Engineering College

## Answers

**Answer 1**

At t = 0.70 ns and y = 26.2 cm, the **magnetic field intensity** is: 3.19 * 10⁷ A/m.

How to find the Magnetic Field Intensity?

In a lossless medium, the relationship between electric field intensity (E) and magnetic field intensity (H) in an electromagnetic wave is given by the expression:

H = E / Z

where:

Z is the **wave impedance** of the medium

The formula to find this impedance is:

Z = √(μ/ε)

Where:

μ is the medium's **permeability**

ε is the **permittivity**

In this case, the medium is **non-magnetic**, and as such the permeability (μ) is equal to the permeability of free space (μ₀ = 4π * 10⁻⁷T·m/A). The **dielectric constant** (εᵣ) of the medium is given as 16.

Thus, the wave impedance (Z) is calculated as:

Z = √(μ₀/εᵣ)

Z = √((4π * 10⁻⁷) / 16)

Z ≈ 3.54 * 10⁻⁸ T·m/A

Finally, the **magnetic field intensity** (H) using the given electric field intensity (E) at the specified time and position is calculated as:

H = E/Z

H = (1131 V/m)/(3.54 * 10⁻⁸) T·m/A)

H ≈ 3.19 * 10⁷ A/m

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## Related Questions

A straight radial centrifugal compressor is designed to provide a pressure ratio of (P03 / P-01 = 2.8). The slip factor is 0.85 and the compressor efficiency is 82%. If the outer radius of the impeller r2 = 0.1 m and the radial component of the velocity at the exit of the rotor is 120 m/s:

a) Determine the rotating speed of the rotor.

b )Determine the specific work required to drive the compressor.

c) If the inlet total pressure is 100 kPa and the total temperature is 30 oC and the Hight of the impeller at the tip is h= 0.01 m, find the flowrate of air consider Cp = 1.02 kJ/kg. K and γ = 1.4. assume constant total pressure in the diffuser

The compressor in problem#1 is driven with a radial turbine on common shaft. Consider the air flow rate to be the same as for the compress find:

d) the required impeller outer diameter for the turbine.

e) The pressure ratio across the turbine if the inlet temperature is 650 oC and considering constant Cp = 1.12 kJ/kg.K and = 1.35. and the turbine efficiency is 87 %

f)If the required exit total pressure is to be 105 kPa, what would be the required inlet pressure ?

### Answers

a) The** rotating speed **of the rotor can be determined by using the slip factor and the pressure ratio.b) The specific work required to drive the compressor can be calculated using the pressure ratio, compressor efficiency, and the specific heat capacity of the air.

** How can the rotating speed of the radial centrifugal compressor be determined?**

a) The rotating speed of the rotor can be determined using the formula: ω = Vr2 / r2, where ω is the rotational speed, Vr2 is the radial component of **velocity **at the exit of the rotor, and r2 is the outer radius of the impeller.

b) The specific work required to drive the compressor can be calculated using the equation: Ws = Cp ˣ (T03 - T01) / ηc, where Ws is the specific work, Cp is the specific heat **capacity **of air, T03 and T01 are the total temperatures at the exit and inlet respectively, and ηc is the compressor efficiency.

c) The flow rate of air can be found using the equation: m_dot = ρ * A * Vr2, where m_dot is the mass flow rate, ρ is the density of air, A is the cross-sectional area of the impeller at the exit, and Vr2 is the radial component of velocity at the exit of the rotor.

d) The required impeller outer diameter for the turbine can be determined using the formula: D = 2 ˣ r2, where D is the impeller outer diameter.

e) The pressure ratio across the **turbine **can be calculated using the equation: P04 / P-05 = (T04 / T-05)^(γ / (γ - 1)), where P04 and P-05 are the total pressures at the exit and inlet respectively, T04 and T-05 are the total temperatures at the exit and inlet respectively, γ is the specific heat ratio, and Cp is the specific heat capacity.

f) The required inlet pressure can be calculated using the equation: P01 = P04 / (P04 / P-05) ˣ P05, where P01 is the inlet pressure, P04 is the exit total pressure, P-05 is the required exit total pressure, and P05 is the known inlet total pressure.

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A very old air cooler was designed to chill 64°C air flowing at Uav = 30 m/s, fully developed, in a 1 m length of 8 cm I.D. smooth, highly conducting tubing. The refrigerant was the now-banned Freon 12 flowing in the opposite direction at Uav 0.5 m/s, within eight smooth 1 cm I.D. tubes equally spaced around the outside of the large tube. The Freon entered at -15°C and was fully de- veloped over almost the entire length. Determine the exiting air temperature, assuming that solder provides perfect thermal contact between the small tubes and the large tube and ignoring conduc- tion resistance in the tube walls. Criticize the heat exchanger and propose a better design.

### Answers

The **temperature **of air **entering **the heat exchanger, T1 = 64 °The velocity of air entering the heat exchanger, V1 = 30 m/diameter of the heat exchanger, D = 0.08 length of the heat exchanger.

Temperature of the **refrigerant **entering the heat exchanger, T3 = -15 °Cow, we need to calculate the temperature of the air leaving the heat exchanger. Let us consider the rate of heat transfer between the hot air and the cold refrigerant.

The **velocity **of refrigerant is quite low as compared to the velocity of air, therefore, the heat transfer coefficient of refrigerant, h2 will be quite small and can be neglected. Therefore, we have [tax]= m × Cp × (T2 – T1) = m × L × h1[/tax]For the air side heat transfer coefficient.

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Water enters the boiler of a steady-flow Carnot engine as a saturated liquid at 2,750 kPa and leaves with a quality of 0.88. Steam leaves the turbine at a pressure of 150 kPa. Show the cycle on a T-s diagram relative to the saturation lines, and determine (a) the thermal efficiency, (b) the quality at the end of the isothermal heat-rejection process, and (c) the net work output in kJ/kg.

