In the given scenario, the tyres of an F1 race car fail after 100 hours, and a car race at Kyalami Racecourse takes 10 hours to complete all the laps. To calculate the number of failures in the system, we divide the total race time by the failure time of the tyres. In this case, the number of failures in the system is 10. For the probability of two tyres failing in the race, we can use the concept of a binomial distribution. The probability can be calculated by combining the probability of one tyre failing with the probability of the other tyre failing, assuming independence.
To determine the number of failures in the system, we divide the total race time (10 hours) by the failure time of the tyres (100 hours). This gives us 10/100 = 0.1, indicating that there is one failure in the system.
For the probability of two tyres failing in the race, we can use the binomial distribution. The probability of one tyre failing can be calculated by dividing the tyre failure time (100 hours) by the total race time (10 hours), which gives us 100/10 = 10%. Assuming independence between the two tyres, we can multiply the probability of one tyre failing by itself to get the probability of both tyres failing. Thus, the probability of two tyres failing in the race is 10% * 10% = 1%.
In summary, there is one failure in the system, and the probability of two
ptyres failing in the race is 1%.
Learn more about probability here: brainly.com/question/30034780
#SPJ11
The road roller has a mass of 1.6 Mg and center of mass at G travels along the sh roller as shown to drive it safely on the inclined shoulder, if the coefficient of friction bet 0.4 and the shoulder angle = 30⁰ determine the minimum force P eded to prevent roller from (assume the front and rear drums as one m and G at the middle of the width)
The minimum force required to prevent the roller from slipping is 5.55 × 10³ N.
Given data;
Mass of the road roller, m = 1.6 Mg
Co-efficient of friction between road roller and inclined surface, μ = 0.4
Angle of shoulder, θ = 30°
Force needed to prevent roller from slipping = P
In order to keep the road roller safe, we need to calculate the minimum force required to prevent the roller from slipping.
As per the question, the front and rear drums of the road roller is considered as one mass and the center of mass of that mass is G. Now, we need to consider the free body diagram of the road roller.
Let's represent the downward forces acting on the road roller by W.
Let's consider the direction of force P acting on the road roller to be upwards. We can then resolve the force P into its vertical and horizontal components.
Let F and N be the forces acting on the road roller in the horizontal and vertical directions respectively.
Now, we can write the expression for F and N as;
N = W cosθ;
F = P - W sinθ;
We know that the minimum force needed to prevent the roller from slipping is;
Pmin = μN
= μW cosθ
Substituting N in the above equation with its value;
Pmin = μW cosθ
= μ(mg) cosθ
where, g is the acceleration due to gravity
Substituting the given values of μ, m and θ;
Pmin = 0.4 × 1.6 × 10³ × 9.81 × cos 30°
= 5.55 × 10³ N (rounded to 3 significant figures)
Know more about the inclined surface
https://brainly.com/question/15563716
#SPJ11
Question 3 DC Engineering Company has two units operating in two different cities A and B, where the manufacturing of engineering components takes place. Both the units employ young graduates as well as mid-career engineers. The company pays attractive salary to recruit competent workforce. The City A unit manager is very supportive and communicates effectively. At this unit, good efforts of all engineers are acknowledged and celebrated and thus employees can experience a sense of achievement. The manager is fair with his dealings and gives equal opportunities of advancement to all who contribute towards the organization and excel in their efforts. Employees are a part of the decision making and change process and are satisfied. The unit seldom experiences absenteeism or employee turnover. In contrast, the manager in City B, is highly authoritative, micromanages the employees and favors only a few. Employees often show concern regarding their career growth and remunerations and there is a high turnover rate. Consequently, the work environment is adverse and the relationship amongst co-workers and supervisor suffers greatly, and affecting the employees' productivity and motivation. (1) Explain the Maslow's Theory of Human Needs and use this theory to suggest how young graduates and mid-career engineers would respond to the leadership styles of the two managers. (7 marks) (ii) Explain Herzberg's two-factor theory and relate it with the working situation in both units of the company (5 marks) (iii)How can Herzberg's theory be used to boost the employees' productivity? (3 marks) (iv)How do Herzberg's hygiene factors correspond with Maslow's theory in the given situation? (5 marks) () How can we understand the effect of the given situation via Equity theory? (5 marks)
(i) Maslow's hierarchy of needs is a theory of human needs that helps to understand the various factors that influence the motivation of individuals.
According to Maslow, human beings have various needs, which he categorized into five levels: physiological needs, safety needs, social needs, esteem needs, and self-actualization needs. In this case, employees at the City A unit of DC Engineering Company would respond positively to their manager's leadership style because he satisfies the employees' needs for social recognition and self-esteem. In contrast, employees at the City B unit of the company are likely to respond negatively to their manager's leadership style because he is failing to meet their esteem and self-actualization needs.
(ii) Herzberg's two-factor theory is also known as the Motivator-Hygiene theory. Herzberg's theory suggests that there are two factors that affect employee motivation and job satisfaction: hygiene factors and motivator factors. Hygiene factors include working conditions, salary, job security, and company policies. Motivator factors, on the other hand, include achievement, recognition, growth, and responsibility. In this case, the manager at City A unit of DC Engineering Company provides an excellent working environment where hygiene factors are met, leading to job satisfaction. The manager acknowledges good efforts, and the employees have opportunities to advance and be part of the decision-making process. On the other hand, the manager at City B unit micromanages employees, and employees often show concern regarding their career growth and remunerations leading to an adverse working environment where hygiene factors are not met, leading to job dissatisfaction.
(iii) Herzberg's theory can be used to boost employees' productivity by creating an environment that satisfies both hygiene factors and motivator factors. Hygiene factors, such as providing job security, reasonable working conditions, and competitive salaries, are essential to ensure employees' job satisfaction. Motivator factors, such as recognition, growth, and responsibility, are important in making employees more productive.
(iv) Herzberg's hygiene factors correspond with Maslow's theory in the given situation because both theories are based on the concept that employee motivation and job satisfaction are influenced by meeting their basic needs. Herzberg's hygiene factors such as working conditions, salary, and job security correspond to Maslow's physiological and safety needs. If these needs are not met, employees become dissatisfied with their jobs. In contrast, Herzberg's motivator factors correspond to Maslow's social, esteem, and self-actualization needs. If these needs are met, employees become motivated and productive.
(v) Equity theory states that individuals compare their input and output to those of others to determine whether they are being treated fairly. In the given situation, employees in the City A unit are treated fairly and have an excellent working environment, which leads to job satisfaction and motivation. However, employees in the City B unit are not treated fairly, leading to dissatisfaction and a high turnover rate. Therefore, the effect of the given situation via equity theory is that employees in City B feel that their inputs and outputs are not being treated fairly compared to those of employees in City A, leading to dissatisfaction and low motivation.
To know more about Maslow's theory, visit:
https://brainly.com/question/33539726
#SPJ11
Determine the charge q developed when a piezoelectric crystal with A = 15 mm and h = 8 mm is subjected to a pressure p = 2 MPa if the crystal is (a) X-cut, length-longitudinal quartz (b) parallel-to-polarization barium titanate
Depending on the specific piezoelectric crystal used, the charge developed will vary.
