoor fan motor is running, the compressor is running, the system charge is correct, R to O on the thermostat is closed, and 24 volts are supplied to the reversing valve solenoid.
Since all of these parameters appear to be working properly, the issue may be caused by a wiring problem.
To know more about circuit visit:
https://brainly.com/question/12608516
#SPJ11
A 1.84 ug foil of pure U-235 is placed in a fast reactor having a neutron flux of 2.02 x 1012 n/(cm?sec). Determine the fission rate (per second) in the foil.
The fission rate is 7.7 × 10⁷ s⁻¹, and it means that 7.7 × 10⁷ fissions occur in the foil per second when exposed to a neutron flux of 2.02 x 1012 n/(cm².sec).
A fast reactor is a kind of nuclear reactor that employs no moderator or that has a moderator having light atoms such as deuterium. Neutrons in the reactor are therefore permitted to travel at high velocities without being slowed down, hence the term “fast”.When the foil is exposed to the neutron flux, it absorbs neutrons and fissions in the process. This is possible because uranium-235 is a fissile material. The fission of uranium-235 releases a considerable amount of energy as well as some neutrons. The following is the balanced equation for the fission of uranium-235. 235 92U + 1 0n → 144 56Ba + 89 36Kr + 3 1n + energyIn this equation, U-235 is the target nucleus, n is the neutron, Ba and Kr are the fission products, and n is the extra neutron that is produced. Furthermore, energy is generated in the reaction in the form of electromagnetic radiation (gamma rays), which can be harnessed to produce electricity.
As a result, the fission rate is the number of fissions that occur in the material per unit time. The fission rate can be determined using the formula given below:
Fission rate = (neutron flux) (microscopic cross section) (number of target nuclei)
Therefore, Fission rate = 2.02 x 1012 n/(cm².sec) × 5.45 x 10⁻²⁴ cm² × (6.02 × 10²³ nuclei/mol) × (1 mol/235 g) × (1.84 × 10⁻⁶ g U) = 7.7 × 10⁷ s⁻¹
Therefore, the fission rate is 7.7 × 10⁷ s⁻¹, and it means that 7.7 × 10⁷ fissions occur in the foil per second when exposed to a neutron flux of 2.02 x 1012 n/(cm².sec).
To know more about fission rate visit:
https://brainly.com/question/31213424
#SPJ11
2. Airflow enters a duct with an area of 0.49 m² at a velocity of 102 m/s. The total temperature, Tt, is determined to be 293.15 K, the total pressure, PT, is 105 kPa. Later the flow exits a converging section at 2 with an area of 0.25 m². Treat air as an ideal gas where k = 1.4. (Hint: you can assume that for air Cp = 1.005 kJ/kg/K) (a) Determine the Mach number at location 1. (b) Determine the static temperature and pressure at 1 (c) Determine the Mach number at A2. (d) Determine the static pressure and temperature at 2. (e) Determine the mass flow rate. (f) Determine the velocity at 2
The mass flow rate is 59.63 kg/s, and the velocity at location 2 is 195.74 m/s.
Given information:The area of duct, A1 = 0.49 m²
Velocity at location 1, V1 = 102 m/s
Total temperature at location 1, Tt1 = 293.15 K
Total pressure at location 1, PT1 = 105 kPa
Area at location 2, A2 = 0.25 m²
The specific heat ratio of air, k = 1.4
(a) Mach number at location 1
Mach number can be calculated using the formula; Mach number = V1/a1 Where, a1 = √(k×R×Tt1)
R = gas constant = Cp - Cv
For air, k = 1.4 Cp = 1.005 kJ/kg/K Cv = R/(k - 1)At T t1 = 293.15 K, CP = 1.005 kJ/kg/KR = Cp - Cv = 1.005 - 0.718 = 0.287 kJ/kg/K
Substituting the values,Mach number, M1 = V1/a1 = 102 / √(1.4 × 0.287 × 293.15)≈ 0.37
(b) Static temperature and pressure at location 1The static temperature and pressure can be calculated using the following formulae;T1 = Tt1 / (1 + ((k - 1) / 2) × M1²)P1 = PT1 / (1 + ((k - 1) / 2) × M1²)
Substituting the values,T1 = 293.15 / (1 + ((1.4 - 1) / 2) × 0.37²)≈ 282.44 KP1 = 105 / (1 + ((1.4 - 1) / 2) × 0.37²)≈ 92.45 kPa
(c) Mach number at location 2
The area ratio can be calculated using the formula, A1/A2 = (1/M1) × (√((k + 1) / (k - 1)) × atan(√((k - 1) / (k + 1)) × (M1² - 1))) - at an (√(k - 1) × M1 / √(1 + ((k - 1) / 2) × M1²)))
