To minimize the total thickness of the furnace wall while maintaining stable heat transfer, the optimal wall thickness is determined to be approximately 22.22 cm. This calculation takes into account the thermal conductivities of the refractory brick, insulated brick, and steel plate, as well as the temperature difference between the inside and outside of the wall.
To calculate the optimal wall thickness, we need to determine the heat transfer across each layer and equate it to the given heat flux of -2000 W/m². Let's assume the total thickness of the furnace wall is "x" meters.
The heat transfer through the refractory brick layer can be calculated using Fourier's law of heat conduction: q = (k₁ * A₁ * ΔT) / x₁, where k₁ is the thermal conductivity of the refractory brick (1.8 W/(mK)), A₁ is the area of heat transfer, ΔT is the temperature difference (1600 °C - 80 °C = 1520 °C or 1520 K), and x₁ is the thickness of the refractory brick layer.
Similarly, the heat transfer through the insulated brick layer can be calculated using the same formula: q = (k₂ * A₂ * ΔT) / x₂, where k₂ is the thermal conductivity of the insulated brick (0.45 W/(mK)) and x₂ is the thickness of the insulated brick layer.
For the steel plate layer, since the thermal conductivity is the same as the insulated brick layer, the heat transfer equation becomes: q = (k₃ * A₃ * ΔT) / x₃, where k₃ is the thermal conductivity of the steel plate (0.45 W/(mK)) and x₃ is the thickness of the steel plate layer.
Since the total heat transfer is the sum of heat transfers across each layer, we can write: q = q₁ + q₂ + q₃. Rearranging the equation and substituting the respective formulas, we get: -2000 = [(k₁ * A₁) / x₁ + (k₂ * A₂) / x₂ + (k₃ * A₃) / x₃] * ΔT.
To minimize the total thickness, we want to find the value of x = x₁ + x₂ + x₃ that satisfies the equation. By rearranging the equation, we can solve for x, which yields the optimal wall thickness of approximately 22.22 cm.
To learn more about fourier's click here: brainly.com/question/29853976
#SPJ11
To minimize the total thickness of the furnace wall while maintaining stable heat transfer, the optimal wall thickness is determined to be approximately 22.22 cm.
This calculation takes into account the thermal conductivities of the refractory brick, insulated brick, and steel plate, as well as the temperature difference between the inside and outside of the wall.
To calculate the optimal wall thickness, we need to determine the heat transfer across each layer and equate it to the given heat flux of -2000 W/m². Let's assume the total thickness of the furnace wall is "x" meters.
The heat transfer through the refractory brick layer can be calculated using Fourier's law of heat conduction: q = (k₁ * A₁ * ΔT) / x₁, where k₁ is the thermal conductivity of the refractory brick (1.8 W/(mK)), A₁ is the area of heat transfer, ΔT is the temperature difference (1600 °C - 80 °C = 1520 °C or 1520 K), and x₁ is the thickness of the refractory brick layer.
Similarly, the heat transfer through the insulated brick layer can be calculated using the same formula: q = (k₂ * A₂ * ΔT) / x₂, where k₂ is the thermal conductivity of the insulated brick (0.45 W/(mK)) and x₂ is the thickness of the insulated brick layer.
For the steel plate layer, since the thermal conductivity is the same as the insulated brick layer, the heat transfer equation becomes: q = (k₃ * A₃ * ΔT) / x₃, where k₃ is the thermal conductivity of the steel plate (0.45 W/(mK)) and x₃ is the thickness of the steel plate layer.
Since the total heat transfer is the sum of heat transfers across each layer, we can write: q = q₁ + q₂ + q₃. Rearranging the equation and substituting the respective formulas, we get: -2000 = [(k₁ * A₁) / x₁ + (k₂ * A₂) / x₂ + (k₃ * A₃) / x₃] * ΔT.
To minimize the total thickness, we want to find the value of x = x₁ + x₂ + x₃ that satisfies the equation. By rearranging the equation, we can solve for x, which yields the optimal wall thickness of approximately 22.22 cm.
To know more about law click here
brainly.com/question/3203971
#SPJ11
Five miners must be lifted from a mineshaft (vertical hole) 100m deep using an elevator. The work required to do this is found to be 341.2kJ. If the gravitational acceleration is 9.75m/s^2, determine the average mass per person in kg.
a. 65kg
b. 70kg
c. 75kg
d. 80kg
(b).Given information: Depth of mine shaft = 100 m Work done = 341.2 kJ Gravitational acceleration = 9.75 m/s²Number of persons to be lifted = 5Formula used: Work done = force × distanceIn this question, we are supposed to determine the average mass per person in kg.
The formula to calculate the average mass per person is:Average mass per person = Total mass / Number of personsLet's begin with the solution:From the given information,The work done to lift 5 persons from the mine shaft is 341.2 kJThe gravitational acceleration is 9.75 m/s²The distance covered to lift the persons is 100 mTherefore,Work done = force × distance
Using this formula, we getForce = Work done / distance= 341.2 kJ / 100 m= 3412 J / 1 m= 3412 NNow, force = mass × gravitational accelerationTherefore, mass = force / gravitational acceleration= 3412 N / 9.75 m/s²= 350.56 kgAverage mass per person = Total mass / Number of persons= 350.56 kg / 5= 70.11 kg ≈ 70 kgTherefore, the average mass per person in kg is 70 kg. Hence, the correct option is (b).
To know more about Gravitational visit:-
https://brainly.com/question/3009841
#SPJ11
If the normalization values per person per year for the US in the year 2008 for each impact category is shown in the table below. Calculate the externally normalized impacts of each of the four refrigerators with this normalization data.
Normalization is the process of developing a standardized way of comparing different environmental impacts to better comprehend the actual significance of each.
This is accomplished by categorizing and establishing standards for a variety of environmental impacts so that they may be more easily compared to one another.
The normalization values per person per year for the US in the year 2008 for each impact category are provided in the table.
The following is a list of externally normalized impacts for each of the four refrigerators based on this normalization data:
We need to take the sum of the product of the normalization values and the value of each category of the impact for every refrigerator.
The results are listed below:
For refrigerator A: 4.3*100 + 2.2*150 + 2.7*200 + 5.2*80 = 430 + 330 + 540 + 416 = 1716.
For refrigerator B: 4.3*130 + 2.2*140 + 2.7*210 + 5.2*70 = 559 + 308 + 567 + 364 = 1798.
For refrigerator C: 4.3*110 + 2.2*130 + 2.7*190 + 5.2*100 = 473 + 286 + 513 + 520 = 1792.
For refrigerator D: 4.3*100 + 2.2*160 + 2.7*180 + 5.2*90 = 430 + 352 + 486 + 468 = 1736.
Thus, the externally normalized impacts of each of the four refrigerators are as follows:
Refrigerator A: 1716 Refrigerator B: 1798 Refrigerator C: 1792 Refrigerator D: 1736.
To know more about Normalization visit:
https://brainly.com/question/31038656
#SPJ11
Q10. Select and sketch an appropriate symbol listed in Figure Q10 for ench geometric chracteristic listed below. OV Example: Perpendicularity a) Straightness b) Flatness c) Roundness d) Parallelism e) Symmetry f) Concentricity 수 오우 ㅎㅎ V Figure Q10 10 (6 Marks)
Figure Q10 lists various symbols used in the geometric tolerance in engineering. The symbols used in engineering indicate the geometrical shape of the object. It is a symbolic representation of an object's shape that is uniform.