### Answers

A **Carnot engine** operates on a **reversible cycle** and is known for its maximum theoretical efficiency. In this case, water enters the boiler of the Carnot engine as a saturated liquid at 2,750 kPa and leaves with a quality of 0.88. The steam then goes through the turbine and exits at a pressure of 150 kPa.

On a T-s diagram, the cycle starts at the saturated liquid line in the boiler and follows the constant **pressure** process until the steam reaches a quality of 0.88. From there, the cycle continues with an isentropic expansion in the turbine until the steam reaches a pressure of 150 kPa. The cycle is completed with an isothermal compression process at 150 kPa until the steam reaches the saturated liquid line again.

To determine the** thermal efficiency** of the Carnot engine, we need to calculate the heat input and the heat output. The heat input is given by the enthalpy difference between the initial and final states of the boiler process, while the heat output is given by the **enthalpy** difference between the initial and final states of the isothermal heat-rejection process. The thermal efficiency is then calculated as the ratio of the net work output to the heat input.

To find the quality at the end of the isothermal heat-rejection process, we can use the fact that it is isothermal and at a constant pressure. By locating the final state on the **T-s diagram**, we can read the quality value from the saturated liquid line.

Finally, the net work output can be determined by calculating the difference between the specific enthalpies at the initial and final states of the turbine process.

In conclusion, the given Carnot cycle can be represented on a T-s diagram. The thermal efficiency can be calculated using the ratio of net work output to heat input. The quality at the end of the isothermal heat-rejection process can be found by locating the final state on the T-s diagram, and the net work output can be determined by calculating the difference in specific enthalpies at the initial and final states of the turbine process.

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Four masses m₁, m2, m3 and m4 are 200 kg, 300 kg, 240 kg and 260 kg respectively. The corresponding radii of rotation are 0.2 m, 0.15 m, 0.25 m and 0.3 m respectively and the angles between successive masses are 45°, 75⁰ and 135º. Find (a) graphically and (b) analytically, the position and magnitude of the balance mass required, if its radius of rotation is 0.2 m.

### Answers

The position and magnitude of the balance mass required, if its **radius of rotation **is 0.2 m is -2597.959 kg.

To find the position and magnitude of the balance mass required, we can start by analyzing the graphical approach and then move on to the analytical approach.

(a) Graphical Approach:

Step 1: Draw a line representing the radius of rotation of the balance mass (0.2 m) from the** center of rotation**.Step 2: Place the masses m₁, m₂, m₃, and m₄ on this line at their respective distances from the center of rotation: 0.2 m, 0.35 m, 0.6 m, and 0.9 m.Step 3: Connect the masses with lines to form a polygon.Step 4: Calculate the vector sum of the gravitational forces(G) acting on the masses.Step 5: To balance the system, the net G acting on the balance mass must be zero. Adjust the magnitude and position of the **balance mass** until the net force is zero.

By visually adjusting the magnitude and position of the balance mass, you can find the solution graphically. The position of the balance mass is the point where the **net gravitational force** becomes zero.

(b) Analytical Approach:

Let's denote the mass of the balance mass as m₅, and the radius of rotation as r₅ (0.2 m).

Using the principle of moments, we can set up an equation based on the torques acting on the system. The torques are calculated by multiplying the mass of each object by its distance from the center of rotation and the **acceleration due to gravity** (9.8 m/s²).

The equation for **torques **acting on the system is:

m₁ * g * r₁ + m₂ * g * r₂ + m₃ * g * r₃ + m₄ * g * r₄ + m₅ * g * r₅ = 0

Substituting the given values:

(200 kg * 9.8 m/s² * 0.2 m) + (300 kg * 9.8 m/s² * 0.35 m) + (240 kg * 9.8 m/s² * 0.6 m) + (260 kg * 9.8 m/s² * 0.9 m) + (m₅ * 9.8 m/s² * 0.2 m) = 0

Simplifying the equation and solving for m₅:

392 + 1029 + 1411.2 + 2269.2 + 1.96 * m₅ = 0

5092.4 + 1.96 * m₅ = 0

1.96 * m₅ = -5092.4

m₅ ≈ -2597.959 kg

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Consider matrix N5 2 12 N=

[1 2 4]

[5 1 2]

[3 -1 1]

Calculate the eigenvalue problem (|N|- λ · I) · V = 0 where λ are eigenvalues and V are eigenvectors.

Answer the following questions and provide a Matlab code for the solution. (a) From the setting of the eigenvalue problem [1-λ 2 4]

[5 1-λ 2]

[3 -1 1-λ]

determine the characteristic equation of the matrix

(b) Determine numerical values of the eigenvalues 1. Represent eigenvalues as a vector. (c) Determine numerical values of the eigenvectors V. Represent eigenvectors as a matrix. (d) Matlab code

### Answers

This code uses the built-in** MATLAB function** `eig` to directly compute the eigenvalues and eigenvectors of the matrix N.To solve the eigenvalue problem for the given **matrix**, you can follow these steps:

(a) Determine the characteristic equation of the matrix:

The characteristic equation is obtained by setting the determinant of the matrix (|N|) minus λ times the identity matrix (I) equal to zero.

The matrix N is given as:

[1-λ 2 12]

[5 1-λ 2]

[3 -1 1-λ]

Setting up the** determinant equation**:

|N - λI| = 0

|1-λ 2 12|

|5 1-λ 2|

|3 -1 1-λ|

Expand the determinant:

(1-λ)[(1-λ)(1-λ) - 2(-1)] - 2[5(1-λ) - 3(-1)] + 12[5(-1) - 3(2-λ)] = 0

Simplifying the equation gives the characteristic equation.

(b) Determine numerical values of the eigenvalues:

To find the numerical values of the eigenvalues, solve the** characteristic equation **obtained in step (a). This can be done using numerical methods or by using built-in functions in software like MATLAB. The eigenvalues will be the solutions of the characteristic equation.

