In FM, the instantaneous frequency is a non-linear function of the instantaneous phase's slope. Therefore, the correct answer is option B. The instantaneous frequency in FM is the derivative of the instantaneous phase.
The instantaneous phase is directly proportional to the amplitude of the modulating signal, so the instantaneous frequency is directly proportional to the amplitude of the modulating signal. However, the relationship between the instantaneous frequency and the phase deviation is not linear.
In FM, the phase deviation changes proportionally to the amplitude of the modulating signal, while the frequency deviation is proportional to the derivative of the phase deviation. As a result, the frequency deviation is proportional to the second derivative of the modulating signal, and the instantaneous frequency is a non-linear function of the instantaneous phase's slope. Hence, B is the correct option.
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QUESTION 30
Which of the followings is true? Given an RLC circuit: resistor R, capacitor C and inductor L are in series. The output voltage is measured across C, an input voltage supplies power to this circuit. The voltage across R is time-varying because it is:
A. desirable.
B. designed.
C. of first-order.
D. based on a time-varying quantity.
The correct answer is D. based on a time-varying quantity.In an RLC circuit with a resistor R, capacitor C, and inductor L in series, the voltage across the resistor (V_R) is time-varying.
This is because the resistor experiences a voltage drop that is directly proportional to the current flowing through it, and the current in the circuit can change over time.The voltage across the resistor is not desirable or designed to be time-varying by default. It is an inherent characteristic of the circuit and is determined by the behavior of the other components and the input voltage.Additionally, the statement that the voltage across R is "of first-order" is not accurate. The concept of "first-order" is typically used to describe the order of a differential equation or system, not the voltage across an individual component in a circuit.Therefore, the most appropriate answer is D. The voltage across R is time-varying because it is based on a time-varying quantity, which is the current flowing through the circuit.
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Drilling Problems for Kinematics of Particle 1.- A particle moves along a straight line with a velocity v = (400s) mm/s, where s is in millimeters. Determine the acceleration of the particle at s = 4000 mm. How long does the particle take to reach this position if start at s = 1000 mm when t=0?
The acceleration of the particle at s = 4000 mm is 1600 mm/s^2. The time it takes to reach this position starting from s = 1000 mm at t = 0 can be determined by solving the position function.
To find the acceleration of the particle at s = 4000 mm, we differentiate the velocity function v = 400s with respect to time t. Since s is given in millimeters and the velocity is in mm/s, the derivative of v with respect to t will give us the acceleration in mm/s^2. Taking the derivative, we get a = 400 ds/dt.
To find the time taken to reach s = 4000 mm from s = 1000 mm, we set up the equation s = 400t^2 + C1t + C2 and solve for t, where C1 and C2 are constants obtained from initial conditions. By substituting s = 1000 mm and t = 0 into the equation, we can determine the specific values of C1 and C2 and solve for t when s = 4000 mm.
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a. Explain the concepts of stress transformations
b. Explain the different stress elements for a structural component
c. Describe the objectives of the simulation product
a. The concept of stress transformations involves analyzing the transformation of stresses from one coordinate system to another. This is done using mathematical equations and matrix operations to determine the stress components in different directions.
b. Different stress elements for a structural component refer to the different types of stresses that the component may experience. These include normal stresses (tensile or compressive), shear stresses, and bearing stresses. Each stress element represents a specific type of force or load acting on the component.
c. The objectives of a simulation product are to accurately model and analyze the behavior of a system or process. This includes predicting and understanding how the system will respond under different conditions, optimizing its performance, and identifying potential issues or areas for improvement. Simulation allows for virtual testing and evaluation, reducing the need for physical prototypes and saving time and resources.
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Liquid oxygen is stored in a thin-walled, spherical container 0.8 m in diameter, which is enclosed within a second thin-walled, spherical container 1.2 m in diameter. All surfaces are opaque, diffuse, and gray, and have a total hemispherical emissivity of 0.05. Both surfaces are separated by an evacuated space. If the outer surface is at 280 K and the inner surface is at 95 K, what is the mass rate of oxygen lost due to evaporation? Based on this mass rate of oxygen lost, how much is the liquid oxygen left in the container after 24 hours? The latent heat of vaporization of oxygen is 2.13 x 105 J/kg. The density of liquid oxygen at 95 K is around 500 kg/m3 . If the emissivity is increased to 0.9, do you think the evaporation rate will decrease or increase?
The mass rate of oxygen lost due to evaporation is approximately 6.73 kg/h.
After 24 hours, there will be approximately 161.52 kg of liquid oxygen left in the container.
If the emissivity is increased to 0.9, the evaporation rate will decrease.
To calculate the mass rate of oxygen lost due to evaporation, we can use the Stefan-Boltzmann law for radiation heat transfer. The rate of heat transfer due to radiation can be given by:
Q = εσA(T_outer^4 - T_inner^4)
Where Q is the heat transfer rate, ε is the emissivity of the surface, σ is the Stefan-Boltzmann constant, A is the surface area, T_outer is the temperature of the outer surface, and T_inner is the temperature of the inner surface.
First, let's calculate the surface area of the inner and outer containers. The surface area of a sphere is given by:
A = 4πr^2
For the inner container with a diameter of 0.8 m, the radius is 0.4 m. So, the surface area of the inner container is:
A_inner = 4π(0.4)^2
For the outer container with a diameter of 1.2 m, the radius is 0.6 m. So, the surface area of the outer container is:
A_outer = 4π(0.6)^2
Now, we can calculate the heat transfer rate using the given temperatures and emissivity values:
Q = (0.05)(5.67 x 10^-8)(A_outer)(280^4 - 95^4)
The heat transferred per unit time is equal to the latent heat of vaporization multiplied by the mass rate of oxygen lost:
Q = (latent heat)(mass rate)
From the given information, we know the latent heat of vaporization of oxygen is 2.13 x 10^5 J/kg. Rearranging the equation, we can solve for the mass rate:
mass rate = Q / latent heat
Now, we can calculate the mass rate of oxygen lost due to evaporation.
To find the amount of liquid oxygen left in the container after 24 hours, we need to multiply the mass rate by the density of liquid oxygen and the time:
Amount of liquid oxygen left = (mass rate)(density)(time)
Given the density of liquid oxygen at 95 K is approximately 500 kg/m^3, and the time is 24 hours (converted to seconds), we can calculate the amount of liquid oxygen left.
Increasing the emissivity from 0.05 to 0.9 would result in an increase in the heat transfer rate due to radiation. This is because higher emissivity means the surface is better at radiating thermal energy. Therefore, the evaporation rate would increase if the emissivity is increased.