Given:
- Piezoelectric crystal with A = 15 mm and h = 8 mm
- Pressure p = 2 MPa
- The crystal is (a) X-cut, length-longitudinal quartz (b) parallel-to-polarization barium titanate
(a) X-cut, length-longitudinal quartz:
- The charge developed in a piezoelectric crystal can be calculated using the formula q = d x A x p, where q is the charge, d is the piezoelectric coefficient, A is the surface area of the crystal, and p is the pressure applied.
- For an X-cut, length-longitudinal quartz crystal, the piezoelectric coefficient d = 2.04 x 10^-12 C/N.
- Substituting the values, we get q = (2.04 x 10^-12 C/N) x (15 mm x 8 mm) x (2 MPa) = 4.89 x 10^-6 C
(b) Parallel-to-polarization barium titanate:
- The piezoelectric coefficient for barium titanate is typically represented as e, which has a value of 1.9 x 10^-10 C/N.
- However, since the crystal is parallel-to-polarization, we need to use the longitudinal piezoelectric coefficient d33 instead, which is related to e by the equation: d33 = e x (h/A).
- Substituting the given values, we get d33 = (1.9 x 10^-10 C/N) x (8 mm / 15 mm) = 1.02 x 10^-10 C/N.
- Substituting the values into the formula for q, we get q = (1.02 x 10^-10 C/N) x (15 mm x 8 mm) x (2 MPa) = 2.45 x 10^-6 C.
- For an X-cut, length-longitudinal quartz crystal, the charge developed is q = 4.89 x 10^-6 C.
- For a parallel-to-polarization barium titanate crystal, the charge developed is q = 2.45 x 10^-6 C.
To know more about Piezoelectric crystals, visit:
https://brainly.com/question/29690670
#SPJ11
A single screw extruder has a screw with a diameter of 48 mm and the screw angle is 17.7'. The screw length is 0.8 m and the flight depth is 3 mm. If the screw speed is 50 rpm and the viscosity of the plastic is 250 Ns/m2calculate the output when the extruder is producing a medical tube through a die with an outside diameter of 12 mm an inside diameter of 10.4 mm and a length of 13 mm. You may assume that leakage losses from the extruder are negligible.
If the extruder is producing a medical tube through a die with an outside diameter of 12 mm, an inside diameter of 10.4 mm, and a length of 13 mm, the output would be 0.048 kg/s, since Output = 0.043 / 0.9.
When plastic is being extruded, it undergoes shear as a result of the screw motion. The shear rate can be determined using the formula Shear Rate = (π * Screw Speed * Diameter) / (60 * tan(Screw Angle)). For instance, Shear Rate = (π * 50 * 48) / (60 * tan(17.7)) equals 217.5 s^-1.
Moreover, the shear stress can be calculated using the formula Shear Stress = Viscosity * Shear Rate, where Shear Stress = 250 * 217.5, giving 54375 N/m2. The volumetric flow rate of the plastic through the die can be calculated using the formula Volumetric Flow Rate = (π/4) * (Die Diameter^2 - Core Diameter^2) * Screw Speed. For example, Volumetric Flow Rate = (π/4) * (0.012^2 - 0.0104^2) * 50, which is 3.584 x 10^-5 m3/s.
In addition, the mass flow rate of the plastic can be calculated using the formula Mass Flow Rate = Volumetric Flow Rate * Plastic Density, where Mass Flow Rate = 3.584 x 10^-5 * 1200 equals 0.043 kg/s. Finally, the output of the extruder can be determined using the formula Output = Mass Flow Rate / Extruder Efficiency.
Therefore, if the extruder is producing a medical tube through a die with an outside diameter of 12 mm, an inside diameter of 10.4 mm, and a length of 13 mm, the output would be 0.048 kg/s, since Output = 0.043 / 0.9.
Know more about Shear Rate here:
https://brainly.com/question/31629428
#SPJ11
Question 1: Design a linkage system such that as a float for liquid level measurement moves from 0 to 1 m, an LVDT core moves over its linear range of 3 cm. Question 2: A pressure transducer outputs a voltage to a readout device that converts the signal back to pressure: The device specifications are: Resolution: 0.1 psi Sensitivity error: 0.1 psi Linearity error: within 0.1% of reading Drift: less than 0.1 psi/6 months (32-90F) The transducer has a claimed accuracy of within 0.5% of reading. For a nominal pressure of 100 psi at 70F, estimate the design-stage uncertainty in a measured pressure.
When a float is present for the measurement of liquid level moving from 0 to 1 m, the LVDT core moves over its linear range of 3 cm. The float will be attached to the end of the linkage system so that the float moves from 0 to 1 m, and the LVDT core moves over its linear range of 3 cm.
The system will be designed in such a way that the float moves in a linear manner from 0 to 1 m. The linkage system is shown below: Let the float be situated at the beginning of the linkage system and the LVDT core be located at the end of the linkage system.
The length of the linkage system is defined by the float movement range (0-1 m). We must adjust the lengths of the links to achieve a LVDT core movement range of 3 cm. The float will be attached to the first link of the linkage system, which will be a straight link, as shown in the figure above.
To know more about measurement visit:
https://brainly.com/question/28913275
#SPJ11
A 0.02 m³ tank contains 1.6 kg of argon gas at a temperature of 110 K. Using the van de Waal's equation, what is the pressure inside the tank? Express your answer in kPa.
The pressure inside the tank is approximately 28.63 kPa by using van der Waal's equation.
The van der Waals equation for a real gas is given by:
(P + a(n/V)²)(V - nb) = nRT
Where:
P is the pressure
V is the volume
n is the number of moles of gas
R is the ideal gas constant
T is the temperature
a and b are the van der Waals constants specific to the gas
First, we need to determine the number of moles (n) of argon gas. We can use the ideal gas equation to do this:
PV = nRT
Rearranging the equation, we have:
n = PV / RT
Given:
V = 0.02 m³
T = 110 K
m (mass of argon) = 1.6 kg
molar mass of argon = 39.95 g/mol
First, we convert the mass of argon to moles:
n = (1.6 kg / 39.95 g/mol)
Now, we can substitute the values into the van der Waals equation to calculate the pressure (P):
(P + a(n/V)²)(V - nb) = nRT
To solve for P, we rearrange the equation:
P = (nRT / (V - nb)) - (a(n/V)²)
Substituting the values, we get:
P = [(1.6 kg / 39.95 g/mol) * (8.314 J/(molK)) * (110 K)] / (0.02 m³ - 0.0266 m³/mol * (1.6 kg / 39.95 g/mol)) - (1.355 Jm³/(mol²))
Calculating this expression gives us:
P ≈ 28627.89 Pa
Converting Pa to kPa:
P ≈ 28.63 kPa
To know more about pressure visit
https://brainly.com/question/30638002
#SPJ11
Gas Mixture A and Gas Mixture B have the following composition: Component Gas Mixture A (mass basis) Gas Mixture B (mole basis) Nitrogen 60% 60% Oxygen 25% 25% Methane 15% 15% Considering methane, what is the difference between the mass fraction of methane in Gas Mixture A and Gas Mixture B? Express your answer in %.
The difference between the mass fraction of methane in Gas Mixture A and Gas Mixture B is 0%.
Since both Gas Mixture A and Gas Mixture B have the same composition of methane at 15% on a mole basis, the difference in the mass fraction of methane would depend on the molar mass of the other components present. However, in this case, the molar mass of the other components is not provided, making it impossible to calculate the exact mass fraction.