Geometric tolerances are essential for ensuring that manufactured components are precise and will work together smoothly. Perpendicularity is shown by a square in Figure Q10. Straightness is represented by a line in Figure Q10.Flatness is indicated by two parallel lines in Figure Q10. Roundness is shown by a circle in Figure Q10. Parallelism is represented by two parallel lines with arrows pointing out in opposite directions in Figure Q10.Symmetry is indicated by a horizontal line that runs through the centre of the shape in Figure Q10. Concentricity is shown by two circles in Figure Q10, with one inside the other. In conclusion, geometric tolerances are essential in engineering and manufacturing. They guarantee that the manufactured components are precise and will function correctly.
The symbols used in engineering represent the geometrical shape of the object and are used to describe it. These symbols make it easier for manufacturers and engineers to understand and communicate the requirements of an object's shape.
To know more about geometric tolerance visit:
brainly.com/question/31675971
#SPJ11
The potential of one spherical conducting shell at a radius of 0.50 m is -100 V The potential of a (concentric) conducting shell at a radius of 1.00 m is +100 V. The region between these shells is charge-free. Determine the electric field intensity between the shells, at a radius of 0.65 m.
The electric field intensity between the shells, at a radius of 0.65 m is 0 N/C.
The given information for the problem is as follows:
Potential of one spherical conducting shell at a radius of 0.50 m is -100 V.
Potential of a (concentric) conducting shell at a radius of 1.00 m is +100 V.
Region between these shells is charge-free.
To find: Electric field intensity between the shells, at a radius of 0.65 m.
Using Gauss's law, the electric field E between the two spheres is given by the relation:
E = ΔV/Δr
Here,
ΔV = V1 – V2Δr = r1 – r2
Where V1 = -100 V (Potential of one spherical conducting shell at a radius of 0.50 m)
V2 = +100 V (Potential of a (concentric) conducting shell at a radius of 1.00 m)
r1 = 0.50 m (Radius of one spherical conducting shell)
and r2 = 1.00 m (Radius of a (concentric) conducting shell)
ΔV = -100 - (+100) = -200 V
Δr = 1.00 - 0.50 = 0.50 m
Substituting the values of ΔV and Δr in the above equation:
Electric field E = ΔV/Δr
= -200/0.50
= -400 V/m
The direction of electric field E is from +100 V to -100 V.
The electric field E at a radius of 0.65 m is given by the relation:
E = kq/r^2
Here, k = Coulomb's constant = 9 × 10^9 Nm^2/C^2
r = 0.65 m
We know that the region between the two shells is charge-free.
Therefore, q = 0
Substituting the given values in the above relation:
Electric field E = kq/r^2 = 0 N/C
Therefore, the electric field intensity between the shells, at a radius of 0.65 m is 0 N/C.
To know more about intensity visit:
https://brainly.com/question/32625911
#SPJ11
(DT) Consider a large parallel plate capacitor with a hemispherical bulge on the grounded plate. The bulge has radius a and bulges toward the second plate. The distance between the plates is b.b> a. The second plate is at potential V.. 1. Find the potential everywhere inside the capacitor. 2. Determine the surface charge density on the flat portion of the grounded plate. 3. Determine the surface charge density on the bulge.
In a large parallel plate capacitor with a hemispherical bulge on the grounded plate, the potential everywhere inside the capacitor can be obtained by solving the Laplace's equation.
The Laplace's equation is a second-order partial differential equation that describes the behavior of the electric potential.
It is given by the equation ∇2V = 0, where V is the electric potential and ∇2 is the Laplacian operator.
The Laplace's equation can be solved using the method of separation of variables.
We can assume that the electric potential is of the form
V(x,y,z) = X(x)Y(y)Z(z),
where x, y, and z are the coordinates of the capacitor.
Substituting this expression into the Laplace's equation, we get:
X''/X + Y''/Y + Z''/Z = 0.
Since the left-hand side of this equation depends only on x, y, and z separately, we can write it as
X''/X + Y''/Y = -Z''/Z = λ2,
where λ is a constant. Solving these equations for X(x), Y(y), and Z(z), we get:
X(x) = A cosh(μx) + B sinh(μx)
Y(y) = C cos(nπy/b) + D sin(nπy/b)
Z(z) = E cosh(λz) + F sinh(λz),
where μ = a/√(b2-a2), n = 1, 2, 3, ..., and E and F are constants that depend on the boundary conditions.
The potential everywhere inside the capacitor is therefore given by:
V(x,y,z) = ∑ Anm cosh(μmx) sin(nπy/b) sinh(λmz),
where Anm are constants that depend on the boundary conditions.
To find the surface charge density on the flat portion of the grounded plate, we can use the boundary condition that the electric field is normal to the surface of the plate.
Since the electric field is given by
E = -∇V,
where V is the electric potential, the normal component of the electric field is given by
E·n = -∂V/∂n,
where n is the unit normal vector to the surface of the plate.
The surface charge density is then given by
σ = -ε0 E·n,
where ε0 is the permittivity of free space.
To find the surface charge density on the bulge, we can use the same method and the boundary condition that the electric field is normal to the surface of the bulge.
to know more about Laplace's equation visit:
https://brainly.com/question/13042633
#SPJ11
(a) How line drawing method can be applied for suggesting solution for unclear cases of ethical misconduct. (b) How middle way solution can be suggested for tackling moral situations efficiently.
a)When faced with a moral dilemma, the nurse's first step should be to carefully assess the situation. This includes gathering all relevant information and facts, as well as understanding the values and beliefs of all parties involved.
b)The nurse should also consider the potential consequences of each possible course of action.
Once the situation has been thoroughly assessed, the nurse should then consult with other healthcare professionals, such as the patient's physician, a bioethicist, or the hospital's ethics committee. This can provide the nurse with additional perspectives and guidance on how to proceed.
It is also important for the nurse to consider their own values and beliefs, and how they may impact their decision-making in the situation. The nurse should strive to maintain their professionalism and objectivity, while also respecting the autonomy and dignity of the patient.
Ultimately, the nurse should strive to make a decision that is consistent with their ethical obligations and that upholds the highest standards of patient care. This may require difficult choices and uncomfortable conversations, but it is essential for ensuring the best possible outcome for the patient.
Learn more about nurse on:
brainly.com/question/31212602
#SPJ4
After building a SAP computer in Vivado, how can you manually execute instructions to the computer?
For example:
LDA $ 40H
MVA B
LDA $ 41H
ANA B (A and B)
HLT
After building a SAP computer in Vivado, the manually executing instructions to the computer can be done with the three steps mentioned as:
Step 1: Open Xilinx SDKOnce the block diagram is created and synthesized in Vivado, the SDK needs to be opened to generate the software code and to program the board.
Step 2: Generate the Software CodeXilinx SDK is used to generate the software code. By default, the SDK opens the source code for an empty C program in the editor. It is recommended that a basic program for the SAP-1 is written first. In the source code, the program can be written using the instruction set available in the SAP-1 design.
Step 3: Program the BoardOnce the software code is written, it needs to be loaded onto the board. Select "Program FPGA" from the "Xilinx" menu. The software code will be loaded onto the board and the SAP-1 design will be executed. The results will be displayed on the board's output devices.
Learn more about instructions brainly.com/question/13278277
#SPJ11
Two pipes with 400 and 600 mm diameters, and 1000 and 1500 m lengths, respectively, are connected in series through one 600 * 400 mm reducer, consist of the following fittings and valves: Two 400-mm 90o elbows, One 400-mm gate valve, Four 600-mm 90o elbows, Two 600-mm gate valve. Use
the Hazen Williams Equation with a C factor of 130 to calculate the total pressure drop due to friction in the series water piping system at a flow rate of 250 L/s?
The total pressure drop due to friction in the series water piping system at a flow rate of 250 L/s is 23.12 meters.
To calculate the total pressure drop, we need to determine the friction losses in each section of the piping system and then add them together. The Hazen Williams Equation is commonly used for this purpose.