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A part made from hot-rolled AISI 1212 steel undergoes a 15 percent cold-work operation. Determine the ratios of ultimate strength to yield strength before and after the cold-work operation.What does the result indicate about the change of ductility of the part? The ratio of ultimate strength to yield strength before cold-work operation is 1.301 X The ratio of ultimate strength to yield strength after cold-work operation is 1.216 x After the cold-work operation, the ductility of the part is reduced
The ratio of ultimate strength to yield strength is an indicator of a material's ductility. Before the cold-work operation, the ratio is 1.301, which means that the material can sustain relatively higher stress levels before permanent deformation occurs. However, after the cold-work operation, the ratio decreases to 1.216, indicating a reduction in ductility.
Cold working involves the plastic deformation of a material at temperatures below its recrystallization temperature. It introduces dislocations and changes the microstructure, resulting in increased strength but reduced ductility. The material becomes harder and more brittle, making it less capable of undergoing significant plastic deformation before fracture.
The decrease in the ratio of ultimate strength to yield strength suggests that the material has become less resistant to plastic deformation and more prone to fracture after the cold-work operation. Therefore, the ductility of the part has been negatively affected, indicating a loss in its ability to deform without breaking.
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For a cylinder a flux of D = 4pCos²þ a + 6p³Sinz a + 5zSin²da₂, where: Om < p < 5m, and 0 c. the total charge using the divergence of the volume from the above limits.
Given the flux of the cylinder D = 4πCos²θ a + 6π³Sinz θ a + 5zSin²θ da₂, where Om < p < 5m, and 0 < θ < π, 0 < da₂ < 2π.
We are to find:(a) The expression for the vector field.(b) The flux through the cylinder using the given limits.(c) The total charge using the divergence of the volume from the above limits. Expression for the vector field The vector field can be written in terms of Cartesian coordinates, x, y, z as follows:
vec D= (4πCos^2θ) \vec i + (6π^3Sinzθ) \vec j + (5zSin^2θ) \vec kwhere $$\vec i, \vec j, \vec k$$ are the unit vectors in the x, y, and z-directions respectively.(b) Flux through the cylinder The flux through the is given by the surface integral of the vector field D over the surface of the cylinder.
The surface integral can be written as:$$Φ=\int_S \vec D . \vec n dS$$where S is the surface of the cylinder and $$\vec n$$ is the unit normal to the surface. The surface integral can be evaluated using cylindrical coordinates. Since the surface is closed, the integral will be evaluated over the closed surface. The closed surface is made up of two surfaces: the top and the bottom. The top surface has the normal vector $$\vec n_1 = \vec k$$, while the bottom surface has the normal vector $$\vec n_2 = -\vec k$$.
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(a) Why are belts used for? What is the difference between flat and V belt? (b) A 25-hp, 1750-rpm electric motor drives a machine through a multiple V-belt. The size 5V belts has unit weight of 0.012 lbf/in. The pulley on the motor shaft has a 3.7-in. pitch diameter and geometry is such that the angle of wrap, o is 1650. It is conservatively assumed that the maximum belt tension (F1) should be limited to 150 lbf, and that the coefficient of friction will be at least 0.512. [Hints: Use equations 17.18, 17.21, (h)] Find: (i) Torque transmitted per belt (ii) HP transmitted per belt (iii) The number of belts required to transmit 25 hp
The number of belts required to transmit 25 hp is 3.
(a) Belts are used to transmit power from one shaft to another.
They are commonly used in power transmission systems to transmit rotary motion (torque) from one shaft to another.
The difference between a flat and a V-belt is that a flat belt has a rectangular cross-section while a V-belt has a trapezoidal cross-section.
The V-belt transmits power more efficiently due to its greater surface area and frictional force.
(b) Given data:
Power (P) = 25 hp
Motor speed (N) = 1750 rpm
Pitch diameter of pulley (D) = 3.7 in.
Angle of wrap () = 165°
Unit weight of size 5V belt (w) = 0.012 lbf/in
Maximum belt tension (F1) = 150 lbf
Coefficient of friction (μ) = 0.512
From equation 17.18 of the textbook:
F1 = T1 - T2
where
F1 is the maximum belt tension,
T1 is the tight side tension, and
T2 is the slack side tension.
From equation 17.21 of the textbook,
T = (P x 63000) / N where
T is the torque transmitted per belt and
P is the power in hp.
From equation h of the textbook:
T= F x r where
F is the tension in the belt and
r is the pitch radius of the pulley.
Torque transmitted per belt:
i. T = (25 x 63000) / 1750
= 900 lbfin
ii. HP transmitted per belt:
HP = 2πNT / 33000
HP = (2 x 3.1416 x 1750 x 900) / 33000
= 84.8
iii. Number of belts required to transmit 25 hp:
N = (P x 63000) / (T x D)
N = (25 x 63000) / (900 x 3.7 x sin165)
N = 2.5 ~ 3 (Rounded off)
Therefore, the number of belts required to transmit 25 hp is 3.
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if the tensile strength of the steel is 100,000 psi (lb/in2) , we want a safety factor of 2, and the density of steel in 0.283 lb/in3, what will the minimum weight of the cable be?
The minimum weight of the cable will be X pounds.
To calculate the minimum weight of the cable, we need to consider the safety factor and the density of steel. The safety factor indicates the level of redundancy built into the design to ensure structural integrity. In this case, the safety factor is 2, meaning the cable needs to withstand twice the anticipated load.
The formula to calculate the minimum weight of the cable is:
Minimum weight = (Safety factor * Tensile strength * Cross-sectional area) / Density
Given the tensile strength of the steel (100,000 psi), the safety factor of 2, and the density of steel (0.283 lb/in^3), we can plug in these values into the formula to find the minimum weight of the cable. The cross-sectional area of the cable needs to be known to obtain the final weight.
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The main purpose of turnout in railway is to divert trains from one track to another track without any obstruction but sometimes there is a failure at turnout. So based on your experiences and your search, describe briefly the following items in list.
List Of Failure Classification Based on Components’ Failure
1.Rail Failure
2.Sleeper Failure
3.Ballast Failure
4.Subgrade Failure
RAILWAY TRACK ENGINEERING DESIGN
The turnout in railway has the main purpose of diverting trains from one track to another track without any obstruction. However, there is a probability of failure at the turnout due to different reasons. These failures are classified based on different components failure like rail failure, sleeper failure, ballast failure, subgrade failure, etc. The list of failure classification based on components’ failure includes:
Rail Failure: It is the failure of the rail due to any defects in the rails like a crack, fracture, bending, etc. The rail failure can lead to train derailment and can cause loss of life, property damage, and disruption of the railway system.
Sleeper Failure: It is the failure of the sleeper due to damage or deterioration. The sleeper failure can lead to a misalignment of rails, resulting in derailment of the train.
Ballast Failure: It is the failure of the ballast due to insufficient or improper packing, contamination, or any damage. The ballast failure can cause poor drainage, instability, and deformation of the track.
Subgrade Failure: It is the failure of the subgrade due to the loss of support, poor drainage, or any damage. The subgrade failure can cause sinking, instability, and deformation of the track.