(c) Determine numerical values of the eigenvectors:

Once you have the eigenvalues, you can find the corresponding **eigenvectors **by substituting each eigenvalue into the equation (|N - λI|) · V = 0 and solving for the eigenvectors V. Again, this can be done using numerical methods or MATLAB functions.

(d) MATLAB code:

Here's an example MATLAB code to solve the eigenvalue problem:

matlab

% Define the matrix N

N = [1 2 12; 5 1 2; 3 -1 1];

% Solve for eigenvalues and eigenvectors

[V, lambda] = eig(N);

% Eigenvalues

eigenvalues = diag(lambda);

% Eigenvectors

eigenvectors = V;

% Display the results

disp("Eigenvalues:");

disp(eigenvalues);

disp("Eigenvectors:");

disp(eigenvectors);

Note: This code uses the built-in MATLAB function `eig` to directly compute the eigenvalues and eigenvectors of the matrix N.

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The system function of a linear time-invariant system is given by H(z) = (1-z-¹)(1-eʲπ/²-¹)(1-e-ʲπ/2-¹) /(1-0.9ʲ²π/³-¹)(1-0.9e-ʲ²π/³-¹) (a) Write the difference equation that gives the relation between the input x[n] and the output y[n]. (b) Plot the poles and the zeros of H(z) in the complex z-plane. (c) If the input is of the form x[n] = Aeʲφe^ʲω0non, for what values of -π≤ω₀≤π will y[n] = 0?

### Answers

The frequency response **H(e^(jω))** is obtained by substituting z = e^(jω) into the system function H(z). From the given system function, we can calculate H(e^(jω)) and equate its magnitude to zero to find the values of ω₀ that satisfy y[n] = 0.

a. To write the difference equation relating the input **x[n]** and the output y[n] for the given system function H(z), we can expand the denominator and numerator polynomials:

**H(z) **= (1 - z⁻¹)(1 - e^(jπ/2⁻¹))(1 - e^(-jπ/2⁻¹)) / (1 - 0.9e^(j²π/3⁻¹))(1 - 0.9e^(-j²π/3⁻¹))

Expanding further, we have:

H(z) = (1 - z⁻¹)(1 - cos(π/2) - j*sin(π/2))(1 - cos(π/2) + j*sin(π/2)) / (1 - 0.9*cos(2π/3) - j*0.9*sin(2π/3))(1 - 0.9*cos(2π/3) + j*0.9*sin(2π/3))

Simplifying the expressions, we get:

H(z) = (1 - z⁻¹)(1 - j)(1 + j) / (1 - 0.9*cos(2π/3) - j*0.9*sin(2π/3))(1 - 0.9*cos(2π/3) + j*0.9*sin(2π/3))

Multiplying the numerator and denominator, we obtain:

H(z) = (1 - z⁻¹)(1 - j)(1 + j) / (1 - 1.8*cos(2π/3) + 0.81)

Finally, expanding and rearranging, we get the difference equation:

y[n] = x[n] - x[n-1] - j*x[n-1] + j*x[n-2] - 1.8*cos(2π/3)*y[n-1] + 1.8*cos(2π/3)*y[n-2] - 0.81*y[n-1] + 0.81*y[n-2]

b. To plot the **poles** and zeros of H(z) in the complex z-plane, we can factorize the numerator and denominator polynomials:

Numerator: (1 - z⁻¹)(1 - j)(1 + j)

**Denominator**: (1 - 1.8*cos(2π/3) + 0.81)(1 - 0.9*cos(2π/3) - j*0.9*sin(2π/3))(1 - 0.9*cos(2π/3) + j*0.9*sin(2π/3))

The zeros are located at z = 1, z = j, and z = -j.

The poles are located at the roots of the denominator polynomial.

c. To find the values of **ω₀** for which y[n] = 0, we need to analyze the frequency response of the system. By setting the magnitude of H(e^(jω₀)) to zero, we can determine the frequencies at which the output becomes zero.

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design a sequential logic circuit that controls an elevator in a 4 floors building, G,1,2,3 (4 states ). there are 4 switches outside the elevator for each floor a switch and 4 switches inside the elevator (G,1,2 3) . Make sure to mention all the steps required. State diagram, truth table, functions and equations, circuit diagram.

Make sure to indicate each switch for which floor and the four outputs

### Answers

State Diagram: The **state diagram **of the sequential logic circuit for the **elevator **is shown below: Truth Table: The truth table is used to derive the Boolean function for each output.

The truth table is shown below: The truth table can be used to derive the Boolean functions for each output as follows: G1 = X'Y'Z' + X'Y'Z + X'YZ' + XYZ1

= X'Y'Z' + X'Y'Z + XY'Z' + XYZ2

= X'Y'Z' + XY'Z' + XYZ3 = X'Y'Z' + XYZ

Functions and Equations:

The** Boolean functions** for each output can be simplified as follows:

G1 = X'Y'Z + X'YZ' + XYZ1

= X'Y'Z' + X'Y'Z + XY'Z' + XYZ2

= X'Y'Z' + XY'Z + XYZ3 = X'Y'Z' + XYZ

The equations for each output can be derived from the Boolean functions as follows:

G1 = (A'B'C + A'BC' + ABC)1

= (A'B'C' + A'B'C + AB'C' + ABC)2

= (A'B'C' + AB'C + ABC)3

= (A'B'C' + ABC)

Circuit Diagram: In the circuit diagram, the inputs are the switches for each floor, and the outputs are the control signals for the elevator. The circuit consists of four **D flip-flops**, one for each state of the elevator, and combinational logic gates that generate the control signals based on the current state of the elevator and the desired floor.

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If you were pouring wals, in an area of the country where the lemperature would vary wp to 40 degrees in one day, starting at 40 degrees F, which pressure from Table 1 would you choose, and why? a. 70 degree design pressure, bncause the tabies are very conservative b. 70 degree design pressure, because by the time the concrete is placed, a ahould be that temperature c. 50 degree design prossure, because that is what the foreman always uses d. 50 degree design pressure, because in design yout safety is paramount

### Answers

The correct answer is option D: 50 degree design **pressure**, because in design your safety is paramount.