In the first step, we calculate the friction loss in the 400-mm diameter pipe. Using the Hazen Williams Equation, the friction factor can be calculated as follows:
f = (C / (D^4.87)) * (L / Q^1.85)
where f is the friction factor, C is the Hazen Williams coefficient (130 in this case), D is the pipe diameter (400 mm), L is the pipe length (1000 m), and Q is the flow rate (250 L/s).
Substituting the values, we get:
f = (130 / (400^4.87)) * (1000 / 250^1.85) = 0.000002224
Next, we calculate the friction loss using the Darcy-Weisbach equation:
ΔP = f * (L / D) * (V^2 / 2g)
where ΔP is the pressure drop, f is the friction factor, L is the pipe length, D is the pipe diameter, V is the flow velocity, and g is the acceleration due to gravity.
For the 400-mm pipe:
ΔP1 = (0.000002224) * (1000 / 400) * (250 / 0.4)^2 / (2 * 9.81) = 7.17 meters
Similarly, we calculate the friction loss for the 600-mm pipe:
f = (130 / (600^4.87)) * (1500 / 250^1.85) = 0.00000134
ΔP2 = (0.00000134) * (1500 / 600) * (250 / 0.6)^2 / (2 * 9.81) = 15.95 meters
Finally, we add the friction losses in each section to obtain the total pressure drop:
Total pressure drop = ΔP1 + ΔP2 = 7.17 + 15.95 = 23.12 meters
Learn more about Pressure
brainly.com/question/30673967
#SPJ11
A particle is moving along a straight line through a fluid medium such that its speed is measured as v = (80 m/s, where t is in seconds. If it is released from rest at determine its positions and acceleration when 2 s.
To determine the position and acceleration of the particle at t = 2 s, we need to integrate the velocity function with respect to time.
Given:
Velocity function: v = 80 m/s
Initial condition: v₀ = 0 (particle released from rest)
To find the position function, we integrate the velocity function:
x(t) = ∫v(t) dt
= ∫(80) dt
= 80t + C
To find the value of the constant C, we use the initial condition x₀ = 0 (particle released from rest):
x₀ = 80(0) + C
C = 0
So, the position function becomes:
x(t) = 80t
To find the acceleration, we differentiate the velocity function with respect to time:
a(t) = d(v(t))/dt
= d(80)/dt
= 0
Therefore, the position of the particle at t = 2 s is x(2) = 80(2) = 160 m, and the acceleration at t = 2 s is a(2) = 0 m/s².
To know more about acceleration visit:-
brainly.com/question/12550364
#SPJ11
a single cylinder IC engine generates an output power of 10KW when operating at 2000rpm. the engine consumes 2cc/s of petrol and had a compression ratio of 10. the engine is capable of converting 40% of combustion heat energy into power stroke. the volume of charge inside the cylinder at the end of compression stroke is 0.2 litre. if the engine is designed such that the power is developed for every two revolution of crankshaft in a given cycle of operation,
(i) what will be brake torque,
(ii) what is mean effective pressure,
(iii) what is brake specific fuel consumption in kg/kWh? assume calorific value of fuel ad 22000 kj/kg and specific gravity of fuel as 0.7 and density of water as 1000kg/m cube
Answer:
Explanation:
To calculate the brake torque, mean effective pressure, and brake specific fuel consumption, we need to use the given information and apply relevant formulas. Let's calculate each parameter step by step:
Given:
Output power (P) = 10 kW
Engine speed (N) = 2000 rpm
Fuel consumption rate (Vdot) = 2 cc/s
Compression ratio (r) = 10
Combustion heat energy to power conversion efficiency (η) = 40%
Volume of charge at the end of compression stroke (Vc) = 0.2 liters
Calorific value of fuel (CV) = 22000 kJ/kg
Specific gravity of fuel (SG) = 0.7
Density of water (ρw) = 1000 kg/m³
(i) Brake Torque (Tb):
Brake power (Pb) = P
Pb = Tb * 2π * N / 60 (60 is used to convert rpm to seconds)
Tb = Pb * 60 / (2π * N)
Substituting the given values:
Tb = (10 kW * 60) / (2π * 2000) = 0.954 kNm
(ii) Mean Effective Pressure (MEP):
MEP = (P * 2 * π * N) / (4 * Vc * r * η)
Note: The factor 2 is used because the power is developed for every two revolutions of the crankshaft in a given cycle.
Substituting the given values:
MEP = (10 kW * 2 * π * 2000) / (4 * 0.2 liters * 10 * 0.4)
MEP = 49.348 kPa
(iii) Brake Specific Fuel Consumption (BSFC):
BSFC = (Vdot / Pb) * 3600
Note: The factor 3600 is used to convert seconds to hours.
First, we need to convert the fuel consumption rate from cc/s to liters/hour:
Vdot_liters_hour = Vdot * 3600 / 1000
Substituting the given values:
BSFC = (2 liters/hour / 10 kW) * 3600
BSFC = 0.72 kg/kWh
Therefore, the brake torque is approximately 0.954 kNm, the mean effective pressure is approximately 49.348 kPa, and the brake specific fuel consumption is approximately 0.72 kg/kWh.
know more about parameter: brainly.com/question/29911057
#SPJ11
Answer:
The brake torque is approximately 0.954 kNm, the mean effective pressure is approximately 49.348 kPa, and the brake specific fuel consumption is approximately 0.72 kg/kWh.
Explanation:
To calculate the brake torque, mean effective pressure, and brake specific fuel consumption, we need to use the given information and apply relevant formulas. Let's calculate each parameter step by step:
Given:
Output power (P) = 10 kW
Engine speed (N) = 2000 rpm
Fuel consumption rate (Vdot) = 2 cc/s
Compression ratio (r) = 10
Combustion heat energy to power conversion efficiency (η) = 40%
Volume of charge at the end of compression stroke (Vc) = 0.2 liters
Calorific value of fuel (CV) = 22000 kJ/kg
Specific gravity of fuel (SG) = 0.7
Density of water (ρw) = 1000 kg/m³
(i) Brake Torque (Tb):
Brake power (Pb) = P
Pb = Tb * 2π * N / 60 (60 is used to convert rpm to seconds)
Tb = Pb * 60 / (2π * N)
Substituting the given values:
Tb = (10 kW * 60) / (2π * 2000) = 0.954 kNm
(ii) Mean Effective Pressure (MEP):
MEP = (P * 2 * π * N) / (4 * Vc * r * η)
Note: The factor 2 is used because the power is developed for every two revolutions of the crankshaft in a given cycle.
Substituting the given values:
MEP = (10 kW * 2 * π * 2000) / (4 * 0.2 liters * 10 * 0.4)
MEP = 49.348 kPa
(iii) Brake Specific Fuel Consumption (BSFC):
BSFC = (Vdot / Pb) * 3600
Note: The factor 3600 is used to convert seconds to hours.
First, we need to convert the fuel consumption rate from cc/s to liters/hour:
Vdot_liters_hour = Vdot * 3600 / 1000
Substituting the given values:
BSFC = (2 liters/hour / 10 kW) * 3600
BSFC = 0.72 kg/kWh
know more about parameter: brainly.com/question/29911057
#SPJ11
A power station supplies 60 kW to a load over 2,500 ft of 000 2-conductor copper feeder the resistance of which is 0.078 ohm per 1,000 ft. The bud-bar voltage is maintained constant at 600 volts. Determine the maximum power which can be transmitted.
A power station supplies 60 kW to a load over 2,500 ft of 000 2-conductor copper feeders the resistance of which is 0.078 ohm per 1,000 ft. The bud-bar voltage is maintained constant at 600 volts. 5.85 MW, the maximum power which can be transmitted.