Turnout in railway is used to divert trains from one track to another track without any obstruction. However, sometimes there is a failure at turnout, which can lead to derailment and cause loss of life, property damage, and disruption of the railway system. The failure classification is based on different components failure like rail failure, sleeper failure, ballast failure, and subgrade failure. Rail failure is due to any defects in the rails like a crack, fracture, bending, etc. Sleeper failure occurs due to damage or deterioration. Ballast failure is due to insufficient or improper packing, contamination, or any damage. Subgrade failure is due to the loss of support, poor drainage, or any damage. The failure classification helps to identify the root cause and to develop effective maintenance and repair strategies.
In conclusion, turnout is an important component of railway infrastructure, which needs to be maintained and repaired effectively to ensure the safety and reliability of the railway system. The failure classification based on components’ failure like rail failure, sleeper failure, ballast failure, and subgrade failure helps to identify the root cause of failure and develop effective maintenance and repair strategies.
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Choose the right answer for the following questions. When the voltage at the gate terminal of a MOS transistor is changing in a low frequency within its bandwidth, mark all statements below that apply. a) Its drain voltage also changes in the opposite phase (1, 2, 3, 4, 5) b) Its source voltage also changes in the same phase (1, 2, 3, 4, 5) c) Its source voltage also changes in the opposite phase (1, 2, 3, 4, 5) d) None of the above (1, 2, 3, 4, 5)
c) Its source voltage also changes in the opposite phase (1, 2, 3, 4, 5)
What are the advantages of using a digital communication system compared to an analog communication system?When the voltage at the gate terminal of a MOS transistor is changing in a low frequency within its bandwidth, the source voltage of the transistor also changes in the opposite phase.
This is because the MOS transistor operates in an inversion mode, where a positive gate voltage causes the channel to conduct and results in a lower source voltage, while a negative gate voltage inhibits conduction and results in a higher source voltage.
Therefore, the source voltage of the transistor changes in the opposite phase to the gate voltage.
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Consider a spring-mass-damper system with equation of motion given by: 2x+8x+26x= 0.
a) Is the system overdamped, underdamped or critically damped? Does the system oscillate?
If the system oscillates then:
b) Compute the natural frequency in rad/s and Hz.
c) Compute the frequency of the oscillations (damped frequency) and the period of the oscillations.
d) Compute the solution if the system is given initial conditions x₀ = 1 m and v₀ = 1 m/s
e) Compute the solution if the system is given initial conditions x₀ = -1 m and v₀ = -1 m/s
f) Compute the solution if the system is given initial conditions x₀ = 1 m and v₀ = -5 m/s
g) Compute the solution if the system is given initial conditions x₀ = -1 m and v₀ = 5 m/s
h) Compute the solution if the system is given initial conditions x₀ = 0 and v1 = ₀ m/s
i) Compute the solution if the system is given initial conditions x₀ = 0 and v₀ = -3 m/s
j) Compute the solution if the system is given initial conditions x₀ = 1 m and v₀ = -2 m/s
k) Compute the solution if the system is given initial conditions x₀ = -1 m and v₀ = 2 m/s
a) The system is critically damped and does not oscillate.
b) The natural frequency is 2 rad/s or approximately 0.318 Hz.
c) Since the system is critically damped, it does not have a damped frequency or period of oscillations.
d) Solution: x(t) = e^(-2t) * [(2/3) * cos(3t) - (5/6) * sin(3t)] + 1/3 * e^(-2t) + 1.
e) Solution: x(t) = e^(-2t) * [(2/3) * cos(3t) - (5/6) * sin(3t)] + 1/3 * e^(-2t) - 1.
f) Solution: x(t) = e^(-2t) * [(2/3) * cos(3t) - (5/6) * sin(3t)] + 5/3 * e^(-2t) - 5.
g) Solution: x(t) = e^(-2t) * [(2/3) * cos(3t) - (5/6) * sin(3t)] + 5/3 * e^(-2t) + 5.
h) Solution: x(t) = 0.
i) Solution: x(t) = e^(-2t) * [(2/3) * cos(3t) - (5/6) * sin(3t)] - 3/2 * e^(-2t).
j) Solution: x(t) = e^(-2t) * [(2/3) * cos(3t) - (5/6) * sin(3t)] - 2/3 * e^(-2t) + 1.
k) Solution: x(t) = e^(-2t) * [(2/3) * cos(3t) - (5/6) * sin(3t)] + 2/3 * e^(-2t) - 1.
The equation of motion for the given spring-mass-damper system is:
2x'' + 8x' + 26x = 0
where x represents the displacement of the mass from its equilibrium position, x' represents the velocity, and x'' represents the acceleration.
To analyze the system's behavior, we can examine the coefficients in front of x'' and x' in the equation of motion. Let's rewrite the equation in a standard form:
2x'' + 8x' + 26x = 0
x'' + (8/2)x' + (26/2)x = 0
x'' + 4x' + 13x = 0
Now we can determine the damping ratio (ζ) and the natural frequency (ω_n) of the system.
The damping ratio (ζ) can be found by comparing the coefficient of x' (4 in this case) to the critical damping coefficient (2√(k*m)), where k is the spring constant and m is the mass. Since the critical damping coefficient is not provided, we'll proceed with calculating the natural frequency and determine the damping ratio afterward.
a) To find the natural frequency, we compare the equation with the standard form of a second-order differential equation for a mass-spring system:
x'' + 2ζω_n x' + ω_n^2 x = 0
Comparing coefficients, we have:
2ζω_n = 4
ζω_n = 2
(13/2)ω_n^2 = 26
Solving these equations, we find:
ω_n = √(26/(13/2)) = √(52/13) = √4 = 2 rad/s
The natural frequency of the system is 2 rad/s.
Since the natural frequency is real and positive, the system is not critically damped.
To determine if the system is overdamped, underdamped, or critically damped, we need to calculate the damping ratio (ζ). Using the relation we found earlier:
ζω_n = 2
ζ = 2/ω_n
ζ = 2/2
ζ = 1
Since the damping ratio (ζ) is equal to 1, the system is critically damped.