Walls are poured at a specific **pressure **to ensure that they are of the right consistency and density.

The pouring of walls can be influenced by many **variables**, one of which is temperature.

It is imperative to use the appropriate pouring pressure when pouring walls in an area of the country where the temperature fluctuates up to 40 degrees in a single day, starting at 40 degrees F.

The appropriate pressure to be used is a 50-degree design pressure, and this is because, in design, safety is of utmost importance.

Table 1 is a reference table that provides the recommended pouring pressure to be used for a specific job.

It is, however, not recommended to use the **pressure value** in the table blindly, as it is subject to change based on the project's variables.

For instance, the **temperature variation **can significantly affect the pouring pressure, and this is why the 50-degree design pressure should be chosen in this scenario.

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A 8.79 kg uniform solid disk of radius 0.74 m is rolling without slipping on a horizontal surface. The angular acceleartion is 9.37 rad/(ss). Determine the magnitude of disk centre acceleration in m/(ss) (hint The answer should be positive).

### Answers

The equation for calculating the **acceleration **of the center of mass of a uniform disk when it rolls on a **horizontal **surface is given as follows.

Centripetal acceleration = Linear acceleration + Angular acceleration × r Where: r = radius of the uniform solid disk

Angular **acceleration **(α) = 9.37 rad/s^2

Mass (m) = 8.79 kg

Radius (r) = 0.74 m. Therefore;

t = sqrt(90° / α)

= sqrt(90° / 9.37 rad/s^2)

= 3 seconds

Now that we know the angular **velocity **(ω).

we can now find the centripetal acceleration (ac).ac = r × α

Where; r = 0.74 mα = 9.37 rad/s^2ac = 0.74 m × 9.37 rad/s^2 = 6.932 m/s^2

Now we can determine the linear acceleration of the center of **mass **(a).a = r × ω^2

Where;r = 0.74 m

[tex]ω = α × t = 9.37 rad/s^2 × 3 s = 28.11 rad/sa = 0.74 m × (28.11 rad/s)^2 = 586.29 m/s^2. a_net = ac + a = 6.932 m/s^2 + 586.29 m/s^2 ≈ 593.222 m/s^2[/tex]

Therefore, the magnitude of the disk center acceleration in m/(s^2) when a uniform solid disk of radius 0.74 m and mass 8.79 kg is rolling without slipping on a horizontal **surface **is approximately 593.222 m/s^2.

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A capacitor consists of two very long coaxial metallic cylindrical surfaces of radii "a" and "b" (b>a) The dielectric material between the surfaces has a relative permittivity of εᵣ = 2 + 4/r

Determine the capacitance per unit length of this capacitor.

### Answers

Capacitance per unit length is the **capacitance** that exists between the two surfaces of the capacitor per unit length. To calculate this, use the following formula, Capacitance per unit length, where F is the farad, m is the meter, εᵣ is the relative **capacitance** of the dielectric material, b is the radius of the outer cylindrical surface, and a is the radius of the inner cylindrical surface.

Given that the relative permittivity of the **dielectric** material between the surfaces is εᵣ = 2 + 4/r. We can use this to rewrite the formula Capacitance per unit length, We can also express r in terms of a and b by using the ratio r/b = x, where x is between 0 and 1.

Therefore, the capacitance per unit length of the capacitor **consisting** of two very long coaxial metallic cylindrical surfaces of radii a and b (b>a) and a **dielectric** material between the surfaces with a relative permittivity.

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The following head loss data between a low pressure service location and the location of the elevated storage tank was determined: itim during average daily demand condition 13m during peak daily demand condition Ir 16 m during peak hourly demand condition a If the minimum allowable pressure in the distribution system is 250kPa and elevation of low-pressure location is 6m, determine the maximum elevation in mi of the water stored in an elevated tank Write the answer up to three decimals

### Answers

To determine the maximum **elevation **of the water stored in an elevated tank, we need to consider the head loss data and the given conditions.

- Minimum allowable pressure in the distribution system = 250 kPa

- Elevation of the low-pressure location = 6 m

- Head loss during average daily demand condition = 13 m

- Head loss during peak daily demand condition = 16 m

- Head loss during peak hourly demand condition = 19 m

We can calculate the maximum elevation using the following formula:

Maximum elevation = Minimum allowable **pressure **- Head loss during peak hourly demand condition - Elevation of the low-pressure location

Substituting the given values into the formula:

Maximum elevation = 250 kPa - 19 m - 6 m

First, we need to convert the pressure from kPa to **meters **of water column (mwc) since head loss is given in meters.

1 kPa ≈ 0.102 mwc

So, 250 kPa ≈ 250 * 0.102 mwc = 25.5 mwc

Now, substituting the converted **values **into the formula:

Maximum elevation = 25.5 mwc - 19 m - 6 m

Maximum elevation = 25.5 mwc - 25 m

Maximum elevation = 0.5 mwc

Therefore, the maximum elevation of the water stored in the elevated tank is 0.5 meters.

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D: (T) In transformer, the series impedance of the primary and the secondary can be calculated from the short circuit test. E :(T) The circuit of (open circuit test) is magnetic and the (short circuit) is electrical circuit. Electromagnetic induction is the base for the principle of operation of F:

### Answers

D: True. The series impedance of the primary and secondary windings of a **transformer **can be calculated from the short circuit test.

E: False. The open circuit test is an electrical circuit, not a magnetic one.

F: True. Electromagnetic induction is the fundamental principle underlying the operation of a transformer.

A short circuit test can be used to assess the primary and secondary windings of a transformer's series impedance. In this test, the secondary winding is shorted, and a voltage is applied to the primary winding. By measuring the resulting current flowing through the winding and the applied voltage, the series impedance can be calculated using** Ohm's Law** (Z = V/I).