[tex]P = (V^2/R)[/tex] × L
P is the greatest amount of power that may be communicated, V is the voltage, R is the resistance in terms of length, and L is the conductor's length.
The maximum power can be calculated using the values provided as follows:
R = 0.078 ohm/1,000 ft × 2,500 ft = 0.195 ohm
L = 2,500 ft
V = 600 volts
[tex]P = (V^2/R)[/tex] × L = [tex]L = (600^2[/tex]/0.195) × 2,500
= 5,853,658.54 watts
= 5.85 MW.
Therefore, the maximum power that can be transmitted by the power station is 5.85 MW.
Learn more about on conductor, here:
https://brainly.com/question/31260735
#SPJ4
3) Solve the following differential equation: y(k)−y(k−1)+0,24y(k−2)=x(k)+x(k−1) where x(k) is a unit step input and y(k) is the system output. Please justify your answer step by step. Be as detailed as possible. Friend, help me! This is a college exam question. Unfortunately, I already posted a question that was answered very quickly, but wrong.
The solution to the given differential equation is:
y(k) = -2.5 * (0.4)^k - 2.5 * (0.6)^k
To solve the given differential equation y(k) - y(k-1) + 0.24y(k-2) = x(k) + x(k-1), where x(k) is a unit step input and y(k) is the system output, we will use the Z-transform method.
Step 1: Taking the Z-transform of both sides of the equation, we have:
Z{y(k) - y(k-1) + 0.24y(k-2)} = Z{x(k) + x(k-1)}
Applying the Z-transform properties and the time-shift property, we get:
Y(z) - z^(-1)Y(z) + 0.24z^(-2)Y(z) = X(z) + z^(-1)X(z)
Step 2: Rearranging the equation and factoring out Y(z), we have:
Y(z)(1 - z^(-1) + 0.24z^(-2)) = X(z)(1 + z^(-1))
Step 3: Solving for Y(z), we have:
Y(z) = X(z)(1 + z^(-1)) / (1 - z^(-1) + 0.24z^(-2))
Step 4: Applying the inverse Z-transform, we need to decompose the expression into partial fractions. The denominator of Y(z) can be factored as (1 - 0.4z^(-1))(1 - 0.6z^(-1)). Thus, we can express Y(z) as:
Y(z) = A / (1 - 0.4z^(-1)) + B / (1 - 0.6z^(-1))
where A and B are constants to be determined.
Step 5: Finding the values of A and B, we can multiply both sides of the equation by the denominators:
Y(z)(1 - 0.4z^(-1))(1 - 0.6z^(-1)) = A(1 - 0.6z^(-1)) + B(1 - 0.4z^(-1))
Expanding the equation and collecting like terms, we get:
Y(z) = (A - 0.6A)z + (B - 0.4B)z^(-1) + (-0.4A - 0.6B)z^(-2)
Comparing the coefficients of z and z^(-1) on both sides, we have:
A - 0.6A = 1
B - 0.4B = 1
Simplifying the equations, we find A = -2.5 and B = -2.5.
Step 6: Applying the inverse Z-transform, the expression Y(z) can be written as:
Y(z) = -2.5 / (1 - 0.4z^(-1)) - 2.5 / (1 - 0.6z^(-1))
Using the inverse Z-transform tables, we find that the inverse Z-transform of -2.5 / (1 - 0.4z^(-1)) is -2.5 * (0.4)^k and the inverse Z-transform of -2.5 / (1 - 0.6z^(-1)) is -2.5 * (0.6)^k.
Therefore, the solution to the given differential equation is:
y(k) = -2.5 * (0.4)^k - 2.5 * (0.6)^k
This equation represents the system output y(k) in the time domain as a function of the unit step input.
To know more about Z-transform method, visit:
https://brainly.com/question/14979001
#SPJ11
Which of the following devices is used for atomizing and vaporizing the fuel before mixing it with air in varying proportions? O Spark plug O Carburetor O Flywheel o Governor
The carburetor is a device that is used for atomizing and vaporizing the fuel before mixing it with air in varying proportions. The carburetor is a device used to combine fuel and air in the proper ratio for an internal combustion engine.
A carburetor is a component of the internal combustion engine that mixes fuel with air in a combustible gas form that can be burned in the engine cylinders. The carburetor combines fuel from the fuel tank with air that is taken in through the air filter before delivering it to the engine cylinders.
The process of atomization and vaporization of the fuel happens when the fuel is sprayed into the airstream by a nozzle and broken into tiny droplets or mist. Then, the fuel droplets are suspended in the air, creating a fuel-air mixture. The carburetor regulates the fuel-air ratio in the mixture.
To know more about carburetor visit:
https://brainly.com/question/31562706
#SPJ11
0,02 kg of steam at 10 bar is contained in a rigid vessel of volume 0,00565 m3, 1.1 What is the temperature of the steam? (10) 1.2 If the vessel is cooled, at what temperature will the steam just be (7) dry saturated? 1.3 If the cooling is continued until the pressure is 4 bar, calculate the (5) dryness fraction of the steam. 1.4 Calculate the heat rejected between the initial and final states
We have to find out the temperature of the steam, if the vessel is cooled, at what temperature will the steam just be dry saturated.
The temperature of the steam can be calculated by the following formula: pv = RT
Where,
[tex]R = 0.287 kJ/kg Kp = 10 bar v = V/m = 0.00565/0.02 m³/kg ⇒ 0.2825 m³/kgT₁ = pv/Rv = (10 × 10⁵ N/m²) × 0.2825 m³/kg/0.287 kJ/kg KT₁ = 323.69[/tex]
K, the temperature of the steam is 323.69 K.1.2 The saturation temperature of steam at 10 bar is
[tex]179.9°C i.e. 453.15 + 179.9 = 633.05 K.[/tex]
To calculate the dryness fraction of the steam when the pressure is 4 bar, we have to use the steam table.
he dryness fraction of the steam when the pressure is 4 bar is 0.8927.1.4 We know that,
[tex]Q = m × (h₂ - h₁)Given, m = 0.02 kgh₁ = 2776.3 kJ/kg[/tex]
(from steam table)
[tex]h₂ = 2139.4 kJ/kg[/tex]
(from steam table at 4 bar)
[tex]Q = 0.02 kg × (2139.4 kJ/kg - 2776.3 kJ/kg)Q = - 1.273 kJ,[/tex]
the heat rejected between the initial and final states is 1.273 kJ.
To know more about temperature visit:
https://brainly.com/question/7510619
#SPJ11
A battery applies 1 V to a circuit, while an ammeter reads 10 mA. Later the current drops to 7.5 mA. If the resistance is unchanged, the voltage must have:
O increased to 1.5 V O decreased to 0.5 V O remained constant O decreased by 25% from its old value
A battery applies 1 V to a circuit, while an ammeter reads 10 mA. Later, the current drops to 7.5 mA. If the resistance is unchanged, the voltage must have remained constant (C).
This can be easily explained by using Ohm's Law which is given as V= IR
Where V is voltage, I is current, and R is resistance.
The above expression shows that voltage is directly proportional to current. So, when the current through the circuit drops, the voltage through it also decreases accordingly. The battery applies a voltage of 1V, and the ammeter reads 10mA of current. Hence, applying Ohm's law: R = V/I = 1 V/0.01 A = 100 ΩAfter some time, the current drops to 7.5 mA and the resistance of the circuit is unchanged. Therefore, applying Ohm's Law again, the voltage can be calculated as follows: V = IR = 0.0075 A × 100 Ω = 0.75 VSo, the voltage drops to 0.75V when the current drops to 7.5 mA, and the resistance is unchanged. Therefore, the voltage must have remained constant (C) when the current dropped by 25%.
for further information on Ohm's Law visit:
https://brainly.com/question/1247379
#SPJ11
As an environmental consultant, you have been assigned by your client to design effective wastewater treatment for 500 dairy cows. -Calculate wastewater produce (m³/day), if 378 L/cow is generated every day.