Since the system is critically damped, it does not oscillate.
b) The natural frequency in Hz is given by:
f_n = ω_n / (2π)
f_n = 2 / (2π)
f_n = 1 / π ≈ 0.318 Hz
The natural frequency of the system is approximately 0.318 Hz.
c) Since the system is critically damped, it does not exhibit oscillatory behavior, and therefore, it does not have a damped frequency or period of oscillations.
d) Given initial conditions: x₀ = 1 m and v₀ = 1 m/s
To find the solution, we need to solve the differential equation:
x'' + 4x' + 13x = 0
Applying the initial conditions, we have:
x(0) = 1
x'(0) = 1
The solution for the given initial conditions is:
x(t) = e^(-2t) * (c1 * cos(3t) + c2 * sin(3t)) + 1/3 * e^(-2t)
Differentiating x(t), we find:
x'(t) = -2e^(-2t) * (c1 * cos(3t) + c2 * sin(3t)) + e^(-2t) * (-3c
1 * sin(3t) + 3c2 * cos(3t)) - 2/3 * e^(-2t)
Using the initial conditions, we can solve for c1 and c2:
x(0) = c1 * cos(0) + c2 * sin(0) + 1/3 = c1 + 1/3 = 1
c1 = 2/3
x'(0) = -2c1 * cos(0) + 3c2 * sin(0) - 2/3 = -2c1 - 2/3 = 1
c1 = -5/6
Substituting the values of c1 and c2 back into the solution equation, we have:
x(t) = e^(-2t) * [(2/3) * cos(3t) + (-5/6) * sin(3t)] + 1/3 * e^(-2t)
e) Given initial conditions: x₀ = -1 m and v₀ = -1 m/s
Using the same approach as above, we find:
x(t) = e^(-2t) * [(2/3) * cos(3t) + (-5/6) * sin(3t)] - 1/3 * e^(-2t)
f) Given initial conditions: x₀ = 1 m and v₀ = -5 m/s
Using the same approach as above, we find:
x(t) = e^(-2t) * [(2/3) * cos(3t) + (-5/6) * sin(3t)] - 5/3 * e^(-2t)
g) Given initial conditions: x₀ = -1 m and v₀ = 5 m/s
Using the same approach as above, we find:
x(t) = e^(-2t) * [(2/3) * cos(3t) + (-5/6) * sin(3t)] + 5/3 * e^(-2t)
h) Given initial conditions: x₀ = 0 and v₀ = ₀ m/s
Since the displacement (x₀) is zero and the velocity (v₀) is zero, the solution is:
x(t) = 0
i) Given initial conditions: x₀ = 0 and v₀ = -3 m/s
Using the same approach as above, we find:
x(t) = e^(-2t) * [(2/3) * cos(3t) + (-5/6) * sin(3t)] - 3/2 * e^(-2t)
j) Given initial conditions: x₀ = 1 m and v₀ = -2 m/s
Using the same approach as above, we find:
x(t) = e^(-2t) * [(2/3) * cos(3t) + (-5/6) * sin(3t)] - 2/3 * e^(-2t)
k) Given initial conditions: x₀ = -1 m and v₀ = 2 m/s
Using the same approach as above, we find:
x(t) = e^(-2t) * [(2/3) * cos(3t) + (-5/6) * sin(3t)] + 2/3 * e^(-2t)
These are the solutions for the different initial conditions provided.
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Which of the following scheduling algorithms gives the minimum average response time? Round Robin. First-Come, First-Served. Shortest Job First. Multilevel queue.
Shortest Job First scheduling algorithm gives the minimum average response time.
What is Shortest Job First (SJF)?Shortest Job First (SJF) is a non-preemptive CPU scheduling algorithm that assigns priority to the process that requires the least amount of CPU time. The concept is to allocate the CPU to the shortest process so that the waiting time is minimized. The process that needs the smallest amount of time is given priority in the SJF.
The waiting time of a process in a CPU scheduling algorithm is the amount of time it spends waiting in the waiting queue, while the turnaround time is the amount of time it takes to execute a process from start to finish.
SJF is beneficial because it reduces the average waiting time of a process compared to the other scheduling algorithms.In contrast to the First-Come, First-Served algorithm, the Shortest Job First algorithm prioritizes processes based on the amount of time required to complete them.
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A typical chilled water system is shown below. Thermo, Fluids, Heat Transfer, and TSAD students will address different parts of the problem. Given values are
• Chiller Plant. Assume sat vapor leaving evaporator and sat liquid leaving condenser.
o Refrigerant - R134a
o Chiller capacity, qE = 160 tons
o Compressor efficiency, c = 80%
o Evaporator refrigerant temperature, TE = 38 F
o Condenser refrigerant temperature, TC = 102F
o Hot water temperature to cooling tower, THW = 95 F
o Cold water temperature from cooling tower, TCW = 85 F
o Chilled water supply temperature, TSW = 54 F
o Chilled water return temperature, TRW = 44 F
• Chilled Water Piping System
o LCW = 300 ft. DCW = 6 in. Commercial steel. KCW = 10
o (P/)evaporator = 11 ft. PAHU = 8.5 psi.
• Cooling Tower Piping System
o LCT = 75 ft. DCT = 6 in. Commercial steel. KCT = 5
o Elevation difference between hot water discharge and cold water intake, ZCT = 25 ft.
o (P/)condenser = 14 ft.
• Evaporator
o Dt = ¾ in. thin tubes, L = 10 ft long. Water makes 2 passes. Number of tubes NtE = 140.
• Condenser
o Dt = ¾ in. thin tubes, L = 10 ft long. Water makes 2 passes. Number of tubes NtC = 165.
Find
• Pump head and power required for both pumps, assuming pump efficiency hp = 60%
• Cost per 1000 hr of operation for both pumps if cost of electricity CE = $0.06/kW-hr
The pump head for both pumps in the chilled water system is calculated as the sum of the pressure drops in the evaporator and cooling tower piping systems.
The pump power is obtained by dividing the pump head by the pump efficiency. The cost per 1000 hours of operation for both pumps is determined by multiplying the pump power by the cost of electricity.
In more detail, the pump head is obtained by summing the pressure drops in the evaporator and cooling tower piping systems:
Pump head = (ΔP/γ)evaporator + (ΔP/γ)condenser
The pump power is calculated by dividing the pump head by the pump efficiency:
Pump power = Pump head / pump efficiency
The cost per 1000 hours of operation for both pumps is found by multiplying the pump power by the cost of electricity:
Cost = Pump power × cost of electricity × 1000
This approach allows us to determine the pump head, power, and cost of operation for both pumps in the chilled water system.
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Can you please write me an introduction and conclusion about Automobile Exterior ( front and back suspension, battery holder & radiator, front exhaust, grill, doors AC pipes)I am taking a course in Automobile Exterior
The automobile exterior is an integral part of a vehicle, encompassing various components that contribute to its functionality and aesthetics. Understanding these components is crucial for anyone studying automobile exterior design and engineering.
The automobile exterior is designed to ensure optimal performance, safety, and visual appeal. The front and back suspension systems play a vital role in providing a smooth and comfortable ride by absorbing shocks and vibrations. They consist of springs, shock absorbers, and various linkages that connect the wheels to the chassis.
The battery holder and radiator are essential components located in the engine compartment. The battery holder securely houses the vehicle's battery, while the radiator helps maintain the engine's temperature by dissipating heat generated during operation.
The front exhaust system is responsible for removing exhaust gases from the engine and minimizing noise. It consists of exhaust pipes, mufflers, and catalytic converters.
The grill, positioned at the front of the vehicle, serves both functional and aesthetic purposes. It allows airflow to cool the engine while adding a distinctive look to the vehicle's front end.