An electrical circuit, not a magnetic one, is used for the open circuit test. In the open circuit test, the secondary winding of the transformer is left open, and a known **voltage** is applied to the primary winding. The purpose of this test is to determine the core losses and magnetizing current of the transformer, providing important information about its no-load characteristics.

A transformer works on the fundamental principle of **electromagnetic **induction. According to this principle, when an alternating current flows through the primary winding, it creates a changing magnetic field, which induces a voltage in the secondary winding. This induced voltage allows for the transfer of electrical energy from the primary winding to the secondary winding.

In conclusion, the short circuit test can be used to determine a transformer's series impedance (Statement D), the open circuit test uses an electrical circuit to measure core losses (Statement E), and the electromagnetic induction principle underpins transformer operation (Statement F).

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(i) How many shear stress components can act on a 3-D object? a) 2 b) 4 c) 5 d) 6 (ii) Which type of stress is plane stress? a) One dimensional b) Two dimensional c) Zero dimensional d) Three dimensional (iii) Principal plane is the plane in which a) Shear stress is maximum b) Normal stress is zero c) Shear stress is zero d) It doesn't depend upon stresses

### Answers

(i) There are six shear stress **components** that can act on a 3-D object.(ii) Plane stress is a type of stress that is two-dimensional. (iii) The principal plane is the plane in which **normal** stress is zero.What is Stress?Stress is a measure of the amount of force that a body is subjected to per unit area. The unit for stress is Pascal (Pa), which is equivalent to 1 N/m².

Stress can be defined in the following ways:Stress = Force/Areaτ = F/A, where τ is the shear stress and F is the force acting in the plane, and A is the area **perpendicular** to the force.In order to identify the stress acting on an object, three types of stresses must be analyzed, including normal stress, shear stress, and **bearing** stress. They are all the stress that acts on an object under a load or force.The answers to your questions are: (i) d) 6(ii) b) Two-dimensional(iii) b) Normal stress is zero.

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0.7 kg of a gas mixture of N₂ and O₂ is inside a rigid tank at 2 bar, 70°C with an initial composition of 24% O₂ by mole. O₂ is added such that the final mass analysis of O2 is 38%. How much O₂ was added? Express your answer in kg.

### Answers

**0.098 kg of O₂** was added to the **gas mixture**.

To determine the amount of O₂ that was added to the gas mixture, we can use the** following** steps:

Convert the initial and **final mass** fractions of O₂ to mass percentages:

Initial mass percentage of O₂ = 24%

Final mass percentage of O₂ = 38%

Calculate the initial mass of the gas mixture:

Initial mass of the gas mixture = 0.7 kg

Calculate the initial mass of O₂ in the gas mixture:

Initial mass of O₂ = Initial mass of the gas mixture * Initial mass percentage of O₂

Initial mass of O₂ = 0.7 kg * 24% = 0.168 kg

Calculate the final mass of O₂ required in the gas mixture:

Final mass of O₂ = Final mass of the gas mixture * Final mass percentage of O₂

Final mass of O₂ = 0.7 kg * 38% = 0.266 kg

Calculate the amount of O₂ that was added:

Amount of O₂ added = Final mass of O₂ - Initial mass of O₂

Amount of O₂ added = 0.266 kg - 0.168 kg = 0.098 kg

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Q5) A work area at bench level is to be illuminated to a value of 300 Ix, using 85 W single fluorescent fittings having an efficacy of 80 lumens/watt. The work area is 10 mx 8 m, the MF is 0.8 and the CU is 0.6. Calculate the number of fittings required.

### Answers

The number of fittings required to **illuminate **a work area at bench level to a value of 300 Ix is 34 fittings. Given:Work area length = 10mWork area width = 8mIllumination level required = 300 Ix Wattage of a single **fluorescent**.

The area is equal to the product of length and width. Area = Length × Width= 10 × 8= 80 m²The total amount of light **required **for the work area can be calculated by multiplying the required illumination level by the area. Light required = Illumination level × Area= 300 × 80= 24000 lm.

The fluorescent fittings required to provide the amount of light required by the work area, divide the total light required by the efficacy of the fitting. Wattage of the fittings = Light required / Efficacy of the fittings= 24000 / 80= 300 WTo account for the **maintenance **factor, divide the total wattage required by the maintenance factor.

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Given a filter with a transmission function: H(z)= 2(1−r 11

z −11

)

(1+r 11

)(1−z −11

)

Where r=0.98 A. Draw the impulse response h[n] of the filter for 0≤n<1001. B. B. Assume sampling frequency fs=2200 Hz. Draw the magnitude of the frequency response of the filter as a function of the measured frequency InHz.

### Answers

A. To draw the **impulse** response h[n] of the filter for 0 ≤ n < 1001, we need to find the inverse z-transform of the given transmission function H(z). By expanding and simplifying the expression, we obtain:

H(z) = 2(1 - r^11 z^(-11))(1 + r^11)(1 - z^(-11))

Using the **inverse z-transform**, we can express H(z) as a sequence h[n]. For this specific filter, the impulse response can be calculated by finding the coefficients of the powers of z in the expression. The impulse response h[n] will have a finite duration from 0 to 1000. **Plotting** **h[n]** will give us the time-domain representation of the filter's response.

B. To draw the magnitude of the frequency response of the filter as a function of the measured **frequency** in Hz, we need to convert the discrete-time frequency to continuous frequency. Given a sampling frequency of fs = 2200 Hz, the frequency range extends from 0 Hz to fs/2 Hz. We can obtain the magnitude response by evaluating the frequency response function H(e^(jω)) at different frequencies in the range 0 Hz to fs/2 Hz. Plotting the magnitude response against the measured frequency will give us the frequency-domain representation of the filter's response.

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Water at 200 C flows through a 30 mm diameter pipe. The loss of head due to fluid friction over a 20 m length of pipe is 1.8 m. Determine.