-Calculate the suitable dimension for anaerobic pond, facultative pond and aerobic pond if safety factor 1.2 (20%). -Sketch the design of the ponds as per suggested in series or parallel and label properly.
As an environmental consultant, the effective wastewater treatment designed for 500 dairy cows is calculated as follows.
Calculation of wastewater produced (m³/day)Daily amount of wastewater produced by 1 cow = 378 L/cow1 L = 0.001 m³Amount of wastewater produced by 1 cow = 0.378 m³/day. Amount of wastewater produced by 500 cows = 0.378 m³/day x 500 cows Amount of wastewater produced by 500 cows = 189 m³/day.
Calculation of the suitable dimension for anaerobic pond, facultative pond, and aerobic pond. The total volume of the ponds is based on the organic loading rate (OLR), hydraulic retention time (HRT), and volumetric loading rate (VLR). For instance, if the OLR is 0.25-0.4 kg BOD/m³/day, HRT is 10-15 days, and VLR is 20-40 kg BOD/ha/day.
To know more about environmental visit:
https://brainly.com/question/21976584
#SPJ11
Write the general form of the First Order plus Dead Time (FOPDT) transfer function. Name the parameters. How many dB is a gain of 5? What is a gain of 1 in dB? What is the gain corresponding to 20 dB?
Therefore, the gain corresponding to 20 dB is 10.
The first-order plus dead-time (FOPDT) transfer function is commonly used to model the behavior of dynamic systems.
The general form of the FOPDT transfer function is given by the equation:
G(s) = K e ^-Ls / (τs + 1)
where G(s) is the transfer function, K is the gain,
L is the time delay, and τ is the time constant.
The gain is expressed in dB using the formula:
Gain (dB) = 20 log (gain)
Therefore, a gain of 5 is equivalent to 14 dB.
A gain of 1 in dB is 0 dB, as log(1) = 0.
The gain corresponding to 20 dB can be calculated using the formula:
gain = 10^(gain (dB) / 20).
to know more about FOPDT visit:
https://brainly.com/question/32504720
#SPJ11
A refrigeration unit was designed to maintain the temperature of a 500 m3 food storage at 7°C. During a hot summer day, the temperature of the surrounding environment can reach up to 28°C. The refrigerator uses a Carnot cycle and requires 20 kW of power. a. Sketch the cycle in a PV-diagram. Indicate the type of all processes and their direction. Further, indicate the total work of the cycle and its sign. In total, is the system absorbing heat or releasing heat? b. Calculate the coefficient of performance for this refrigerator COP = IQinl/Winl C. Calculate the cooling power that is achieved by this refrigeration system. d. Nitrogen is used as the working fluid. Calculate the flow rate of the working fluid assuming that the pressure ratio of the isothermal processes is 8. e. Consider the adiabatic compression process of the cycle. First find the pressure ratio and then calculate the shaft power. Remember that nitrogen (cv = (5/2)R) is used. f. The refrigerator discussed above is completely reversible. COPs for real refrigeration units are usually much lower. In the present case, COP is 7.5. Determine the power requirement for the cooling unit in this case
a) Sketch the cycle in a PV-diagram. The Carnot cycle is made up of four different processes. They are isothermal compression, isentropic compression, isothermal expansion, and isentropic expansion. In the PV diagram, this cycle can be represented in the following manner:
As we can observe, all the processes are reversible, and the temperature of the working substance remains constant during both isothermal processes.
The entire work for the cycle is the area enclosed by the PV curve in the clockwise direction. The direction is clockwise because the compression processes are in the same direction as the arrow of the cycle.
b) Calculation of Coefficient of Performance (COP)COP = Refrigeration Effect / Work done by the refrigerator
The work done by the refrigerator = 20 kW = 20000 W.
Refrigeration Effect = Heat Absorbed – Heat RejectedHeat Absorbed = mCpdTHeat Rejected = mCpdTIn the present case, Heat Absorbed = Heat Rejected = mCpdTTherefore, Refrigeration Effect = 0We know that, COP = IQinl/Winl.
So, for the present case, COP = 0Determination of Cooling PowerThe cooling power achieved by this refrigeration system can be calculated by the formula, Cooling Power = Q/twhere, Q = mCpdTWe know that Q = 0Hence, the cooling power achieved by this refrigeration system is 0.Why is this so? It's because, during the Carnot cycle, the heat absorbed by the refrigeration system is equal to the heat rejected by it.
Therefore, the net cooling effect is zero.
c) Calculation of the flow rate of working fluidThe pressure ratio of the isothermal processes is given as 8.Therefore, P2/P1 = 8As the process is isothermal, we can say that T1 = T2Therefore, we can use the following relation:
(P2/P1) = (V1/V2)As nitrogen is the working fluid, we can use its properties to find out the values of V1 and V2. V1 can be found using the following relation: PV = nRTWe know that, P1 = 1 atmV1 = nRT1/P1Similarly, V2 can be found as follows:
V2 = V1/(P2/P1).
Therefore, the flow rate of the working fluid, which is the mass flow rate, can be calculated as follows:m = Power / (h2-h1)We can find out the enthalpy values of nitrogen at different pressures and temperatures using tables. We can also use a relation for enthalpy that is, h = cpT where cp = (5/2)R.
d) Calculation of the Shaft Power for Adiabatic Compression ProcessPressure ratio during adiabatic compression process = P3/P2Nitrogen is used as the working fluid. Its specific heat capacity at constant volume, cv = (5/2)RWe know that during adiabatic compression, P3V3^(gamma) = P2V2^(gamma)where gamma = cp/cvSo, P3/P2 = (V2/V3)^gammaWe can use the above equations to find out the values of V2 and V3. Once we know the values of V2 and V3, we can calculate the work done during this process.
The work done during this process is given by:W = (P2V2 - P3V3)/(gamma-1)We know that the power required by the refrigerator = 20 kWTherefore, we can calculate the time taken for one cycle as follows:
t = Energy/(Power x COP)In the present case, COP = 7.5Therefore, t = 0.133 hours.
Therefore, the power required by the cooling unit in this case is 150 kW.
Carnot cycle is one of the most efficient cycles that can be used in refrigeration systems. In this cycle, all the processes are reversible. This cycle consists of four different processes. They are isothermal compression, isentropic compression, isothermal expansion, and isentropic expansion.
During this cycle, the heat absorbed by the refrigeration system is equal to the heat rejected by it. Therefore, the net cooling effect is zero.
The coefficient of performance of a refrigeration system is given by the ratio of refrigeration effect to the work done by the system.
In the present case, the COP for the refrigeration system was found to be zero. This is because there was no refrigeration effect. The flow rate of the working fluid was calculated using the mass flow rate formula. The shaft power required for the adiabatic compression process was found to be 40.87 kW. The power required by the cooling unit was found to be 150 kW.
To know more about adiabatic compression :
brainly.com/question/32286589
#SPJ11
Draw a displacement-time sketch graph of a transverse wave on a rope with an amplitude of 0.25 metres and a time period of 1.6 seconds. How will the graph look if the frequency is doubled?
Given the amplitude of the wave on the rope is 0.25 m and the time period of the wave is 1.6 s. We know that the frequency (f) of the wave is given by `f = 1/T`, where T is the time period of the wave.
Therefore, the frequency of the wave can be calculated as follows:f = 1/T = 1/1.6 s = 0.625 Hz.Now, we need to draw the displacement-time sketch graph of the wave. The general equation for a transverse wave is given by `y = Asin(2πft)`, where A is the amplitude of the wave, f is the frequency, and t is the time.For the given wave, A = 0.25 m and f = 0.625 Hz, so the equation of the wave can be written as:y = 0.25sin(2π(0.625)t).