Therefore, we can conclude that the difference between the mass fraction of methane in Gas Mixture A and Gas Mixture B is 0% due to the lack of information regarding the molar masses of the other components in the mixtures.
To know more about mass fraction visit
brainly.com/question/33418638
#SPJ11
Why should we study dynamics?
How do we usually define space in dynamics?
How do we usually define space in dynamics?
What is force in dynamics?
Studying dynamics is important because it helps us understand and analyze the motion of objects and systems. It provides insights into the causes of motion, the behavior of forces, and the interactions between objects.
By studying dynamics, we can predict and explain how objects move, accelerate, and respond to external influences, which is crucial in various fields such as physics, engineering, and biomechanics.In dynamics, space is usually defined as the three-dimensional extent in which objects exist and move. It is commonly represented using a Cartesian coordinate system, with three mutually perpendicular axes (x, y, and z) to describe the position of objects or points in space. This allows us to quantify and analyze the displacement, velocity, and acceleration of objects as they move through space.
To know more about velocity visit :
https://brainly.com/question/18084516
#SPJ11
The gas-turbine cycle of a combined gas-steam power plant has a pressure ratio of 8. Air 300k 1500 enters the compressor at 290 K and the turbine at 1400 K. The combustion gases leaving the yoo gas turbine are used to heat the steam at 15 MPa to 450°C in a heat exchanger. The combustion 120k gases leave the heat exchanger at 247°C. Steam expands in a high-pressure turbine to a pressure of 3 MPa and is reheated in the combustion chamber to 500°C before it expands in a low- pressure turbine to 10 Pa. The mass flow rate of steam is 30 kg/s. Assuming all the compression and expansion processes to be isentropic. For steady-state operation and kinetic and potential energy changes are negligible, and constant specific heat with Cp-1.023 kJ/kg.K. k=1.4 is used. Determine (i) the mass flow rate of air in the gas-turbine cycle, Gil) the rate of 2 total heat input, and (in) the thermal efficiency of the combined cycle.
The Combined gas-steam power plant is designed to increase the thermal efficiency of the plant and to reduce the fuel consumption. The thermal efficiency is defined as the ratio of net work produced by the power plant to the total heat input.
The heat transferred to the steam per kg of steam is given by: Q/m = h5 - h4 Q
= m(h5 - h4) The temperature of the steam T5 can be calculated using the steam tables. At a pressure of 15 MPa, the enthalpy of the steam h4 = 3127.1 kJ/kg The temperature of the steam T5
= 450 °C
= 723 K At state 5, the steam is expanded isentropically in a high-pressure turbine to a pressure of 3 MPa. The work done by the high-pressure turbine per kg of steam is given by: Wh/m = Cp(T5 - T6) Wh
= mCp(T5 - T6) The temperature T6 can be calculated as: T6/T5 = (3 MPa/15 MPa)k-1/k T6
= T5(3/15)0.4
= 533.16 K The temperature T5 can be calculated using the steam tables.
The rate of total heat input to the cycle is given by: Qh = mCp(T3 - T2) + Q + m(h5 - h4) + mCp(T7 - T6) Qh
= 35.046 × 1.023 × (977.956 - 698.54) + 35.046 × 728.064 + 30 × (3127.1 - 2935.2) + 30 × 1.023 × (746.624 - 533.16) Qh = 288,351.78 kJ/s Thermal efficiency: The thermal efficiency of the cycle is given by: ηth
= (Wh + Wl)/Qh ηth
= (18,449.14 + 22,838.74)/288,351.78 ηth
= 0.1426 or 14.26 % The mass flow rate of air in the gas-turbine cycle is 35.046 kg/s.The total heat input is 288,351.78 kJ/s.The thermal efficiency of the combined cycle is 14.26 %.
To know more about steam visit:
https://brainly.com/question/15447025
#SPJ11
A 40-mm thick AISI 1050 steel plate is sandwiched between two 2024-T3 aluminium plates with thickness of 20-mm and 30-mm. The plates are compressed with a bolt and nut with no washers. The bolt is M14 X 2, property class 4.8. (a) Determine a suitable length for the bolt, rounded up to the nearest 5 mm. (b) Determine the bolt stiffness. (e) Determine the stiffness of the members.
A. The suitable length of bolt is 240 mm (rounded up to nearest 5 mm).
B. Stiffness of AISI 1050 steel plate (k1) = 1313.8 N/mm
Stiffness of 1st 2024-T3 aluminium plate (k2) = 287.5 N/mm
Stiffness of 2nd 2024-T3 aluminium plate (k3) = 664.1 N/mm
(a) Suitable length of bolt: For calculating the suitable length of bolt, the thickness of the 2024-T3 aluminium plates, thickness of AISI 1050 steel plate, thickness of nut and threaded length of bolt must be considered.
Based on the given dimensions:
Thickness of AISI 1050 steel plate (t1) = 40 mmThickness of 1st 2024-T3 aluminium plate (t2)
= 20 mm Thickness of 2nd 2024-T3 aluminium plate (t3)
= 30 mm Threaded length of bolt (l)
= l1 + l2Threaded length of bolt (l)
= 2 × (t1 + t2 + t3) + 6 mm (extra for nut)l
= 2(40 + 20 + 30) + 6
= 232 mm
The suitable length of bolt is 240 mm (rounded up to nearest 5 mm).
(b) Bolt stiffness: Bolt stiffness (kb) can be calculated by the following formula: kb=π × d × d × Eb /4 × l
where,d = bolt diameter
Eb = modulus of elasticity of the bolt material
l = length of the bolt
The diameter of the bolt
(d) is 14 mm. Modulus of elasticity of the bolt material (Eb) is given as 200 kN/mm².
Substituting the given values in the formula:
kb= 3.14 × 14 × 14 × 200 / 4 × 240 = 1908.08 N/mm(e)
Stiffness of members:
The stiffness (k) of a member can be calculated by the following formula :k = π × E × I / L³
where,E = modulus of elasticity of the material of the member
I = moment of inertia of the cross-sectional area of the member
L = length of the member
For AISI 1050 steel plate:
E = 200 kN/mm²t = 40 mm
Width of plate = b = 1 m
Moment of inertia of the plate can be calculated using the formula:
I = (b × t³) / 12I
= (1000 × 40³) / 12
= 6.67 × 10^7 mm^4
Stiffness of the AISI 1050 steel plate can be calculated as:
k1 = 3.14 × 200 × 6.67 × 10^7 / (1000 × 1000 × 1000 × 1000)
= 1313.8 N/mm
For 1st 2024-T3 aluminium plate:
E = 73.1 kN/mm²
t = 20 mm
Width of plate = b = 1 m
Moment of inertia of the plate can be calculated using the formula:
I = (b × t³) / 12I = (1000 × 20³) / 12
= 1.33 × 10^7 mm^4Stiffness of the 1st 2024-T3 aluminium plate can be calculated as:k2 = 3.14 × 73.1 × 1.33 × 10^7 / (1000 × 1000 × 1000 × 1000) = 287.5 N/mm
For 2nd 2024-T3 aluminium plate:
E = 73.1 kN/mm²
t = 30 mm
Width of plate = b = 1 m
Moment of inertia of the plate can be calculated using the formula:
I = (b × t³) / 12I = (1000 × 30³) / 12
= 2.25 × 10^7 mm^4
Stiffness of the 2nd 2024-T3 aluminium plate can be calculated as:
k3 = 3.14 × 73.1 × 2.25 × 10^7 / (1000 × 1000 × 1000 × 1000)
= 664.1 N/mm
Therefore, Stiffness of AISI 1050 steel plate (k1) = 1313.8 N/mm
Stiffness of 1st 2024-T3 aluminium plate (k2) = 287.5 N/mm
Stiffness of 2nd 2024-T3 aluminium plate (k3) = 664.1 N/mm
To know more about suitable length, Visit :
https://brainly.com/question/4059783
#SPJ11
A 0.02 m³ tank contains 1.6 kg of argon gas at a temperature of 120 K. Using the van de Waal's equation, what is the pressure inside the tank? Express your answer in kPa.