(a) the average velocity of flow,

(b) the volume flow rate,

(c) the wall shear stress and

(d) the Darcy’s friction factor. Viscosity of water at 200 C is 0.001 Pa-s

### Answers

To determine the required values, we can use the** Darcy-Weisbach equation**, which relates the loss of head due to fluid friction in a pipe to various parameters. The equation is as follows:

Δh = f * (L/D) * (V^2 / 2g)

Where:

Δh = Loss of head due to **fluid friction**

f = **Darcy's friction factor**

L = Length of the pipe

D = Diameter of the pipe

V = Velocity of flow

g = Acceleration due to gravity

Given:

Temperature of water = 20 °C

Pipe diameter (D) = 30 mm = 0.03 m

Loss of head (Δh) = 1.8 m

Length of pipe (L) = 20 m

**Viscosity of water** (µ) = 0.001 Pa-s

Acceleration due to gravity (g) = 9.81 m/s²

(a) Average Velocity of Flow:

The average velocity of flow (V) can be determined by rearranging the Darcy-Weisbach equation and solving for V:

V = √((2 * g * Δh) / (f * (L/D)))

(b) Volume Flow Rate:

The volume flow rate (Q) can be calculated using the formula:

Q = A * V

Where A is the cross-sectional area of the pipe, which can be calculated as:

A = π * (D/2)^2

(c) Wall Shear Stress:

The wall shear stress (τ) can be determined using the relation:

τ = f * (ρ * V^2) / 2

Where ρ is the density of water. For water, ρ is approximately 1000 kg/m³.

(d) Darcy's Friction Factor:

The Darcy's friction factor (f) can be determined using various empirical correlations, such as the Colebrook-White equation or the Moody chart. These correlations involve iterations or interpolation, and their calculations are beyond the scope of a text-based response. However, you can use these methods or consult engineering references to determine the friction factor.

By applying these formulas, you can calculate the required values for (a), (b), (c), and (d) based on the given information.

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QUESTION 1

Which of the followings is true? Comparing PM and FM, if the area under the curve of the message cannot be given in closed form, A. FM becomes mathematically non-converged. B. FM becomes mathematically converged. C. FM becomes mathematically non-converged but PM is converged. D. PM becomes mathematically non-converged. QUESTION 2 Which of the followings is true? For the generic FM carrier signal, the frequency deviation is defined as a function of the O A. message because the instantaneous frequency is a function of the message frequency. B. message. C. message frequency. D. message because it resembles the same principle of PM. QUESTION 3 Which of the followings is true? Given an RL circuit: resistor R-inductor L in series. The output voltage is measured across L, an input voltage supplies power to this circuit. For the transfer function of the RL circuit with respect to input voltage: A. Its magnitude response is independent of R. B. Its magnitude response is independent of L. C. Its magnitude response is inversely proportional to square root of sum of R square and square of product of L and frequency. D. Its magnitude response is proportional to square root of L. QUESTION 4 Which of the followings is true? To convert from sin(x) to cos(x), one would A. add 180 degrees to the angle x. B. add-90 degrees to the angle x. C. add -180 degrees to the angle x. D. add 90 degrees to the angle x.

### Answers

Answer 1Comparing PM and FM, if the area under the **curve **of the message cannot be given in closed form, FM becomes **mathematically **non-converged. Hence, the correct option is (A).

Answer 2For the generic FM carrier signal, the **frequency **deviation is defined as a function of the message because the instantaneous frequency is a function of the message frequency. Hence, the correct option is (A).

Answer 3The magnitude response of the RL circuit with respect to input **voltage **is inversely proportional to square root of sum of R square and square of product of L and frequency.

Hence, the correct option is (C).Answer 4To **convert **from sin(x) to cos(x), one would add 90 degrees to the angle x. Hence, the correct option is (D).Therefore, the correct options are (A), (A), (C), and (D).

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Take a look at the equation below: θ(s) / E(s) = 50 / s(s+20) : = Y(s) / U(s)' Which can be written with form: x (t) = A. x(t) + B.u(t) x(t) = [ x₁ x₂] = [θ θ] and y(t) = θ Design a sliding mode control with these conditions: a) System without setpoint and initial condition # 0 b) Linear Sliding Surface: σ = S.x = [S₁ S₂].x c) Controller structure: u = k₁x₁ + k₂x₂ with k₁ or k₂ is selected between 2 random numbers (which determined on the design structure)

### Answers

To design a** sliding mode control** system for the given equation and conditions, the system should be without a setpoint and **initial condition.** The sliding surface is defined as σ = S.x, where S is a matrix and x represents the system state. The controller structure is u = k₁x₁ + k₂x₂, where k₁ and k₂ are randomly selected numbers.

In sliding mode control, the objective is to drive the system state onto a specific **sliding surface** and keep it there. In this case, since there is no setpoint and initial condition, the system needs to stabilize at the origin.

The sliding surface is defined as σ = S.x, where S is a matrix and x represents the system state. The specific form of S depends on the system dynamics and control objectives. The goal is to design the sliding surface in such a way that it can force the system state onto the desired trajectory.

The controller structure is u = k₁x₁ + k₂x₂, where k₁ and k₂ are randomly selected numbers. The choice of k₁ and k₂ is determined during the design process and depends on factors such as **system stability**, performance requirements, and control objectives.

The sliding mode control **algorithm **operates by continuously adjusting the control input u based on the sliding surface and the system state. The controller drives the system state onto the sliding surface and maintains it there, ensuring robustness to disturbances and uncertainties.

By implementing the sliding mode control with the given conditions, the system can achieve stability and robust performance without a setpoint or initial condition. The specific values of S, k₁, and k₂ would need to be determined through a detailed design process and analysis of the **system dynamics**

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Explain why cetane number is a major property of diesel fuel but not for gasoline. Explain why octane number is a major property of gasoline but not for diesel fuel.

### Answers

Cetane number is a **significant property** of diesel fuel, while octane number is a significant property of gasoline. Here's why: Cetane number is a major property of diesel fuel because it** determines** how well the fuel ignites.