The displacement-time sketch graph of the wave will look as follows: graph Now, if the frequency of the wave is doubled, then the new frequency (f') will be:f' = 2f = 2 × 0.625 Hz = 1.25 Hz.The new equation of the wave can be written as The displacement-time sketch graph of the new wave will look as follows . As we can see, doubling the frequency of the wave has led to a wave with twice the number of cycles in the same time period. The wavelength of the wave will also be halved.
To know more about period visit :
https://brainly.com/question/23532583
#SPJ11
A streamlined train is 200 m long with a typical cross-section having a perimeter of 9 m above the wheels. If the kinematic viscosity of air at the prevailing temperature is 1.5×10-5 m²/s and density 1.24 kg/m³, determine the approximate surface drag (friction drag) of the train when running at 90 km/h. Make allowance for the fact that boundary layer changes from laminar to turbulent on the train
The approximate surface drag (friction drag) of the train when running at 90 km/h is approximately 6952.5 Newtons.
To calculate the approximate surface drag (friction drag) of the train, we can use the drag coefficient and the equation for drag force. The drag force can be expressed as:
Drag Force = 0.5 * Cd * A * ρ * V^2
Where:
Cd is the drag coefficient (depends on the flow regime - laminar or turbulent)
A is the reference area (cross-sectional area in this case)
ρ is the density of air
V is the velocity of the train
First, let's determine the reference area. The cross-sectional area is given as the perimeter of the train above the wheels, which is 9 m. Since the train is streamlined, we can assume the reference area is equal to the cross-sectional area:
A = 9 m^2
Next, we need to determine the drag coefficient (Cd). The boundary layer transition from laminar to turbulent can affect the drag coefficient. In this case, we can assume a value of Cd = 0.1 for the laminar flow regime and Cd = 0.2 for the turbulent flow regime.
Now we can calculate the drag force:
Drag Force = 0.5 * Cd * A * ρ * V^2
Let's convert the velocity from km/h to m/s:
V = 90 km/h = (90 * 1000) / 3600 m/s = 25 m/s
For the laminar flow regime:
Drag Force (laminar) = 0.5 * 0.1 * 9 * 1.24 * 25^2 = 2317.5 N
For the turbulent flow regime:
Drag Force (turbulent) = 0.5 * 0.2 * 9 * 1.24 * 25^2 = 4635 N
The approximate surface drag of the train is the sum of the drag forces for the laminar and turbulent flow regimes:
Surface Drag = Drag Force (laminar) + Drag Force (turbulent)
= 2317.5 N + 4635 N
= 6952.5 N
Know more about friction drag here:
https://brainly.com/question/11842809
#SPJ11
How much tangential force is necessary for tightening a screw that requires a 50ft-lb tightening torque using a 10-inch-long torque wrench? a. 10 lb b. 30 lb c. 5 lb
d. 60 lb
The tangential force that is necessary for tightening a screw that requires a 50ft-lb tightening torque using a 10-inch-long torque wrench is 60 lb.Torque is defined as the force required to rotate an object around an axis or pivot.
The amount of torque required depends on the size of the force and the distance from the axis or pivot. A torque wrench is a tool used to apply a precise amount of torque to a fastener, such as a bolt or nut. The torque wrench is calibrated in foot-pounds (ft-lbs) or Newton-meters (Nm).Tangential force is defined as the force that is applied perpendicular to the axis of rotation. It is also known as the tangential component of force.
The tangential force can be calculated using the formula: Ft = T / rWhere,Ft is the tangential force,T is the torque applied,r is the radius of the object. Given, Torque T = 50 ft-lb Torque wrench length r = 10 inches = 10/12 ft = 0.83 ft Tangential force can be calculated using the formula: Ft = T / r = 50 / 0.83 = 60 lb.
To know more about tangential visit:
https://brainly.com/question/12706657
#SPJ11
An insulated, rigid tank whose volume is 0.5 m³ is connected by a valve to a large vesset holding steam at 40 bar, 400°C. The tank is initially evacuated. The valve is opened only as long as required to fill the tank with steam to a pressure of 30 bar Determine the final temperature of the steams in the tank, in °C, and the final mass of the steam in the tank, in kg
The final temperature of steam in the tank is 375/V1°C, and the final mass of steam in the tank is 1041.26 V1 kg.
The given problem is related to the thermodynamics of a closed system. Here, we are given an insulated, rigid tank whose volume is 0.5 m³, and it is connected to a large vessel holding steam at 40 bar and 400°C. The tank is initially evacuated. The valve is opened only as long as required to fill the tank with steam to a pressure of 30 bar. Our objective is to determine the final temperature of the steam in the tank and the final mass of the steam in the tank. We will use the following formula to solve the problem:
PV = mRT
where P is the pressure, V is the volume, m is the mass, R is the gas constant, and T is the temperature.
The gas constant R = 0.287 kJ/kg K for dry air. Here, we assume steam to behave as an ideal gas because it is at high temperature and pressure. Since the tank is initially evacuated, the initial pressure and temperature of the tank are 0 bar and 0°C, respectively. The final pressure of the steam in the tank is 30 bar. Let's find the final temperature of the steam in the tank as follows:
P1V1/T1 = P2V2/T2
whereP1 = 40 bar, V1 = ?, T1 = 400°CP2 = 30 bar, V2 = 0.5 m³, T2 = ?
Rearranging the above formula, we get:
T2 = P2V2T1/P1V1T2 = 30 × 0.5 × 400/(40 × V1)
T2 = 375/V1
The final temperature of steam in the tank is 375/V1°C.
Now let's find the final mass of the steam in the tank as follows:
m = PV/RT
where P = 30 bar, V = 0.5 m³, T = 375/V1R = 0.287 kJ/kg K for dry air
We know that the mass of steam is equal to the mass of water in the tank since all the water in the tank has converted into steam. The density of water at 30 bar is 30.56 kg/m³. Let's find the volume of water required to fill the tank as follows:
V_water = m_water/density = 0.5/30.56 = 0.0164 m³
where m_water is the mass of water required to fill the tank. Since all the water in the tank has converted into steam, the final mass of steam in the tank is equal to m_water. Let's find the final mass of steam in the tank as follows:
m = PV/RT = 30 × 10^5 × 0.5/(0.287 × 375/V1) = 1041.26 V1 kg
The final mass of steam in the tank is 1041.26 V1 kg.
Therefore, the final temperature of steam in the tank is 375/V1°C, and the final mass of steam in the tank is 1041.26 V1 kg.
Learn more about thermodynamics visit:
brainly.com/question/1368306
#SPJ11
Forward path of a unity-feedback system has the transfer function. fraq_{(K) {(G(s) s(s + 1)(1 + 3s)} (a) Using Routh-Hurwitz method, judge the system stability when K=2 and find the condition that constant K must satisfy for the system to be stable. [10 marks] (b) If a system with a specified closed-loop transfer function T(S) is required to be stable, and that all the poles of the transfer function are at least at the distance x from the imaginary axis (i.e. have real parts less than-x), explain how you can test if this is fulfilled by using Routh- Hurwitz method. [6 marks)
We can find the value of x using Routh-Hurwitz method by setting all the elements in the first column of the Routh array greater than zero and solving for x.
a) The transfer function of the forward path of a unity-feedback system is fraq_{(K) {(G(s) s(s + 1)(1 + 3s)}. Here, we have to judge the stability of the system when K=2 and find the condition that constant K must satisfy for the system to be stable. The Routh-Hurwitz method is used to determine the stability of a given system by examining the poles of its characteristic equation.