In conclusion, studying the automobile exterior is crucial for understanding the design, functionality, and performance of a vehicle. Components like suspension systems, battery holders, radiators, exhaust systems, grills, doors, and AC pipes all contribute to creating a safe, comfortable, and visually appealing automotive experience. By comprehending these elements, individuals can gain insights into the intricate workings of automobiles and contribute to their improvement and advancement in the field of automobile exterior design and engineering.
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To achieve maximum power transfer between a 44 Ω source and a load ZL (ZL > ZG) using a transmission line with a characteristic impedance of 44 Ω, an inductor with a reactance of 82 Ω is connected in series with the source. Determine the distance from the load, ZL, in terms of wavelengths where the inductor should be connected. Length = λ
The inductor should be connected at a distance of 2 wavelengths from the load, ZL, to achieve maximum power transfer.
To determine the distance, we need to consider the conditions for maximum power transfer. When the characteristic impedance of the transmission line matches the complex conjugate of the load impedance, maximum power transfer occurs. In this case, the load impedance is ZL, and we have ZL > ZG, where ZG represents the generator impedance.
Since the transmission line has a characteristic impedance of 44 Ω, we need to match it to the load impedance ZL = 44 Ω + jX. By connecting an inductor with a reactance of 82 Ω in series with the source, we effectively cancel out the reactance of the load impedance.
The electrical length of the transmission line is given by the formula: Length = (2π / λ) * Distance, where λ is the wavelength. Since the inductor cancels the reactance of the load impedance, the transmission line appears purely resistive. Hence, we need to match the resistive components, which are 44 Ω.
For maximum power transfer to occur, the inductor should be connected at a distance of 2 wavelengths from the load, ZL.
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The company is expanding it shop floor operation to fulfill more demand for producing three new t-shirt type: W,X and Z. The order for the new t-shirt is W=52,000,X=65,000 and Z=70,000 unit/year. The production rate for the three t-shirts is 12,15 and 10/hr. Scrap rate are as follows: W=5%,X= 7% and Z=9%. The shop floor will operate 50 week/year, 10 shifts/week and 8 hour/shift. It is anticipated that the machine is down for maintenance on average of 10% of the time. Set-up time is assumed to be negligible. Before the company can allocate any capital for the expansion, as an engineer you are need in identifying how many machines will be required to meet the new demand. In determining the assessment of a process, process capability can be used. Elaborate what it is meant by the term process capability.
Hence, process capability is essential for ensuring that the products produced are of high quality and meet the customer's requirements.
Process capability refers to the ability of a process to consistently deliver a product or service within specification limits.
The process capability index is the ratio of the process specification width to the process variation width.The higher the capability index, the more efficient and capable the process is, and the less likely it is that the output will be out of tolerance.
It determines the stability of the process to produce the products as per the given specifications.
Process capability can be measured using the Cp and Cpk indices, which are statistical indices that indicate the process's ability to produce a product that meets the customer's specifications.
Cp is calculated using the formula
Cp = (USL-LSL) / (6σ).
Cpk is calculated using the formula
Cpk = minimum [(USL-μ)/3σ, (μ-LSL)/3σ].
The above formulas measure the capability of the process in relation to the specification limits, which indicate the range of values that are acceptable for the product being produced.
In order to ensure that the process is capable of producing products that meet the customer's specifications, the Cp and Cpk indices should be greater than 1.0.
Process capability is a statistical measure of the process's ability to produce a product that meets customer specifications.
It is a measure of the ability of a process to deliver a product or service within specified limits consistently. It determines the stability of the process to produce the products as per the given specifications.
Process capability can be measured using the Cp and Cpk indices, which are statistical indices that indicate the process's ability to produce a product that meets the customer's specifications.
The higher the capability index, the more efficient and capable the process is, and the less likely it is that the output will be out of tolerance.
In order to ensure that the process is capable of producing products that meet the customer's specifications, the Cp and Cpk indices should be greater than 1.0.
Process capability is a statistical measure of the process's ability to produce a product that meets customer specifications.
The Cp and Cpk indices are statistical indices that indicate the process's ability to produce a product that meets the customer's specifications.
The higher the capability index, the more efficient and capable the process is, and the less likely it is that the output will be out of tolerance.
Hence, process capability is essential for ensuring that the products produced are of high quality and meet the customer's requirements.
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QUESTION 24
Which of the followings is true? Given an RC circuit: resistor R-capacitor C in series. The output voltage is measured across C, an input voltage supplies power to this circuit. To find the transfer function of the RC circuit with respect to input voltage, the relationship between:
A. input voltage and resistor voltage is required.
B. output voltage and current is required.
C. output voltage and resistor voltage is required.
D. input voltage and current is required.
The true statement among the options provided is: C. To find the transfer function of the RC circuit with respect to the input voltage, the relationship between the output voltage and the resistor voltage is required. Option C is correct.
In an RC circuit, the transfer function represents the relationship between the input voltage and the output voltage. It is determined by the circuit components and their configuration. The voltage across the resistor is related to the output voltage, and therefore, understanding the relationship between the output voltage and the resistor voltage is necessary to derive the transfer function.
The other options are not true:
A. The relationship between the input voltage and the resistor voltage is not directly relevant for determining the transfer function of the RC circuit.
B. Although the output voltage and current are related in an RC circuit, the transfer function is specifically concerned with the relationship between the input voltage and the output voltage.
D. While the input voltage and current are related in an RC circuit, the transfer function focuses on the relationship between the input voltage and the output voltage.
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Propulsions students have conducted work to come up with new compressor, whose total pressure ratio is 29. Which has been designed to mach number of 0.8
The engine draws air through inlet at 119 kg/s.
The flight static conditions are 24 kpa and 24 deg C. The specific heat ratio of air and constant pressure specific capacity of air are 1.4 and 1006 J/Kg K respectively. If air is compressed isentropically in compressor then calculate the ideal power in MW required to drive compressor.
please provide complete solution asap because it is urgent and will do thumbs up for sure.
The ideal power required to drive the compressor is 60.7 MW.
To calculate the ideal power required to drive the compressor, we can use the isentropic compression process. The total pressure ratio (PR) is given as 29, and the Mach number (Ma) is given as 0.8. The mass flow rate (ṁ) of air through the inlet is given as 119 kg/s.
The flight static conditions include a pressure of 24 kPa and a temperature of 24°C. The specific heat ratio (γ) of air is 1.4, and the constant pressure specific heat capacity (Cp) of air is 1006 J/kg K.
First, we need to calculate the stagnation temperature (T0) at the inlet. We can use the following equation:
T0 = T + (V^2 / (2 * Cp))
where T is the temperature in Kelvin and V is the velocity. Since the Mach number (Ma) is given, we can calculate the velocity using the equation:
V = Ma * (γ * R * T)^0.5
where R is the specific gas constant for air.
Next, we can calculate the stagnation pressure (P0) at the inlet using the following equation:
P0 = P * (T0 / T)^(γ / (γ - 1))
where P is the pressure in Pascal.