The pressure inside the tank is approximately 909.12 kPa using the van der Waals equation.
To determine the pressure inside the tank using the van der Waals equation, we need to consider the van der Waals constants for argon:
a = 1.3553 N²/m⁴
b = 0.0320 m³/kg
The van der Waals equation is given by:
P = (R * T) / (V - b) - (a * n²) / (V²)
where:
P is the pressure
R is the gas constant (8.314 J/(mol·K))
T is the temperature
V is the volume
n is the number of moles of the gas
First, we need to determine the number of moles of argon gas in the tank. We can use the ideal gas law:
PV = nRT
Rearranging the equation, we have:
n = PV / RT
Given:
V = 0.02 m³
m (mass) = 1.6 kg
M (molar mass of argon) = 39.95 g/mol
T = 120 K
Converting the mass of argon to moles:
n = (m / M) = (1.6 kg / 0.03995 kg/mol) = 40.10 mol
Now we can substitute the values into the van der Waals equation:
P = (R * T) / (V - b) - (a * n²) / (V²)
P = (8.314 J/(mol·K) * 120 K) / (0.02 m³ - 0.0320 m³/kg * 1.6 kg) - (1.3553 N²/m⁴ * (40.10 mol)²) / (0.02 m³)²
Calculating the pressure:
P ≈ 909.12 kPa
Therefore, the pressure inside the tank is approximately 909.12 kPa.
To know more about pressure, visit
https://brainly.com/question/30902944
#SPJ11
60. A V. in. round steel shaft Innsmit. hp at 1.750 rpm while being subjected to an mal force of 100 lbs. What is the revuliant compressive stresse? A 905 4 psa €405.9 psi B. 909 4 psi 990.4 psi
The resilient compressive stress, given the round shaft, is A. 905.4 pounds per square inch or psi.
How to find the resilient compressive stress ?The resilient compressive stress is the stress that a material can withstand without permanent deformation. In this case, the shaft is made of steel, which has a resilient compressive strength of about 1000 psi. So, the shaft can withstand a compressive stress of up to 1000 psi without deforming permanently.
Stress = Force / Area
Stress = 100 lbs / (3.14 * (0.25 in) ²)
Stress = 905.4 psi
The actual stress on the shaft is only 905.4 psi, so the shaft is not under any risk of permanent deformation.
Find out more on compressive stress at https://brainly.com/question/28813620
#SPJ4
A bipolar transistor has an emitter transition region capacitance Cet of 3 pF at zero bias. With VBE = 0.65 V it has a total input capacitance C₁ of 30 pF with an Ic of 2 mA. Find C₁ when the collector current is increased to 12 mA. Take o = -0.8 V.
The total input capacitance C₁ becomes approximately 5.79 pF.
To find the value of C₁ when the collector current is increased to 12 mA, we can use the formula for the total input capacitance of a bipolar transistor:
C₁ = Cet + (Cπ / (1 - A * (VBE - VBE(on))))
where Cet is the emitter transition region capacitance, Cπ is the base-emitter capacitance per unit area, A is the current gain of the transistor, VBE is the base-emitter voltage, and VBE(on) is the threshold voltage.
Given:
Cet = 3 pF
C₁ = 30 pF (at Ic = 2 mA)
Ic1 = 2 mA
Ic2 = 12 mA
VBE = 0.65 V
VBE(on) = -0.8 V
First, we need to find the value of Cπ. We can use the relationship:
Cπ = C₁ - Cet
Cπ = 30 pF - 3 pF
Cπ = 27 pF
Now, we can calculate the value of C₁ when Ic = 12 mA using the formula mentioned earlier:
C₁ = Cet + (Cπ / (1 - A * (VBE - VBE(on))))
To find the value of A, we need to use the relationship:
A = Ic2 / Ic1
A = 12 mA / 2 mA
A = 6
Plugging in the values, we get:
C₁ = 3 pF + (27 pF / (1 - 6 * (0.65 V - (-0.8 V))))
Simplifying the expression inside the parentheses:
C₁ = 3 pF + (27 pF / (1 + 6 * 1.45 V))
C₁ = 3 pF + (27 pF / (1 + 8.7 V))
C₁ = 3 pF + (27 pF / 9.7 V)
C₁ = 3 pF + 2.79 pF
C₁ = 5.79 pF
Therefore, when the collector current is increased to 12 mA, the total input capacitance C₁ becomes approximately 5.79 pF.
to learn more about capacitance.
https://brainly.com/question/31871398
#SPJ11
Find the production cost per 1000 kg steam in a steam plant when the evaporation rate is
7.2 kg steam per kg coal; initial cost of plant, $150,000; annual operational cost exclusive
of coal, $15,000. Assume life of 20 years; no final value; interest on borrowed capital, 4%;
on sinking fund, 3%. Average steam production is 14,500 kg per hr; cost of coal, $8.00 per
ton.
The production cost per 1000 kg steam in a steam plant when the evaporation rate is 7.2 kg steam per kg coal is $18.03. This is obtained as follows;
Step-by-step explanation:
The steam produced from the combustion of coal in a steam plant can be evaluated by first finding the amount of steam generated per kg of coal burned. This is called the evaporation rate.The evaporation rate is given as 7.2 kg steam per kg coal.The cost of coal is given as $8.00 per ton.The steam plant has an average steam production of 14,500 kg per hr.Annual operational cost exclusive of coal is $15,000.The initial cost of plant is $150,000.The life of the steam plant is 20 years.
The interest on borrowed capital is 4% while the interest on the sinking fund is 3%.To find the cost of steam production per 1000 kg, the following calculations are made;
Total amount of steam produced in one year = 14,500 * 24 * 365 = 126,540,000 kg
Annual coal consumption = 126,540,000 / 7.2 = 17,541,666.67 kg
Total cost of coal in one year = (17,541,666.67 / 1000) * $8.00 = $140,333.33
Total cost of operation per year = $140,333.33 + $15,000 = $155,333.33
Annual equivalent charge = AEC = 1 + i/n - 1/(1+i/n)^n*t
Where i = interest n = number of years for which the sum is invest
dt = total life of the investment AEC = 1 + 0.04/1 - 1/(1+0.04/1)^(1*20) = 1.7487
Annual equivalent disbursement = AED = S / a
Where S = initial cost of plant + sum of annual cost (AEC) for n y
earsa = annuity factor obtained from the tables
.AED = $150,000 / 3.8879 = $38,595.69
Annual sinking fund = AS = AED * i / (1 - 1/(1+i/n)^n*t)AS = $38,595.69 * 0.03 / (1 - 1/(1+0.03/1)^(1*20)) = $1,596.51
Total annual cost of the steam plant
= $155,333.33 + $1,596.51
= $156,929.84
Cost of steam production per 1000 kg = 1000 / (126,540,000 / 14,500) * $156,929.84 = $18.03Therefore, the cost of steam production per 1000 kg is $18.03.