Substituting the values and solving further, we get,Mach number at location 2, M2 = √(((P1/PT1) * ((k + 1) / 2))^((k - 1) / k) * ((1 - ((P1/PT1) * ((k - 1) / 2) / (k + 1)))^(-1/k)))≈ 0.40
(d) Static temperature and pressure at location 2
The static temperature and pressure can be calculated using the following formulae;T2 = Tt1 / (1 + ((k - 1) / 2) × M2²)P2 = PT1 / (1 + ((k - 1) / 2) × M2²)Substituting the values,T2 = 293.15 / (1 + ((1.4 - 1) / 2) × 0.40²)≈ 281.06 KP2 = 105 / (1 + ((1.4 - 1) / 2) × 0.40²)≈ 91.20 kPa
(e) Mass flow rate
The mass flow rate can be calculated using the formula;ṁ = ρ1 × V1 × A1Where, ρ1 = P1 / (R × T1)
Substituting the values,ρ1 = 92.45 / (0.287 × 282.44)≈ 1.210 kg/m³ṁ = 1.210 × 102 × 0.49≈ 59.63 kg/s
(f) Velocity at location 2
The velocity at location 2 can be calculated using the formula;V2 = (ṁ / ρ2) / A2Where, ρ2 = P2 / (R × T2)
Substituting the values,ρ2 = 91.20 / (0.287 × 281.06)≈ 1.217 kg/m³V2 = (ṁ / ρ2) / A2= (59.63 / 1.217) / 0.25≈ 195.74 m/s
Therefore, the Mach number at location 1 is 0.37, static temperature and pressure at location 1 are 282.44 K and 92.45 kPa, respectively. The Mach number at location 2 is 0.40, static temperature and pressure at location 2 are 281.06 K and 91.20 kPa, respectively. The mass flow rate is 59.63 kg/s, and the velocity at location 2 is 195.74 m/s.
To know more about flow rate visit:
brainly.com/question/19863408
#SPJ11
Represent the system below in state space in phase-variable form s² +2s +6 G(s) = s³ + 5s² + 2s + 1
The system represented in state space in phase-variable form, with the given transfer function s² + 2s + 6 = s³ + 5s² + 2s + 1, is described by the state equations: x₁' = x₂, x₂' = x₃, x₃' = -(5x₃ + 2x₂ + x₁) + x₁''' and the output equation: y = x₁
To represent the given system in state space in phase-variable form, we'll start by defining the state variables. Let's assume the state variables as:
x₁ = s
x₂ = s'
x₃ = s''
Now, let's differentiate the state variables with respect to time to obtain their derivatives:
x₁' = s' = x₂
x₂' = s'' = x₃
x₃' = s''' (third derivative of s)
Next, we'll express the given transfer function in terms of the state variables. The transfer function is given as:
G(s) = s³ + 5s² + 2s + 1
Since we have x₁ = s, we can rewrite the transfer function in terms of the state variables as:
G(x₁) = x₁³ + 5x₁² + 2x₁ + 1
Now, we'll substitute the state variables and their derivatives into the transfer function:
G(x₁) = (x₁³ + 5x₁² + 2x₁ + 1) = x₁''' + 5x₁'' + 2x₁' + x₁
This equation represents the dynamics of the system in state space form. The state equations can be written as:
x₁' = x₂
x₂' = x₃
x₃' = -(5x₃ + 2x₂ + x₁) + x₁'''
The output equation is given by:
y = x₁
Learn more about state visit:
https://brainly.com/question/33222795
#SPJ11
Draw the critical load combinations for a five-span continuous beam, indicating the approximate location of the maximum bending moment in each case.
Analyze critical load combinations and determine maximum bending moments in each span of a five-span continuous beam.
Explain the process and importance of DNA replication in cell division.In the given problem, a five-span continuous beam is considered. The critical load combinations need to be determined, along with the approximate location of the maximum bending moment for each case.
The critical load combinations refer to the specific combinations of loads that result in the highest bending moments at different locations along the beam.
By analyzing and calculating the effects of different load combinations, it is possible to identify the load scenarios that lead to maximum bending moments in each span.
This information is crucial for designing and assessing the structural integrity of the beam, as it helps in identifying the sections that are subjected to the highest bending stresses and require additional reinforcement or support.
Learn more about combinations
brainly.com/question/31586670
#SPJ11
Question A pendulum has a length of 250mm. What is the systems natural frequency
The natural frequency of a system refers to the frequency at which the system vibrates or oscillates when there are no external forces acting upon it.