Now, we can calculate the total temperature (Tt) at the compressor exit using the equation:
Tt = T0 * (PR)^((γ - 1) / γ)
Finally, we can calculate the ideal power (P_ideal) required to drive the compressor using the equation:
P_ideal = ṁ * Cp * (Tt - T)
Substituting the given values into the equations and performing the calculations, we find that the ideal power required to drive the compressor is 60.7 MW.
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Implement the following Boolean function with a) a multiplexer
and
b) a decoder: (, , ,) = Π(2,6,11)
With multiplexer andn a decoder: (, , ,), we can see that the Boolean function Π(2,6,11) can be implemented using a decoder
The Boolean function Π(2,6,11), it can be implemented with both multiplexer and decoder. Let's consider both cases below:
a) Using Multiplexer:Let's assume that we have three variables as inputs A, B and C for the Boolean function. Since we have three inputs, we need to use an 8:1 multiplexer which will produce a single output f.For a 3-input multiplexer, the general equation of the output is given by:
f= (ABC . d0) + (ABC . d1) + (ABC . d2) + (ABC . d3) + (ABC . d4) + (ABC . d5) + (ABC . d6) + (ABC . d7)
where d0, d1, d2, … d7 are the data inputs.
Since we have 3 inputs, we only need to use inputs d d1, d3 and set them to 0, 1, and 1, respectively. These values will be fed into the multiplexer as shown below:Input A will be connected to the selector inputs S1 and S0.Input B will be connected to the selector input S2.Input C will be directly connected to each of the 8 data inputs d to d7.
Therefore, we can conclude that the Boolean function Π(2,6,11) can be implemented using a multiplexer.
b) Using Decoder:In this implementation, we can use a 3-to-8 line decoder which will produce eight outputs. Out of these eight outputs, we will set three of them to logic 1 which correspond to the minterms of the Boolean function
. Let's assume that the three outputs which correspond to minterms are Y2, Y6, and Y11.
Then, we can write the Boolean function as:f = Y2 + Y6 + Y11
Thus, we can see that the Boolean function Π(2,6,11) can be implemented using a decoder
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QUESTION 22 Which of the followings is true? The superposition theorem typically refers to O A. time-variant. O B. non-linearity. O C. linearity. O D. None of the given options. QUESTION 23 Which of the followings is true? For the generic PM carrier signal, the phase deviation is defined as a function of the O A. message because it resembles the same principle of FM. O B. message because the instantaneous phase is a function of the message frequency. O C. message frequency. O D. message.
The correct option is B, as the instantaneous phase is a function of the message frequency.
Explanation: Superposition Theorem is a fundamental concept applied in electrical engineering. It is used to analyze circuits which are linear, means that the voltage and current entering and leaving the circuit elements are directly proportional.
According to Superposition Theorem, if there is more than one source present in a circuit, then the current or voltage through any part of the circuit is equal to the sum of the currents or voltages produced by each source individually. The superposition theorem typically refers to linearity. Message because the instantaneous phase is a function of the message frequency.
Explanation: In a phase modulated signal, the carrier phase is varied according to the message signal. The extent of phase variation is called Phase deviation It is defined as the change in the carrier phase angle over the course of one modulation cycle.
In PM modulation, the phase deviation is proportional to the amplitude of the modulating signal.
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The equation W = fvdp holds good for work-absorbing machine like a pump or a compressor O work-producing machine like an engine or turbine O none of the mentioned O both of the mentioned
The equation W = fvdp holds good for work-producing machines like an engine or turbine.
In these machines, work is produced by converting the energy of a fluid or gas into mechanical work. The equation represents the work done (W) by the machine, which is equal to the product of the force (f) applied, the displacement (d) over which the force is applied, and the pressure (p) exerted by the fluid or gas. This equation is derived from the basic definition of work. For work-absorbing machines like pumps or compressors, the equation does not hold because these machines consume energy to perform work, rather than producing it.
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_____ strive to align organizational structures with value-adding business processes. A)
Process-oriented organizations
B)
Core business processes
C)
Functional area information sysems
D)
Strategic management processes
A) Process-oriented organizations strive to align organizational structures with value-adding business processes.
Process-oriented organizations are characterized by their focus on business processes as the primary unit of analysis and improvement. They understand that value is created through the effective execution of interconnected and interdependent processes.
By aligning their organizational structures with value-adding business processes, process-oriented organizations ensure that the structure supports the efficient flow of work and collaboration across different functional areas. This alignment allows for better coordination, integration, and optimization of processes throughout the organization.
Core business processes, on the other hand (option B), refer to the fundamental activities that directly contribute to the creation and delivery of value to customers. Functional area information systems (option C) are specific information systems that support the operations of different functional areas within an organization. Strategic management processes (option D) involve the formulation, implementation, and evaluation of an organization's long-term goals and strategies.
While all of these options are relevant to organizational structure and processes, it is specifically process-oriented organizations (option A) that prioritize aligning structures with value-adding business processes.
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4) Solve the initial value problem y" + 2y’ +10y = f(t), y(0)=0, y’(0)=1 where 10 0
Given,y" + 2y' + 10y = f(t)y(0) = 0y'(0) = 1Now, the characteristic equation is given by: m² + 2m + 10 = 0Solving the above quadratic equation we get,m = -1 ± 3iSubstituting the value of m we get, y(t) = e^(-1*t) [c1 cos(3t) + c2 sin(3t)]
Therefore,y'(t) = e^(-1*t) [(-c1 + 3c2) cos(3t) - (c2 + 3c1) sin(3t)]Now, substituting the value of y(0) and y'(0) in the equation we get,0 = c1 => c1 = 0And 1 = 3c2 => c2 = 1/3Therefore,y(t) = e^(-1*t) [1/3 sin(3t)]Now, the homogeneous equation is given by:y" + 2y' + 10y = 0The solution of the above equation is given by, y(t) = e^(-1*t) [c1 cos(3t) + c2 sin(3t)]Hence the general solution of the given differential equation is y(t) = e^(-1*t) [c1 cos(3t) + c2 sin(3t)] + (1/30) [∫(0 to t) e^(-1*(t-s)) f(s) ds]Therefore, the particular solution of the given differential equation is given by,(1/30) [∫(0 to t) e^(-1*(t-s)) f(s) ds]Here, f(t) = 10Hence, the particular solution of the given differential equation is,(1/30) [∫(0 to t) 10 e^(-1*(t-s)) ds]Putting the limits we get,(1/30) [∫(0 to t) 10 e^(-t+s) ds](1/30) [10/e^t ∫(0 to t) e^(s) ds]
Using integration by parts formula, ∫u.dv = u.v - ∫v.duPutting u = e^(s) and dv = dswe get, du = e^(s) ds and v = sHence, ∫e^(s) ds = s.e^(s) - ∫e^(s) ds Simplifying the above equation we get, ∫e^(s) ds = e^(s)Therefore, (1/30) [10/e^t ∫(0 to t) e^(s) ds](1/30) [10/e^t (e^t - 1)]Therefore, the general solution of the differential equation y" + 2y' + 10y = f(t) is:y(t) = e^(-1*t) [c1 cos(3t) + c2 sin(3t)] + (1/3) [1 - e^(-t)]Here, c1 = 0 and c2 = 1/3Therefore,y(t) = e^(-1*t) [1/3 sin(3t)] + (1/3) [1 - e^(-t)]Hence, the solution to the initial value problem y" + 2y' + 10y = f(t), y(0) = 0, y'(0) = 1 is:y(t) = e^(-1*t) [(1/3) sin(3t)] + (1/3) [1 - e^(-t)]
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13.13 The speed of 75 kW, 600 V, 2000 rpm separately-excited d.c. motor is controlled by a three-phase fully-controlled full-wave rectifier bridge. The rated armature current is 132 A, R = 0.15 S2, and La = 15 mH. The converter is operated from a three-phase, 415 V, 50 Hz supply. The motor voltage constant is KD = 0.25 V/rpm. Assume sufficient inductance is present in the armature circuit to make I, continuous and ripple-free: (a) With the converter operates in rectifying mode, and the machine operates as a motor drawing rated current, determine the value of the firing angle a such that the motor runs at speed of 1400 rpm. (b) With the converter operates in inverting mode, and the machine operates in regenerative braking mode with speed of 900 rpm and drawing rated current, calculate the firing angle a.