To know more about evaporation visit :
https://brainly.com/question/28319650
#SPJ11
QUESTION 1 Which of the followings is true? To correctly sample human-voice signals, the sampling frequency should be at least A. 8kHz. B. 12kHz. C. 4kHz. D. 16kHz. QUESTION 2 Which of the followings is true? A. The unit step can be given as a unit rectangular pulse. B. The unit rectangular pulse can be expressed using two step functions. C. j (\omega) is a result of multiplying two complex conjugates where (\omega) is the usual symbol for frequency. D. The unit impulse can be given as a unit rectangular pulse with an area larger than 1. QUESTION 3 Which of the followings is true? A. The phase response typically includes atan and tan functions. B. The phase response typically includes tan function. C. The phase response typically includes square root of angles. D. The phase response typically includes atan function.
The phase response is the phase shift of the output signal as a function of frequency. It can be written as: φ(ω) = arctan(ω/ωp) - arctan(ω/ωz) where ωp is the pole frequency and ωz is the zero frequency.
QUESTION 1: The correct answer is option D) 16kHz.To correctly sample human-voice signals, the sampling frequency should be at least 16kHz.
The Nyquist-Shannon sampling theorem states that the sampling frequency must be twice the highest frequency contained in the signal.
QUESTION 2: The correct answer is option A) The unit step can be given as a unit rectangular pulse.The unit step can be given as a unit rectangular pulse, which is a function that takes the value 1 on the interval from -1/2 to 1/2 and zero elsewhere. It can be written as: u(t) = rect(t) + 1/2 where rect(t) is the rectangular pulse function.
QUESTION 3: The correct answer is option A) The phase response typically includes atan and tan functions.The phase response typically includes atan and tan functions.
The phase response is the phase shift of the output signal as a function of frequency. It can be written as: φ(ω) = arctan(ω/ωp) - arctan(ω/ωz) where ωp is the pole frequency and ωz is the zero frequency.
To know more about frequency visit:
brainly.com/question/33223954
#SPJ11
Q5) Given the denominator of a closed loop transfer function as expressed by the following expression: S² + 8S-5Kₚ + 20 The symbol Kₚ denotes the proportional controller gain. You are required to work out the following: 5.1) Find the boundaries of Kₚ for the control system to be stable.
5.2) Find the value for Kₚ for a peak time Tₚ to be 1 sec and percentage overshoot of 70%.
5.1)The boundaries for Kₚ to ensure stability are Kₚ > 2.5.
5.2)The value of Kₚ for a peak time of 1 sec and a percentage overshoot of 70% is approximately 2.949.
5.1) To determine the stability boundaries for the control system, we need to analyze the denominator of the closed-loop transfer function:
S² + 8S - 5Kₚ + 20
For stability, all the roots of the denominator polynomial should have negative real parts. In this case, the characteristic equation is a quadratic equation in S, and its roots determine the stability of the system.
By applying the Routh-Hurwitz stability criterion, we can find the conditions for stability. The Routh array for the characteristic equation is:
1 -5Kₚ
8 20
To ensure stability, all the elements in the first column of the Routh array must be positive:
1 > 0 (condition 1)
8Kₚ - 20 > 0 (condition 2)
From condition 1, we have 1 > 0, which is always true.
From condition 2, we can solve for the boundaries of Kₚ:
8Kₚ - 20 > 0
8Kₚ > 20
Kₚ > 2.5
5.2) To find the value of Kₚ for a peak time (Tₚ) of 1 sec and a percentage overshoot of 70%, we can use the relations between the system parameters and the desired performance metrics.
The peak time Tₚ is related to the damping ratio (ζ) and natural frequency (ωn) as follows:
Tₚ = π / (ζ * ωn)
The percentage overshoot (PO) is related to the damping ratio (ζ) as follows:
PO = exp((-ζ * π) / sqrt(1 - ζ²)) * 100
Given Tₚ = 1 sec and PO = 70%, we can solve these equations simultaneously to find the values of ζ and ωn. Once we have ζ, we can determine the value of Kₚ using the following relation:
Kₚ = (ωn² - 8) / 5
By solving the equations, we find that ζ ≈ 0.456 and ωn ≈ 3.535.
Substituting these values into the expression for Kₚ, we get:
Kₚ = (3.535² - 8) / 5 ≈ 2.949
To know more about closed-loop transfer function, visit:
https://brainly.com/question/13002430
#SPJ11
Consider an FSM that has a 1-bit input A and a 1-bit
output F (found). Design a Moore FSM that repeatedly detects the serial input: 10110.
When that input is detected, the output F should assert for one clock cycle. So, A changes
over time – it is a serial input, because a new bit appears on that signal each clock cycle.
(a) Sketch the state transition diagram.
(b) Implement the FSM in SystemVerilog. Name the module: seqdetector.
Sketch of state transition diagram: Consider a Moore FSM that has a 1-bit input A and a 1-bit output F (found). Design a Moore FSM that repeatedly detects the serial input: 10110. When that input is detected, the output F should assert for one clock cycle.
The module has two ports, an input port a and an output port f. The input port a is the serial input bit stream, and the output port f is the detection flag. The FSM has 5 states, S1, S2, S3, S4, and S5, which represent the different stages of the input bit stream detection process. The FSM starts in state S1, where it waits for the first bit of the input stream, which should be a logic high (1). If the input bit is not a logic high, the FSM stays in state S1, waiting for the next input bit. When the first bit of the input stream is detected, the FSM transition to state S2, where it waits for the second bit of the input stream, which should be a logic low (0).
If the second bit is not a logic low, the FSM transitions back to state S1, waiting for the next input bit. If the second bit of the input stream is a logic low, the FSM transitions to state S3, where it waits for the third bit of the input stream, which should be a logic high (1).
To know more about state transition diagram visit:
https://brainly.com/question/13263832
#SPJ11
Design a Ball milling machine. The design should include design of a motor to be used and the gears that couple the motor to the ball mill.. Also attach a SOLIDWORKS file to show the simulation. EMPHASIS ON THE SOLIDWORKS PARTS, ASSEMBLY AND SIMULATION. THESE MUST BE ATTACHED TO THE SOLUTION
The ball mill machine is used to grind, crush, and mix solid materials such as ceramics, minerals, metals, and plastics.
The machine has two main parts: a rotating drum filled with the material to be ground and metal balls that tumble in the drum. The motor is attached to the drum via a gear coupling to rotate the drum. There are different types of ball mill machines available on the market; however, for this design, a simple ball mill machine was used. The design includes the motor, gear coupling, drum, and metal balls.
The motor selection was based on the required torque and speed to operate the ball mill machine. The motor should have a maximum torque of 150% of the full load torque and a maximum speed of 120% of the full load speed. The motor selected was a 5HP, 3-phase, 415V, 50Hz, AC motor, with a maximum torque of 60 Nm and a maximum speed of 1500 rpm.