The natural frequency of a pendulum is dependent upon its length. Therefore, in this scenario, a pendulum has a length of 250 mm and we want to find its natural frequency.Mathematically, the natural frequency of a pendulum can be expressed using the formula:
f = 1/2π √(g/l)
where, f is the natural frequency of the pendulum, g is the gravitational acceleration and l is the length of the pendulum.
Substituting the given values into the formula, we get :
f= 1/2π √(g/l)
= 1/2π √(9.8/0.25)
= 2.51 Hz
Therefore, the natural frequency of the pendulum is 2.51 Hz. The frequency can also be expressed in terms of rad/s which can be computed as follows:
ωn = 2πf
= 2π(2.51)
= 15.80 rad/s.
Hence, the system's natural frequency is 2.51 Hz or 15.80 rad/s. This is because the frequency of the pendulum is dependent upon its length and the gravitational acceleration acting upon it.
To know more about pendulum visit:
https://brainly.com/question/29268528
#SPJ11
1. (a) Let A and B be two events. Suppose that the probability that neither event occurs is 3/8. What is the probability that at least one of the events occurs? (b) Let C and D be two events. Suppose P(C)=0.5,P(C∩D)=0.2 and P((C⋃D) c)=0.4 What is P(D) ?
(a) The probability that at least one of the events A or B occurs is 5/8.
(b) The probability of event D is 0.1.
(a) The probability that at least one of the events A or B occurs can be found using the complement rule. Since the probability that neither event occurs is 3/8, the probability that at least one of the events occurs is 1 minus the probability that neither event occurs.
Therefore, the probability is 1 - 3/8 = 5/8.
(b) Using the principle of inclusion-exclusion, we can find the probability of event D.
P(C∪D) = P(C) + P(D) - P(C∩D)
0.4 = 0.5 + P(D) - 0.2
P(D) = 0.4 - 0.5 + 0.2
P(D) = 0.1
Therefore, the probability of event D is 0.1.
To know more about probability visit:
https://brainly.com/question/15270030
#SPJ11
Design a excel file of an hydropower turgo turbine in Sizing and Material selection.
Excel file must calculate the velocity of the nozel, diameter of the nozel jet, nozzle angle, the runner size of the turgo turbine, turbine blade size, hub size, fastner, angular velocity,efficiency,generator selection,frequnecy,flowrate, head and etc.
(Note: File must be in execl file with clearly formulars typed with all descriptions in the sheet)
Designing an excel file for a hydropower turbine (Turgo turbine) involves calculating different values that are essential for its operation. These values include the velocity of the nozzle, diameter of the nozzle jet, nozzle angle, runner size of the turbine, turbine blade size, hub size, fastener, angular velocity, efficiency, generator selection, frequency, flow rate, head, etc.
To create an excel file for a hydropower turbine, follow these steps:Step 1: Open Microsoft Excel and create a new workbook.Step 2: Add different sheets to the workbook. One sheet can be used for calculations, while the others can be used for data input, output, and charts.Step 3: On the calculation sheet, enter the formulas for calculating different values. For instance, the formula for calculating the velocity of the nozzle can be given as:V = (2 * g * H) / (√(1 - sin²(θ / 2)))Where V is the velocity of the nozzle, g is the acceleration due to gravity, H is the head, θ is the nozzle angle.Step 4: After entering the formula, label each column and row accordingly. For example, the velocity of the nozzle formula can be labeled under column A and given a name, such as "Nozzle Velocity Formula".Step 5: Add a description for each formula entered in the sheet.
The explanation should be clear, concise, and easy to understand. For example, a description for the nozzle velocity formula can be given as: "This formula is used to calculate the velocity of the nozzle in a hydropower turbine. It takes into account the head, nozzle angle, and acceleration due to gravity."Step 6: Repeat the same process for other values that need to be calculated. For example, the formula for calculating the diameter of the nozzle jet can be given as:d = (Q / V) * 4 / πWhere d is the diameter of the nozzle jet, Q is the flow rate, and V is the velocity of the nozzle. The formula should be labeled, given a name, and described accordingly.Step 7: Once all the formulas have been entered, use the data input sheet to enter the required data for calculation. For example, the data input sheet can contain fields for flow rate, head, nozzle angle, etc.Step 8: Finally, use the data output sheet to display the calculated values. You can also use charts to display the data graphically. For instance, you can use a pie chart to display the percentage efficiency of the turbine. All the sheets should be linked correctly to ensure that the data input reflects on the calculation sheet and output sheet.
To know more about turbines visit:
https://brainly.com/question/25105919
#SPJ11