Cetane is a measure of how well diesel fuel ignites when it comes into contact with hot compressed air in a diesel engine's combustion chamber. The cetane number represents the percentage of cetane in the fuel; the higher the number, the more efficiently the fuel ignites. Because diesel engines use compression to ignite fuel, cetane number is a **crucial factor** in diesel fuel quality. Fuels with a high cetane number burn more efficiently and produce less smoke, while fuels with a low cetane number burn less efficiently and produce more smoke.

Octane number is a significant property of gasoline because it determines how well the fuel resists knocking. The octane rating is a measure of a fuel's ability to resist "knocking" or "pinging" during combustion. Knocking is the result of fuel detonation, which produces a distinctive knocking or pinging sound in the engine. The **engine's power **output and efficiency are reduced by knocking. The higher the octane number of a fuel, the more resistant it is to detonation. As a result, **higher-octane** fuels are commonly utilized in high-performance gasoline engines.

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Let’s consider 130 grams of air in a piston–cylinder device. The assembly is also fitted with a fan. Now the system is heated by the amount of 12 kJ heat transfer through a constant-pressure process while the fan is rotating transferring energy to the air. If the initial and final temperatures of the air are 27°C and 127°C, respectively, how much is the work done on the air by the fan in kJ?

### Answers

Given data: Mass of air (m) = 130 grams Heat transferred (Q) = 12 kJ Initial **temperature **of air (T1) = 27°CFinal temperature of air (T2) = 127°CWe are **required **to find the work done on the air by the fan in kJ. Solution: We know that heat transferred to a gas at constant pressure.

() is given by = × × Δwhere is the specific heat at constant pressure and Δ is the change in temperature. Also, the work done (W) on the gas is given by[tex]W = × × Δwhere [/tex]is the specific heat at constant volume.As the process is constant pressure, we use[tex] = × × Δ = + × × Δ∴ = − × × Δ[/tex]Now, specific heat at constant pressure () and at **constant **volume () can be related as = + where is the gas constant.∴ [tex] = − × ( − ) × Δ[/tex]Putting the values of the given data, we get[tex] = 12 kJ − 0.13 kg × (1.005 kJ/kgK − 0.287 kJ/kgK) × (127 − 27)°C = 12 − 1.1044 × 10 = 10.8956 kJ[/tex]Hence, the work done on the air by the fan is 10.8956 kJ (approx) or 10.9 kJ (rounded to one decimal place).Therefore, the work done on the air by the fan in kJ is 10.9 kJ (approx).

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____________ fuel is an alternative fuel for spark-ignition engine, but also can be used in Fuel Cell Electric Vehicles (FCEV) to produce electricity.

Group of answer choices

Hydrogen

biodiesel

Ethanol

JP-8

### Answers

The fuel that is an **alternativ**e fuel for spark-ignition engines and can also be used in Fuel Cell Electric Vehicles (FCEV) to produce **electricity** is hydrogen.

What is hydrogen?

Hydrogen is a colorless, odorless, tasteless, and highly flammable gas that has the highest energy density of any fuel.

It can be used in a variety of ways, including as a fuel for vehicles, in heating systems, and in the production of electricity.

Hydrogen fuel cells convert the **energy** stored in hydrogen fuel directly into electricity, producing only water and heat as byproducts.

This makes them a clean and efficient alternative to fossil fuels.

**Hydrogen **fuel cells can** power **a wide range of vehicles, from cars and trucks to buses and trains.

Hydrogen has great potential as a fuel for transportation, as it produces no greenhouse gases or pollutants when burned. It is also abundant, with hydrogen gas being the most common element in the universe.

However, the production and distribution of hydrogen fuel can be costly and complex, and there are currently few hydrogen fueling stations available for public use.

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In a mixed flow pump 1) Fluid flows along the axis of the machine. 2) Fluid flows along the radial direction through its rotating blades. 3) Axial flow is changed to moderate amount of radial flow.

### Answers

A** mixed-flow pump,** also known as an axial-radial pump or a diagonal pump, is a type of **centrifugal pump** that has a mixed flow impeller design. These pumps are typically used in applications where high flow rates and moderate pressure are required, such as in irrigation systems and stormwater management.

Mixed flow pumps use a combination of axial and **radial flow **to move fluid through the impeller and discharge it at a high velocity. As fluid enters the pump, it flows along the axis of the machine, where it encounters the rotating blades of the impeller. The impeller blades force the fluid to change direction and flow in a moderate amount of radial flow before being discharged out of the pump's outlet.I

n comparison to** pure axial flow** and pure radial flow pumps, mixed flow pumps have a broader operating range. They have higher efficiencies than axial flow pumps, but lower efficiencies than radial flow pumps. Because of their unique impeller design, mixed flow pumps are ideal for applications that require a **combination **of high flow rates and moderate pressure.Drop me a message if you want me to help you out with more information.

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find the teeth number of the bevel gear

gear ratio=2

pressure angle=20 degree

full depth teeth (k=1)

### Answers

The teeth number of the **bevel gear** is approximately 21.

To find the teeth number of the bevel gear, the gear ratio, pressure angle, and full depth teeth (k = 1) are given. Here are the steps to find the teeth number:

Calculate the pitch cone angle of the bevel gear.The pitch cone angle is given as π/2 or 90 degrees for straight bevel gears.

However, for a spiral bevel gear, it will be greater than π/2. This can be calculated using the formula:

Pitch cone angle = arctan (tan (pressure angle) / gear ratio)

For this problem, the gear ratio is given as 2 and the pressure angle is given as 20 degrees.

Pitch cone angle = arctan (tan (20) / 2) = 9.4624 degrees

Calculate the base cone angle of the bevel gear.

The base cone angle is given as the pitch cone angle plus the angle of the tooth face.

For full-depth teeth (k = 1), the angle of the tooth face is equal to the pressure angle. This can be calculated using the formula:

Base cone angle = pitch cone angle + pressure angleFor this problem, the pressure angle is given as 20 degrees.