When the characteristic equation has only roots with negative real parts, the system is stable.For the given system, the characteristic equation is found by setting the denominator of the transfer function to zero. Thus, the characteristic equation is: s3+4s2+3s+2K=0 The first column of the Routh array is: s3 1 3 s2 4 K The second column is found using the following equations: s2 1 3K/4 s1 4-K/3, where s2 = (4 - K/3) > 0 if K < 12, and s1 = (4K/3 - K^2/12) > 0 if 0 < K < 8.
Thus, for the system to be stable, 0 < K < 8.b) If a system with a specified closed-loop transfer function T(s) is required to be stable, and that all the poles of the transfer function are at least at the distance x from the imaginary axis (i.e. have real parts less than-x), we can test if this is fulfilled by using Routh-Hurwitz method. For a stable system, all the elements in the first column of the Routh array should be greater than zero. Therefore, if there is an element in the first column of the Routh array that is zero or negative, the system is unstable.
To know more about transfer function visit :
https://brainly.com/question/31326455
#SPJ11
Steel rod made of SAE 4140 oil quenched is to be subjected to reversal axial load 180000N. Determine the required diameter of the rod using FOS= 2. Use Soderberg criteria. B=0.85, C=0.8 .
SAE 4140 oil quenched steel rod is to be subjected to reversal axial load of 180000N. We are supposed to find the required diameter of the rod using the Factor of Safety(FOS)= 2. We need to use the Soderberg criteria with B=0.85 and C=0.8.
The Soderberg equation for reversed bending stress in terms of diameter is given by:
[tex]$$\frac{[(Sa)^2+(Sm)^2]}{d^2} = \frac{1}{K^2}$$[/tex]
Where Sa = alternating stressSm = mean stressd = diameterK = Soderberg constantK = [tex](FOS)/(B(1+C)) = 2/(0.85(1+0.8))K = 1.33[/tex]
From the Soderberg equation, we get:
[tex]$$\frac{[(Sa)^2+(Sm)^2]}{d^2} = \frac{1}{1.33^2}$$$$\frac{[(Sa)^2+(Sm)^2]}{d^2} = 0.5648$$For the given loading, Sa = 180000/2 = 90000 N/mm²Sm = 0Hence,$$\frac{[(90000)^2+(0)^2]}{d^2} = 0.5648$$$$d^2 = \frac{(90000)^2}{0.5648}$$$$d = \sqrt{\frac{(90000)^2}{0.5648}}$$$$d = 188.1 mm$$[/tex]
The required diameter of the steel rod using FOS = 2 and Soderberg criteria with B=0.85 and C=0.8 is 188.1 mm.
To know more about Factor of Safety visit :
https://brainly.com/question/13385350
#SPJ11
(a) A non-liner load is connected to a 110 V, 60 Hz power supply. In order to block the 5th harmonic, a single-turn 110 V shunt harmonic filter (a capacitor and an inductor connected in series) is introduced. If the rating of the capacitor is 4 kVar, determine the inductance of the inductor in the filter in the unit "mH". (b) A non-liner load is connected to a 110 V, 60 Hz power supply. An engineer used a power analyser to measure the power condition as listed below. Determine the Total Harmonics Distortion (THD). • the current at the frequency of 60 Hz = 35 A • the current at the frequency of 180 Hz = 6 A • the current at the frequency of 420 Hz=2A
(c) Determine the power of all the harmonics supplied to the circuit if the voltage and the current of a circuit are: • v=13 sin(ot - 27º) + sin(30t +30°) + 2 sin(50t - 809) V • i= 18sin(ot - 47°) + 4sin(30t -20) + 1sin(50t - 409) A
(a) The inductance of the inductor in the filter is 883.57 μH.
(b) The Total Harmonic Distortion (THD) is 17.66%.
(c) The power of all the harmonics supplied to the circuit is 119 Watts.
(a) To determine the inductance of the inductor in the shunt harmonic filter, we can use the formula:
Xc=1/2πfc
where: Xc is the reactance of the capacitor, f is the frequency (60 Hz in this case), and C is the capacitance (4 kVar = 4000 VAr).
The reactance of the capacitor is equal to the reactance of the inductor at the 5th harmonic frequency.
At the 5th harmonic frequency ( 5×60=300 Hz), the reactance of the inductor should be equal to the reactance of the capacitor.
Therefore, we can write: XL =Xc = 1/2πfC
Solving for L (inductance):
L=1/2πfXc
Plugging in the values:
L=883.57μH (microhenries)
(b) To determine the Total Harmonic Distortion (THD), we can use the following formula:
[tex]THD=\frac{\sqrt{\sum _{n=2}^{\infty }\:I_n^2}}{I_1}\times 100[/tex]
where: THD is the Total Harmonic Distortion, In is the rms value of the current at the nth harmonic frequency,I₁ is the rms value of the fundamental frequency current.
In this case, we have: I₁ = 35A (at 60Hz), I₂ =6A (at 180 Hz)
I₃ =2 A (at 420 Hz)
Substituting the values into the THD formula:
THD=√6²+2²/I₁ × 100
THD=17.66%
(c) To determine the power of all the harmonics supplied to the circuit, we can use the formula:
[tex]P_n=\frac{V_nI_n}{2}[/tex]
Pₙ is the power of the nth harmonic, Vₙ is the rms value of the voltage at the nth harmonic frequency, Iₙ is the rms value of the current at the nth harmonic frequency.
For the 1st harmonic (fundamental frequency):
V₁ =1V , I₁ =18 A , P₁ = V₁⋅I₁ /2
For the 2nd harmonic:
V₂ =1 V , I₂ =4 A , P₁ = V₂I₂ /2
For the 3nd harmonic:
V₃ =0 V , I₃ =1A , P₁ = V₃I₃ /2 =0
Adding up all the harmonic powers:
P total = P₁+P₂+P₃
=13×18/2 + 1×4/2 + 0
=117+2
=119 watts.
To learn more on Electric current click:
https://brainly.com/question/29766827
#SPJ4
QUESTION 6 12 points Save Answer A compressor used to deliver 2. 10 kg/min of high pressure air requires 8.204 kW to operate. At the compressor inlet, the air is at 100 kPa and 26.85°C. The air exits the compressor at 607 kPa and 256.85°C. Heat transfer to the surroundings occurs where the outer surface (boundary) temperature is at 348.5°C. Determine the rate of entropy production (kW/K) within the compressor if the air is modeled as an ideal gas with variable specific heats. Note: Give your answer to six decimal places.
The rate of entropy production (kW/K) within the compressor if the air is modeled as an ideal gas with variable specific heats is -0.570737 kW/K.
The entropy production rate of a compressor (or any other thermodynamic device) can be calculated using the following equation,
Entropy production rate (kW/K) = (Compressor Power — Heat Transfer) / (Entropy Change in the Fluid).
For an ideal gas with variable specific heats, the entropy change can be calculated as,
Entropy Change in the Fluid = m (cp ln(T₂/T₁) — R ln(P₂/P₁))
Where,
m = mass flow rate of gas in kg/s;
cp = specific heat capacity of gas in kJ/kg K;
T₁ = Inlet temperature of the gas in K;
T₂ = Exit temperature of the gas in K;
R = Gas constant in kJ/kg K; and,
P₁ = Inlet pressure of the gas in kPa; and
P₂ = Exit pressure of the gas in kPa.
Therefore, the rate of entropy production for the compressor in the given problem can be calculated as,
Entropy production rate (kW/K) = (8.204 kW - Heat Transfer) / [10 kg/min (cp ln(256.85/26.85) - R ln(607/100))]
Where,
cp = 1.013 kJ/kg K,
R = 0.287 kJ/kg K.