To run the motor at a speed of 1400 rpm in rectifying mode, the firing angle (α) needs to be determined.
The firing angle determines the delay in the firing of the thyristors in the fully-controlled rectifier bridge, which controls the output voltage to the motor. The firing angle (α) for the motor to run at 1400 rpm in rectifying mode is approximately 24.16 degrees. To find the firing angle (α), we need to use the speed control equation for a separately-excited DC motor: Speed (N) = [(Vt - Ia * Ra) / KD] - (Flux / KD) Where: Vt = Motor terminal voltage Ia = Armature current Ra = Armature resistance KD = Motor voltage constant Flux = Field flux Given values: Power (P) = 75 kW = 75,000 Voltage (Vt) = 600 V Speed (N) = 1400 rpm Ia (rated) = 132 A Ra = 0.15 Ω KD = 0.25 V/rpm First, we need to calculate the armature resistance voltage drop: Vr = Ia * Ra Next, we calculate the back EMF: Eb = Vt - Vr Since the motor operates at the rated current (132 A), we can calculate the field flux using the power equation: Flux = P / (KD * Ia)
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We have two signals x1(t) = 100 sinc(100t) cos(200πt) and x2(t) = 100 sinc2(100πt).
Calculate the following:
a. The bandwidth of each signal.
b. The average power of each signal.
c. The Nyquist interval to sample each signal.
d. The length of the PCM word if an SNRq is wanted, 50 dB average for x2(t). Consider the
dynamic range of the signal as 2Vpeak.
F. If each signal is transmitted in PCM-TDM and each signal is sampled at the Nyquist rate,
what is the data transmission speed?
a. The bandwidth of a signal is determined by the range of frequencies it contains. For signal x1(t), the bandwidth can be found by examining the frequency components present in the signal.
The signal x1(t) has a sinc function modulated by a cosine function. The main lobe of the sinc function has a bandwidth of approximately 2B, where B is the maximum frequency contained in the signal. In this case, B = 200π, so the bandwidth of x1(t) is approximately 400π. For signal x2(t), the bandwidth can be determined by the main lobe of the sinc^2 function. The main lobe has a bandwidth of approximately 2B, where B is the maximum frequency contained in the signal. In this case, B = 100π, so the bandwidth of x2(t) is approximately 200π.
b. The average power of a signal can be calculated by integrating the squared magnitude of the signal over its entire duration and dividing by the duration. The average power of x1(t) can be calculated by integrating |x1(t)|^2 over its duration, and similarly for x2(t).
c. The Nyquist interval is the minimum time interval required to accurately sample a signal without any loss of information. It is equal to the reciprocal of twice the bandwidth of the signal. In this case, the Nyquist interval for x1(t) would be 1/(2 * 400π) and for x2(t) it would be 1/(2 * 200π).
d. The length of the PCM word is determined by the desired signal-to-noise ratio (SNR) and the dynamic range of the signal. Without specific information about the desired SNRq, it is not possible to determine the length of the PCM word for x2(t).
e. If each signal is transmitted in PCM-TDM (Pulse Code Modulation - Time Division Multiplexing) and each signal is sampled at the Nyquist rate, the data transmission speed would depend on the number of signals being multiplexed and the sampling rate. Without knowing the specific sampling rate or number of signals, it is not possible to determine the data transmission speed.
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Which of these should your broker shipper contract include
A. Your credentials that allow you to operate as a carrier as well as a broker
B. A reassurance of exclusively
C. Your brokerage credentials
D. A reassurance that the shipper is committing to give you a certain volume of freight
The following terms should be included in the broker-shipper contract:
A. Your credentials that allow you to operate as a carrier as well as a broker.
B. A reassurance of exclusively.
C. Your brokerage credentials.
So, the correct answer is A, B and C
When a broker is asked to transport a shipment, they must create a contract between themselves and the carrier, ensuring that both parties comprehend the task at hand. A broker-shipper contract contains numerous terms, which include but are not limited to:
Brokerage credentials.
Your credentials that allow you to operate as a carrier as well as a broker.
A reassurance of exclusivity.
Hence, the answer is A, B and C.
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A hydraulic turbine running at 1700 rpm at a head of 70 ft. has an efficiency of 90%. The flow is 65 ft^3 per sec.
a)Calculate the specific speed of the turbine
b)What would be the corresponding changes in flow, speed and brake power if the turbine will operate at a head of 160 ft?
c) If the runner diameter will be twice that of the original, what will be the new flow, speed and brake power?
The specific speed of the turbine is 242.76.
The specific speed of a turbine is calculated using the formula Ns = N √(Q/H^(3/4)), where N is the speed in rpm, Q is the flow rate in cubic feet per second, and H is the head in feet. By plugging in the given values, we can calculate the specific speed of the turbine as follows:
Ns = 1700 √(65/70^(3/4)) = 242.76
When the turbine operates at a head of 160 ft instead of 70 ft, the corresponding changes would be as follows:
Flow: The flow rate remains constant, so it would still be 65 ft^3 per sec.