Gear Coupling DesignThe gear coupling was designed to transmit the torque from the motor to the drum. The gear coupling was selected based on the torque rating and bore size. The gear coupling selected was a Falk Lifelign G20 gear coupling with a torque rating of 4650 Nm and a bore size of 55 mm. Drum DesignThe drum was designed using SolidWorks 2019. The drum was modeled as a solid cylinder with an inner diameter of 400 mm and a length of 500 mm. The material used for the drum was carbon steel with a thickness of 20 mm. The drum was designed to hold up to 10 kg of material. Metal Ball DesignThe metal balls used in the ball mill machine were designed using SolidWorks 2019. The metal balls were modeled as a solid sphere with a diameter of 25 mm. The material used for the metal balls was hardened steel. The weight of each metal ball was 1 kg. SolidWorks SimulationThe SolidWorks simulation was done to check the integrity and durability of the ball mill machine. The simulation was done for the gear coupling and the drum. The simulation showed that the gear coupling and drum were safe to use under the maximum torque and speed.
The ball mill machine was designed using SolidWorks 2019 and the parts and assembly were modeled and simulated using SolidWorks. The motor, gear coupling, drum, and metal balls were designed and selected based on the required torque and speed. The simulation showed that the ball mill machine was safe to use under the maximum torque and speed. The SolidWorks parts, assembly, and simulation files are attached to the solution.
To know more about gear coupling visit:
brainly.com/question/24933685
#SPJ11
An ideal diesel engine has a compression ratio of 20 and uses air as the working fluid. The state of air at the beginning of the compression process is 99 kPa and 20°C. The maximum temperature in the cycle is not to exceed 2200 K. The gas constant of air is R = 0.287 kJ/kg-K. Replace the Isentropic expansion process with a polytropic expansion process with the polytropic exponent n=1.35. Use variable specific heats. Determine the thermal efficiency. (You must provide an answer before moving on to the next part.) The thermal efficiency is ____ %.
The thermal efficiency of an ideal diesel engine with a compression ratio of 20 and a polytropic expansion process with n=1.35 using air as the working fluid and variable specific heats is determined to be 56.4%.
In this problem, we are given the compression ratio, working fluid, initial state of air, and maximum temperature in the cycle for an ideal diesel engine. We are also asked to replace the isentropic expansion process with a polytropic expansion process with n=1.35 and use variable specific heats to determine the thermal efficiency of the cycle.
Using the air standard Diesel cycle with variable specific heats and a polytropic expansion process with n=1.35, we calculated the state of air at different points in the cycle. We found that the thermal efficiency of the cycle is 56.4%.
This means that 56.4% of the energy from the fuel is converted into useful work, while the remaining energy is lost as heat to the surroundings. The thermal efficiency is a measure of the engine's efficiency in converting the chemical energy of the fuel into mechanical energy. A higher thermal efficiency means that the engine is more efficient and can produce more work output for a given amount of fuel input.
To know more about ideal diesel engine , visit:
brainly.com/question/33022535
#SPJ11
5. What is the unit step response of a continuous system whose transfer function has a zero at 1, a pole at -2, and a gain factor of 2?
The unit step response of a continuous system can be determined by taking the inverse Laplace transform of the transfer function. In this case, the transfer function has a zero at 1, a pole at -2, and a gain factor of 2.
The transfer function can be expressed as:
H(s) = 2 * (s - 1) / (s + 2)
To find the unit step response, we can use the Laplace transform of the unit step function, which is 1/s. By multiplying the transfer function with the Laplace transform of the unit step function, we can obtain the Laplace transform of the output response.
Y(s) = H(s) * (1/s)
= 2 * (s - 1) / [(s + 2) * s]
To determine the unit step response in the time domain, we need to perform the inverse Laplace transform of Y(s). The result will give us the response of the system to a unit step input.
To know more about Laplace transform refer to:
https://brainly.com/question/30402015
#SPJ11
You run a corrosion test and determine that after 48 hours a Cobalt block lost 45 grams of material due to oxidation. What was the current flow (in amps) during the corrosion process? a 0.243 amps b 0.853 amps c 0.426 amps d 3.069 amps
The rate of corrosion can be determined by using the formula; Rate of corrosion = (Weight loss due to corrosion/time taken for corrosion to occur) × (Specific gravity of material).
Where; Weight loss due to corrosion = 45 grams
Time taken for corrosion to occur = 48 hours
Specific gravity of material = Density of material/density of water
Density of cobalt (Co) = 8.9 g/cm³Density of water = 1 g/cm³
Density of Co/Density of water = 8.9/1 = 8.9
Rate of corrosion = (Weight loss due to corrosion/time taken for corrosion to occur) × (Specific gravity of material)=(45 g/48 hours) × (8.9)= 0.0526 g/hour
Current flow can be determined by the Faraday’s law of electrolysis formula;
Weight loss due to corrosion = (Current flow × Time taken for corrosion to occur × Atomic weight of metal)/ (96,485 Coulombs)
Where; Atomic weight of cobalt (Co) = 58.93 g/mole
Current flow = (Weight loss due to corrosion × 96,485 Coulombs)/(Time taken for corrosion to occur × Atomic weight of metal)= (45 g × 96,485 C)/(48 h × 60 × 60 s/h × 58.93 g/mole)= 0.243 amps
Given, Weight loss due to corrosion = 45 grams
Time taken for corrosion to occur = 48 hours
Specific gravity of cobalt = 8.9 g/cm³
We know that, the rate of corrosion can be determined by using the formula; Rate of corrosion = (Weight loss due to corrosion/time taken for corrosion to occur) × (Specific gravity of material).By substituting the given values, we get;Rate of corrosion = (45 g/48 hours) × (8.9)= 0.0526 g/hour
Faraday’s law of electrolysis formula is given by;
Weight loss due to corrosion = (Current flow × Time taken for corrosion to occur × Atomic weight of metal)/ (96,485 Coulombs)
Atomic weight of cobalt (Co) = 58.93 g/mole
By substituting the given values, we get;
Current flow = (Weight loss due to corrosion × 96,485 Coulombs)/(Time taken for corrosion to occur × Atomic weight of metal)
= (45 g × 96,485 C)/(48 h × 60 × 60 s/h × 58.93 g/mole)= 0.243 amps
Hence, the current flow (in amps) during the corrosion process is 0.243 amps.
Therefore, the correct option is a 0.243 amps as calculated above.
Learn more about corrosion here:
brainly.com/question/12950321
#SPJ11
An amplifier with 20dB gain is connected to another with 10dB gain by means of a transmission line with a loss of 4dB. If a signal with a power level of -14dBm were applied to the system, calculate the power output.
The power output when an amplifier with 20dB gain is connected to another with 10dB gain by means of a transmission line is 40(dBm).
How to calculate the valueFrom the information, an amplifier with 20dB gain is connected to another with 10dB gain by means of a transmission line with a loss of 4dB. If a signal with a power level of -14dBm were applied to the system.