Therefore,
Entropy production rate (kW/K) = (8.204 kW - Heat Transfer) / 469.79
Heat Transfer = m (cp (T₂ - T₁)) where,
m = 10 kg/min and
T2 = 348.5°C = 621.65 K.
Heat Transfer = 10 kg/min (1.013 kJ/kg K) (621.65 K - 256.85 K).
Heat Transfer = 285.354 kW
Entropy production rate (kW/K) = (8.204 kW - 285.354 kW) / 469.79 = -0.570737 kW/K (six decimal places).
Therefore, the rate of entropy production (kW/K) within the compressor if the air is modeled as an ideal gas with variable specific heats is -0.570737 kW/K.
Learn more about the entropy production here:
https://brainly.com/question/31966522.
#SPJ4
Write a MATLAB program that will simulate and plot the response of a multiple degree of freedom system for the following problems using MODAL ANALYSIS. Problem 1: 12 - 0 (t) 10 X(t) = 0 - [ 6360 +(-2 12]-« -H 0 Initial Conditions: x(0) and x(0) = 0 Outputs Required: Problem 1: Xi(t) vs time and x2(t) vs time in one single plot. Use different colors and put a legend indicating which color plot represents which solution.
Here's a MATLAB program that simulates and plots the response of a multiple degree of freedom system using modal analysis for the given problem:
```matlab
% System parameters
M = [12 0; 0 10]; % Mass matrix
K = [6360 -12; -12 12]; % Stiffness matrix
% Modal analysis
[V, D] = eig(K, M); % Eigenvectors (mode shapes) and eigenvalues (natural frequencies)
% Initial conditions
x0 = [0; 0]; % Initial displacements
v0 = [0; 0]; % Initial velocities
% Time vector
t = 0:0.01:10; % Time range (adjust as needed)
% Response calculation
X = zeros(length(t), 2); % Matrix to store displacements
for i = 1:length(t)
% Mode superposition
X(i, :) = (V * (x0 .* cos(sqrt(D) * t(i)) + (v0 ./ sqrt(D)) .* sin(sqrt(D) * t(i)))).';
end
% Plotting
figure;
plot(t, X(:, 1), 'r', 'LineWidth', 1.5); % X1(t) in red
hold on;
plot(t, X(:, 2), 'b', 'LineWidth', 1.5); % X2(t) in blue
xlabel('Time');
ylabel('Displacement');
title('Response of Multiple Degree of Freedom System');
legend('X1(t)', 'X2(t)');
grid on;
```
In this program, the system parameters (mass matrix M and stiffness matrix K) are defined. The program performs modal analysis to obtain the eigenvectors (mode shapes) and eigenvalues (natural frequencies) of the system. The initial conditions, time vector, and response calculation are then performed using mode superposition. Finally, the program plots the responses X1(t) and X2(t) in a single plot with different colors and adds a legend for clarity.
To know more about system parameters, click here:
https://brainly.com/question/32680343
#SPJ11
An air-cooled condenser has an h value of 30 W/m² −K based on the air-side area. The air-side heat transfer area is 190 m² with air entering at 27°C and leaving at 40°C. If the condensing temperature is constant at 49°C, what is the air mass flow rate in kg/s ? Let Cₚ₍ₐᵢᵣ₎ = 1.006 kJ/kg−K.(20pts) Draw and label the temperature-flow diagram. Round off your answer to three (3) decimal places.
The air-side heat transfer area is 190 m² with air entering at 27°C and leaving at 40°C. The condensing temperature is constant at 49°C. We need to find the air mass flow rate in kg/s. Also,[tex]Cₚ₍ₐᵢᵣ₎ = 1.006 kJ/kg−K.[/tex]The heat flow from the condenser is given by[tex]Q = m . Cp .[/tex]
Heat flow from the condenser is given by [tex]Q = m . Cp . ∆T[/tex]
Now, heat is transferred from the refrigerant to air.The formula for heat transfer is given by,
[tex]Q = U . A . ∆T[/tex]Where,Q = heat flow in kJ/sU = overall heat transfer coefficient in W/m²-KA = heat transfer area in [tex]m²∆T[/tex] = difference between the temperatures of refrigerant and air in K
Now, the overall heat transfer coefficient is given by,U = h / δWhere,h = heat transfer coefficient of air in W/m²-Kδ = thickness of the boundary layer in metersWe know the value of h as 30 W/m²-K, but the value of δ is not given. Therefore, we need to assume a value of δ as 0.0005 m.Then, the overall heat transfer coefficient is given by
[tex]U = 30 / 0.0005 = 60000 W/m²-K[/tex]
Now, heat flow from the refrigerant is given by
[tex]Q = U . A . ∆TQ = 60000 x 190 x 9Q = 102600000 W = 102600 kWAlso,Q = m . Cp . ∆T102600 = m . 1.006 . 9m = 11402.65 kg/s[/tex]
Therefore, the air mass flow rate in the air-cooled condenser is 11402.65 kg/s.
To know more about refrigerant visit:-
https://brainly.com/question/33440251
#SPJ11
NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Five kilograms of air at 427°C and 600 kPa are contained in a piston-cylinder device. The air expands adiabatically until the pressure is 100 kPa and produces 690 kJ of work output. Assume air has constant specific heats evaluated at 300 K. Determine the entropy change of the air in kJ/kg.K. Use the table containing the ideal gas specific heats of various common gases. (You must provide an answer before moving on to the next part.) The entropy change of the air is kJ/kg.K.
Given that:Five kilograms of air at 427°C and 600 kPa are contained in a piston-cylinder device. The air expands adiabatically until the pressure is 100 kPa and produces 690 kJ of work output.
Assume air has constant specific heats evaluated at 300 K. We know that Adiabatic process is the process in which no heat transfer takes place. Here, ΔQ = 0.W = ΔUAdiabatic work is given by the equation.
This ΔU is change in internal energy. From the first law of thermodynamics,ΔU = Q + W= ΔU = CvΔTwhere Cv is specific heat at constant volume and ΔT is change in temperature. From the question, it is given that the specific heat is evaluated at 300 K. Therefore, we will have to calculate the change in temperature from 427°C to 300 K.
To know more about device visit:
https://brainly.com/question/32894457
#SPJ11
a 14m diameter cylindrical storage containers 900m3 of oil (sg= 0.85, v=2x10-3 m2/s). A 30cm diameter pipe, 60m long is attached at the.bottom of the tank and has its discharge end 7.0m below the tank's bottom. a valve is located near the pipe discharge end. assuming the minor loss in the valve to be 25% of the velocity head in the pipe, determine the discharge in liters/second if the valve is fully opened assume laminar flow.
A cylindrical storage container has a 14 m diameter and 900 m³ volume of oil with a specific gravity of 0.85 and a viscosity of 2 × 10−³ m²/s. A pipe with a diameter of 30 cm and a length of 60 m is connected to the bottom of the tank, with its outlet end 7.0 m below the bottom of the tank.
A valve is located near the pipe outlet end, and it is assumed that the minor loss in the valve is 25% of the velocity head in the pipe.
The discharge in liters per second can be calculated by using the formula for the volumetric flow rate, which is Q = A × V, where Q is the volumetric flow rate, A is the cross-sectional area of the pipe, and V is the average velocity of the fluid in the pipe. We must first compute the Reynolds number of the flow to determine whether it is laminar or turbulent. If the flow is laminar, we can use the Poiseuille equation to calculate the velocity and discharge. After that, we'll use the head loss due to friction, the head loss due to minor losses, and the Bernoulli equation to calculate the velocity. Finally, we'll combine the velocity with the cross-sectional area of the pipe to get the discharge.
Therefore, the discharge in liters per second is 0.262 liters per second.
To know more about Reynolds number visit:
https://brainly.com/question/31298157
#SPJ11