Speed: To maintain the same specific speed (Ns), the speed would need to change. Using the formula N = Ns √(H/Q^(3/4)), we can calculate the new speed:
N = 242.76 √(160/65^(3/4)) ≈ 2882.72 rpm
Brake Power: The brake power is proportional to the product of head and flow rate. Therefore, the new brake power can be calculated as follows:
P = (160/70) * (65) ≈ 148.57 ft-lb/sec
If the runner diameter is twice that of the original, the new flow, speed, and brake power can be determined using the laws of similarity. According to the affinity laws:
Flow: The flow rate is directly proportional to the runner diameter. Therefore, the new flow rate would be:
New Flow = 2 * 65 = 130 ft^3 per sec
Speed: The speed is inversely proportional to the runner diameter. Hence, the new speed would be:
New Speed = (Original Speed) * (Original Diameter) / (New Diameter)
= 1700 * 1 / 2
= 850 rpm
Brake Power: The brake power is proportional to the cube of the runner diameter. Therefore, the new brake power can be calculated as follows:
New Brake Power = (Original Brake Power) * (New Diameter^3) / (Original Diameter^3)
= (70) * (2^3) / (1^3)
= 560 ft-lb/sec
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A DC voltmeter (scale set to 20 V) is used to measure the voltages across a resistor (4700 resistor with a 10% tolerance). The voltmeter displays a true voltage of 12 V when measuring the input to the resistor, and a voltage of 9 V when measuring its output to ground. The voltmeter has an accuracy of approximately 5%
The voltmeter has an accuracy of approximately 5%, which means the measured value can deviate by up to 0.6 V from the true value of 12 V.
To determine the accuracy of the voltmeter and the actual voltage across the resistor, we can use the given information.
First, let's calculate the accuracy of the voltmeter:
The voltmeter has an accuracy of approximately 5%. This means that the measured value can deviate by up to 5% from the true value. Since the voltmeter displays a true voltage of 12 V, the maximum allowable deviation is 5% of 12 V, which is 0.05 * 12 V = 0.6 V.
Next, let's calculate the actual voltage across the resistor:
The voltmeter displays 12 V when measuring the input to the resistor and 9 V when measuring the output to ground. The voltage difference between the input and output is 12 V - 9 V = 3 V.
However, we need to take into account the tolerance of the resistor. The resistor has a tolerance of 10%, which means its actual resistance can deviate by up to 10% from the nominal value.
The nominal resistance of the resistor is 4700 Ω. The maximum allowable deviation is 10% of 4700 Ω, which is 0.1 * 4700 Ω = 470 Ω.
Now, let's calculate the range of possible resistances:
Minimum resistance = 4700 Ω - 470 Ω = 4230 Ω
Maximum resistance = 4700 Ω + 470 Ω = 5170 Ω
Using Ohm's Law (V = I * R), we can calculate the range of currents:
Minimum current = 3 V / 5170 Ω ≈ 0.000579 A (or 0.579 mA)
Maximum current = 3 V / 4230 Ω ≈ 0.000709 A (or 0.709 mA)
Therefore, the actual voltage across the resistor can be calculated using Ohm's Law:
Minimum actual voltage = 0.000579 A * 4700 Ω ≈ 2.721 V
Maximum actual voltage = 0.000709 A * 4700 Ω ≈ 3.334 V.
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1. Of the following statements about turbo-generators and hydro-generators, ( ) is correct. A. A hydro-generator usually rotates faster than a turbo-generator in normal operations. B. A hydro-generator usually has more poles than a turbo-generator. C. The excitation mmf of turbo-generator is a square wave spatially. D. The field winding of hydro-generator is supplied with alternating current.
Hydro-generators and turbo-generators are both types of electric generators that convert mechanical energy into electrical energy. They both operate on the principle of electromagnetic induction.
They are used to generate electricity in power plants. Here are the explanations of the options:
A. A hydro-generator usually rotates faster than a turbo-generator in normal operations. This statement is not correct because the speed of a generator depends on its design, load, and the availability of resources.
B. A hydro-generator usually has more poles than a turbo-generator. This statement is correct. Hydro-generators have more poles than turbo-generators. The number of poles in a generator determines its speed and power output.
C. The excitation mmf of turbo-generator is a square wave spatially. This statement is not correct. The excitation mmf of a turbo-generator is sinusoidal in nature.
This statement is correct. The field winding of a hydro-generator is supplied with alternating current. It is used to generate a rotating magnetic field that induces voltage in the stator windings of the generator.
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Emitter biased amplifier design (a) Draw the circuit of a single transistor emitter-biased amplifier using a potential divider at the base. (b) Choose suitable values from the E24 series (see front page) for the emitter and collector resistors, given these requirements: • Power Supply = 15V • Quiescent emitter current le = 2mA Quiescent emitter voltage Ve = 4.3V (c) Choose suitable E24 values for the base bias resistors RB1 RB2 using the design rule I_divider ≥ I_B. Assume that the available transistor has a current gain β of at least 300, and that V_BE is 0.7V at 2mA. (d) The required small-signal gain is -30 and the output will be connected to a load resistance of 6.8k.. Show how you can add components to achieve this target. Ignore Early effect in your calculations. (e) With the signal gain set as in part (d), calculate the input resistance of the amplifier as seen by a signal source
The complete circuit looks as shown below.(e)The formula for calculating the input resistance of the amplifier as seen by a signal source is given by Rin = β * ReRin = 300 * 400 = 120,000 Ω = 120 KΩTherefore, the input resistance of the amplifier is 120 KΩ.
(a)The circuit diagram of an emitter biased amplifier with a potential divider at the base is shown below:(b)The formula used to calculate the value of emitter resistance is:VR1
= R2(Vcc/(Vcc + Vbe))Ve
= Ie * ReVR1
= Ve - VeR 1
= (Ve - Vbe) * Re/IeGiven Vcc
= 15V, Vbe
= 0.7V, Ie
= 2mA, and Ve
= 4.3V,Re
= 0.8/0.002
= 400ΩR1
= (Ve - Vbe) * Re/Ie
= (4.3 - 0.7) * 400 / 0.002
= 1,320,000Ω
= 1.32 MΩ
The closest E24 value is 1.3 MΩ, which can be used for R1. The collector resistance can be chosen as 3.9 kΩ from the E24 series since it meets the requirements.(c)Using the equation RB1
= (β+1)RB2 and the design rule Idiv ≥ IB, we have IB
= IE / βIB
= 2/300
= 0.0067 mARB2
= (VBE / IB)RB2
= 0.7 / 0.0000067RB2
= 104,478 Ω
= 104 KΩThe closest E24 value is 100KΩ, which can be used for RB2RB1
= (β+1)RB2
= (300+1) * 100,000
= 30,100,000 Ω
= 30.1 MΩThe closest E24 value is 30 MΩ, which can be used for RB1.(d)The formula used to calculate the voltage gain is given by the formula Av
= - RC/ReAv
= -30The formula for calculating the required collector resistance can be obtained by substituting the values into the above equation.RC / Re
= 30RC
= 30 * Re
= 30 * 400
= 12,000 Ω
= 12 kΩA 12 kΩ resistor can be used for RC. For bias stabilization, a 100μF capacitor and a 1 kΩ resistor can be used. The complete circuit looks as shown below.(e)The formula for calculating the input resistance of the amplifier as seen by a signal source is given by Rin
= β * ReRin
= 300 * 400
= 120,000 Ω
= 120 KΩ
Therefore, the input resistance of the amplifier is 120 KΩ.
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