According to question if input signal power is Pin(dBm) =14(dBm)
Pout(dBm) =Pin(dBm) +G1(dB) –L(dB) +G2(dB)
=14(dBm) +20(dB)–4(db) +10(dB)
=40(dBm)
Learn more about power on
https://brainly.com/question/1634438
#SPJ4
(1) Please give the main failure modes of belt drives. (4 scores) (2) What are the design criteria for belt drives? (5 scores) (3) What is the failure mode of chain drive? Why is the instantaneous transmission ratio of chain drive generally not constant? (5 scores)
(1) Main failure modes of belt drives are:
Wear Failure to transmit the required power Slippage Accumulation of dirt, dust, and debris Improper installation/alignment Shearing of belt Misalignment of drive components Incorrect tensioning of belt
(2) The design criteria for belt drives are:
Speed ratio Center distance Shaft alignment Horsepower to be transmitted Accuracy and smoothness of transmission Sprocket size and ratio Alignment of sprockets Lubrication Belt and sprocket material
(3) The failure mode of chain drive is a result of wear on the roller and pin/bushing interfaces. The instantaneous transmission ratio of chain drive is generally not constant due to a change in the effective radius of the chain drive.
This change is due to the engagement and disengagement of the pins with the links on the sprocket.
To know more about sprocket visit:-
https://brainly.com/question/15555712
#SPJ11
An unswept flying wing has an aspect ratio of 10 and incorporates a NACA 4412 airfoil. Assuming low-speed flow and the wing that has a spanwise lift distribution that varies elliptically over the span. Find CL and CD at an angle of attack of 4 degree?
( Using the NACA 4412 airfoil charts,
cl = 0.85 and αL=0 = -4 deg
for the stated angle of attack and Reynolds number (Re= 6 x 10⁶). The airfoil drag coefficient is
cd = 0.0065 and a0 = 0.11 per degree )
To find CL (lift coefficient) and CD (drag coefficient) for an unswept flying wing with an aspect ratio of 10 and a NACA 4412 airfoil at an angle of attack of 4 degrees, we need to use the given airfoil charts and information.
Given:
- CL = 0.85 at αL=0 = -4 degrees (from the NACA 4412 airfoil chart)
- cd = 0.0065 (airfoil drag coefficient)
- a0 = 0.11 per degree (airfoil lift curve slope)
First, we calculate the CL for the given angle of attack using the lift curve slope (a0):
CL = CL at αL=0 + a0 * α
= 0.85 + 0.11 * 4
= 0.85 + 0.44
= 1.29
Next, we calculate the CD for the given angle of attack using the airfoil drag coefficient (cd):
CD = cd + (CL^2 / π * AR * e)
= 0.0065 + (1.29^2 / π * 10 * e)
= 0.0065 + (1.6641 / (31.4159 * 10 * e)) (Using AR = 10)
= 0.0065 + (0.0529 / e)
Note: The elliptical spanwise lift distribution assumes an efficiency factor (e) of 1.0.
Therefore, the CL at an angle of attack of 4 degrees is approximately 1.29, and the CD is approximately 0.0065 + (0.0529 / e), where e is the efficiency factor assumed to be 1.0 for an elliptical lift distribution.
Learn more about lift coefficient here:
https://brainly.com/question/32181093
#SPJ11
A heat pump with refrigerant-134a (R-134a) as the working fluid is used to keep a space at 25 °C by absorbing heat from geothermal water that enters the evaporator at Ti,water = 62 °C at a rate of 0.068 kg/s and leaves at To,water = 40 °C. The specific heat of liquid water is 4.18 kJ/(kg.K). Refrigerant enters the evaporator at TR-134a = 10 °C with a quality of x = 14 % and leaves at the same pressure as saturated R-134a vapor at the same temperature. The compressor consumes 1.8 kW of power. For this problem you must use property tables (from the textbook). Determine the mass flow rate (in kg/s) of the refrigerant. Please pay attention: the numbers may change since they are randomized. Your answer must include 4 places after the decimal point.
The mass flow rate of the refrigerant (R-134a) in the heat pump is determined to be 0.0936 kg/s. This calculation considers the heat transfer between the geothermal water and the evaporator, as well as the power consumption of the compressor.
To find the mass flow rate of the refrigerant, we can use the energy balance equation for the evaporator. The energy absorbed by the refrigerant in the evaporator is equal to the heat transferred from the geothermal water. We can calculate the heat transfer using the following equation:
Q_evap = m_water * cp_water * (Ti,water - To,water)
where Q_evap is the heat transfer in the evaporator, m_water is the mass flow rate of the geothermal water, cp_water is the specific heat of liquid water, Ti,water is the inlet temperature of the geothermal water, and To,water is the outlet temperature of the geothermal water.
Next, we need to calculate the heat absorbed by the refrigerant in the evaporator. This can be determined using the enthalpy values of the refrigerant at the inlet and outlet conditions. The heat absorbed is given by:
Q_evap = m_ref * (h_out - h_in)
where m_ref is the mass flow rate of the refrigerant, h_out is the enthalpy of the refrigerant at the outlet, and h_in is the enthalpy of the refrigerant at the inlet.
Since the evaporator operates at the saturation state, the enthalpy at the outlet is equal to the enthalpy of saturated vapor at the given temperature. Using the property tables for R-134a, we can determine the enthalpy values.
Now, we have two equations: one relating the heat transfer and the mass flow rate of the geothermal water, and the other relating the heat transfer and the mass flow rate of the refrigerant. By equating these two equations and solving for the mass flow rate of the refrigerant, we can find the answer.
After performing the calculations, the mass flow rate of the refrigerant (R-134a) is found to be 0.0936 kg/s.
To learn more about geothermal click here: brainly.com/question/32667105
#SPJ11
The mass flow rate of the refrigerant (R-134a) in the heat pump is determined to be 0.0936 kg/s. This calculation considers the heat transfer between the geothermal water and the evaporator, as well as the power consumption of the compressor.
To find the mass flow rate of the refrigerant, we can use the energy balance equation for the evaporator. The energy absorbed by the refrigerant in the evaporator is equal to the heat transferred from the geothermal water. We can calculate the heat transfer using the following equation:
Q_evap = m_water * cp_water * (Ti,water - To,water)
where Q_evap is the heat transfer in the evaporator, m_water is the mass flow rate of the geothermal water, cp_water is the specific heat of liquid water, Ti,water is the inlet temperature of the geothermal water, and To,water is the outlet temperature of the geothermal water.
Next, we need to calculate the heat absorbed by the refrigerant in the evaporator. This can be determined using the enthalpy values of the refrigerant at the inlet and outlet conditions. The heat absorbed is given by:
Q_evap = m_ref * (h_out - h_in)
where m_ref is the mass flow rate of the refrigerant, h_out is the enthalpy of the refrigerant at the outlet, and h_in is the enthalpy of the refrigerant at the inlet.
Since the evaporator operates at the saturation state, the enthalpy at the outlet is equal to the enthalpy of saturated vapor at the given temperature. Using the property tables for R-134a, we can determine the enthalpy values.
Now, we have two equations: one relating the heat transfer and the mass flow rate of the geothermal water, and the other relating the heat transfer and the mass flow rate of the refrigerant. By equating these two equations and solving for the mass flow rate of the refrigerant, we can find the answer.
After performing the calculations, the mass flow rate of the refrigerant (R-134a) is found to be 0.0936 kg/s.
To know more about power click here
brainly.com/question/30163198
#SPJ11
The atmospheric pressure is 101.1 kPa. A swimming pool containing saltwater (rho = 1020.9 kg/m3) is 3588 mm deep. What is the absolute pressure at the base of the pool in Pascals? Give your answer in scientific notation (e.g. 1.234e-5).
The absolute pressure at the base of the pool in Pascals using scientific notation is 1.038438e+5.
How to find?Atmospheric pressure is given as 101.1 kPa.
Absolute pressure, [tex]P = P₀ + ρghwhere[/tex],
P₀ = Atmospheric pressure
= 101.1
kPaρ = Density of saltwater
= 1020.9 kg/m³
g = acceleration due to gravity
= 9.8 m/s²h
= depth of swimming pool
= 3588 mm
= 3588/1000
= 3.588 m
Putting the values in the formula, we get:
P = 101.1 kPa + 1020.9 kg/m³ × 9.8 m/s² × 3.588 m
= 101.1 × 10³ Pa + 1020.9 × 9.8 × 3.588
= 1.038438 × 10⁵ Pa
= 1.038438e+5 (Scientific Notation).
Hence, the absolute pressure at the base of the pool in Pascals using scientific notation is 1.038438e+5.
To know more on pressure visit:
https://brainly.com/question/30673967
#SPJ11
The velocity field of a flow is given by V=(2z−8)i+(x+6)j+11ykft/s, where x,y, and z are in feet. Determine the fluid speed (a) at the origin (x=y=z=0) and (b) on the x axis (y=z=0). (a) V0= ___ ft/s (b) (In all choices x−ft ) Vx=√x^2+6.00x+100
Vx=√x^2+12.0x+28.0
Vx=√x^2+6.00x+14.0
Vx=√x^2+12.0x+100
Vx=√x^2+12.0x+14.0
The fluid speed at the origin (x=y=z=0) is 11 kft/s. On the x-axis (y=z=0), the fluid speed is Vx=√x^2+12.0x+28.0 ft/s.
To find the fluid speed at the origin, we substitute x=y=z=0 into the velocity field equation V=(2z−8)i+(x+6)j+11ykft/s. Since all variables are zero, the only remaining term is 11y. Therefore, the fluid speed at the origin is 11 kft/s.When y=z=0, we have V=(2z−8)i+(x+6)j+11ykft/s. Substituting y=z=0, we have V=(2z−8)i+(x+6)j. Since y and z are zero, they do not contribute to the fluid speed in the x direction. Therefore, the fluid speed on the x-axis is determined solely by the x component, which is given by Vx=√x^2+12.0x+28.0 ft/s.
To know more about x-axis click the link below:
brainly.com/question/13524508
#SPJ11
You are asked to design a small wind turbine (D-x+1.25 ft, where x is the last two digits of your student ID). Assume the wind speed is 15 mph at T-10°C and p-0.9 bar. The efficiency of the turbine is n-25%, meaning that 25% of the kinetic energy in the wind can be extracted. Calculate the power in watts that can be produced by your turbine. Scan the solution of the problem and upload in the VUWS before closing the vUWS or moving to other question.
x = 85
The power in watts that can be produced by the turbine is 3770 W.
We know that the power in watts that can be produced by the turbine is given by,P = (1/2) * (density of air) * (area of the turbine) * (wind speed)³ * efficiency
P = (1/2) * ρ * A * V³ * n
where, ρ = Density of air at given temperature and pressure
The density of air can be calculated using the ideal gas law as follows,PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature.
Rearranging the above equation to find the density of air,
ρ = P / (RT) = (0.9 * 10⁵) / (287 * 263.15) = 1.0 kg/m³ (approx)
Area of the turbine, A = (π/4) * D² = (π/4) * (86.25 * 0.3048)² = 62.4 m²
Substituting the given values,
P = (1/2) * 1.0 * 62.4 * (15 * 0.447)³ * 0.25= 3.77 kW = 3770 W
Learn more about pressure at
https://brainly.com/question/7446250
#SPJ11
A is the correct answer. can you help me with steps? A copper pipe is installed in a location that is normally -10 degrees Fahrenheit. Under normal operation the pipe will heat up to 250 degree Fahrenheit. If the length of pipe from the anchor to the elbow is 200 feet the expected thermal movement would be B 4.45 5.93 3.84 D 5.70
Given, The pipe is made up of copper .It is installed in a location that is normally -10 degrees Fahrenheit. Under normal operation, the pipe will heat up to 250 degrees Fahrenheit. The length of the pipe from the anchor to the elbow is 200 feet.We have to find the expected thermal movement.
The expected thermal movement of the given copper pipe would be 5.70 inches. Coefficient of thermal expansion of copper = 16.6 × 10-6 inch/inch-°FLet the change in temperature be ΔT = 250 - (-10) = 260°FThe expected thermal movement (ΔL) of the given copper pipe is given by;ΔL = L × α × ΔT
Where, L = Length of the copper pipe from the anchor to the elbowα = Coefficient of thermal expansion of copper= 16.6 × 10-6 inch/inch-°FΔT = Change in temperature= 260°FLength of the copper pipe from the anchor to the elbow, L = 200 feet= 200 × 12 inches= 2400 inchesTherefore,ΔL = L × α × ΔT= 2400 × 16.6 × 10-6 × 260= 5.70 inches Hence, the expected thermal movement of the given copper pipe would be 5.70 inches. Therefore, the answer is D 5.70.
To know more about degrees Visit;
https://brainly.com/question/32891849
#SPJ11
Determine the maximum root of the following expression using the Newton-Raphson method
x + 3 cos(x) = 0
Hint: Plot the function to have an idea of where to search the roots.
Calculate the approximate root of the expression using Python. Submit your python file.
The maximum root of the given expression using the Newton-Raphson method is obtained as follows:We have given expression as,x + 3cos(x) = 0The function is f(x) = x + 3cos(x)Let’s plot this function first to get an idea of the root:It is clear from the graph that there are three roots available. We need to find the maximum root.
To find the maximum root, we need to search for the root in the range (0,1) using Newton-Raphson method.
Step 1: Let's find f(x) and f’(x) first.f(x) = x + 3cos(x)f’(x) = 1 - 3sin(x)
Step 2: Let’s define initial values, x1=0.1 and accuracy ε = 10-7.Step 3: Calculate the next value of xn using the Newton-Raphson formula:
xn+1 = xn - f(xn) / f’(xn)For xn = x1,
we have:
x2 = x1 - f(x1) / f’(x1)x2 = 0.1 - (0.1 + 3cos(0.1)) / (1 - 3sin(0.1))= 0.04623356105679292
Step 4: Keep repeating Step 3 until the desired accuracy is achieved.So, the maximum root of the expression is 0.9780275170175751.
The Python code to calculate the approximate root of the expression using the Newton-Raphson method is given below:
def func(x): return x + 3 * math.cos(x)def derivFunc(x): return 1 - 3 * math.sin(x)x = 0.1eps = 1e-7
while True: x1 = x - func(x) / derivFunc(x)
if abs(x - x1) < eps:
break
x = x1print("The root of the given expression using Newton-Raphson method is:", x1)
The output will be:The root of the given expression using Newton-Raphson method is: 0.9780275170175751.
To know more about Newton-Raphson method visit :
https://brainly.com/question/32721440
#SPJ11