Base cone angle = 9.4624 + 20 = 29.4624 degrees

Calculate the teeth number of the bevel gear.The teeth number of the **bevel gear **can be calculated using the formula:

Teeth number = (module * reference diameter) / cos (base cone angle)For full-depth teeth (k = 1), the module is equal to the reference diameter divided by the number of teeth.

This can be expressed as:

module = reference diameter / teeth number

Therefore, the formula can be rewritten as:

Teeth number = reference diameter^2 / (module * **pitch *** cos (base cone angle))

For this problem, the module is not given. However, we can assume a module of 1 for simplicity. The reference diameter can be calculated using the formula:Reference diameter = (teeth number + 2) / module

For a module of 1, the reference **diameter **is equal to the teeth number plus 2.

Therefore, the formula can be rewritten as:

Teeth number = (teeth number + 2)^2 / (pitch * cos (base cone angle))

Solving this equation gives the teeth number as approximately 21.

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please use MATLAB to solve NASA is launching a new rocket and its path is required to be y = t’sin(nt) 1) Find actual values for rocket position, velocity and acceleration for the interval of time t = 20 sec. Plot it using Matlab 2) Use 3 different numeric differentiation forms to find estimated velocity and acceleration of the rocket. Use Forward, Backward and Center finite-divided difference with higher accuracy O(ha) 3) Plot actual velocity and acceleration compared with numeric derivatives. Use Matlab. 4) Find the error due to the numeric differentiation. 5) What is your conclusion regarding accuracy?

### Answers

At t = 20 sec, the rocket **position **(y) can be determined using the given formula as:y = t sin(nt)

y = 20 sin(2πt)The position of the rocket at

t = 20 sec is:

y = 20 sin(2π × 20) ≈ -0.08For velocity, we can differentiate the given equation w.r.t. t:y = t sin(nt)Differentiating both sides w.r.t. t gives us:dy/dt = sin(nt) + nt cos(nt)dy/

dt = sin(2πt) + 2πt cos(2πt)At

t = 20 sec, the velocity of the rocket is:

dy/dt = sin(2π × 20) + 2π(20) cos(2π × 20)≈ 4

≈ 125.6637For **acceleration**, differentiating the velocity equation w.r.t. t yields:d2y/dt2 = cos(nt) - n^2 t sin(nt)d2y/dt2

= cos(2πt) - 4π^2t sin(2πt)At t = 20 sec, the acceleration of the **rocket **is:d2y/dt2 = cos(2π × 20) - 4π^2(20) sin(2π × 20)≈ -502.65

ylabel('Acceleration (m/s^2)'); title('Rocket **Acceleration**'); grid on;2) Using 3 different numeric differentiation forms to find estimated velocity and acceleration of the rocket: Using Forward Difference,Backward Difference, and Centered Difference; Forward **Difference **Formulary/dt ≈ (y(t+h) - y(t))/hwhere h is the small change in time.

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Remember to match Adiabatic, ideal gas, Sealed, Rigid. options: 1. Pressure is constant 2. PV=MRT 3. Volume is constant. 4. Mass is constant 5. PV = MRT 6. Q=0 7. W=0

### Answers

**Pressure** is constant - Rigid

PV = MRT - Adiabatic

Volume is constant - Sealed

Mass is constant - **Ideal gas**

PV = MRT - Ideal gas

Q = 0 - Adiabatic

W = 0 - Adiabatic

To match the given options with the appropriate terms:

Pressure is constant - Rigid (In a rigid system, the pressure remains constant.)

PV = MRT - Adiabatic (The adiabatic process follows the** equation **PV = MRT.)

Volume is constant - Sealed (In a sealed system, the volume remains constant.)

Mass is constant - Ideal gas (In an ideal gas, the mass of the gas remains constant.)

PV = MRT - Ideal gas (The ideal gas law equation is PV = MRT.)

Q = 0 - Adiabatic (In an adiabatic process, there is no **heat transfer**, hence Q = 0.)

W = 0 - Adiabatic (In an adiabatic process, there is no work done on or by the system, hence W = 0.)

So, the matching is as follows:

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Pelton and Kaplan turbines are used in power generation. Explain

how these turbines are used in this activity with neat sketches.

### Answers

**Hydroelectric **power generation plants have **turbines **that operate on hydraulic pressure and turn the energy from water into electricity.

The Pelton and Kaplan turbines are two types of turbines that are used in hydroelectric power generation. These two turbines are different in terms of their construction and applications. The **Pelton turbine** is suitable for high heads, and the Kaplan turbine is used for low to medium heads. Both these turbines are used in power generation

.Pelton Turbine: The Pelton turbine has a unique construction that allows it to work in high-head applications. This turbine is used for hydroelectric power generation in mountainous areas where the water head is large. This turbine is not recommended for low-head applications. The basic structure of this turbine consists of a wheel with multiple cups. These cups are arranged symmetrically in a circular pattern. Water is directed onto the cups using nozzles. The high velocity of water from the nozzles impinges on the cups, causing the wheel to rotate. The rotation of the wheel is converted into electrical energy.

**Kaplan Turbine**: The Kaplan turbine is a propeller-type turbine that is used for low to medium heads. This turbine is suitable for applications in areas where the water head is less than 20 meters. The basic structure of the Kaplan turbine consists of a cylindrical turbine shell with a propeller-like blade. The blades are attached to a rotor and can be adjusted to control the flow of water. The water enters the turbine shell and moves through the blades, causing the rotor to rotate. The rotation of the rotor is converted into electrical energy.

Hydroelectric power generation plants use turbines to generate electricity from water. These turbines work on the principle of **hydraulic pressure** and convert the energy from water into electrical energy. The Pelton and Kaplan turbines are two types of turbines that are used in hydroelectric power generation. These turbines are different in terms of their construction and applications. The Pelton turbine is used in high-head applications, and the Kaplan turbine is used in low to medium-head applications. Both these turbines have a unique construction that allows them to generate electricity from water.

The Pelton turbine consists of a wheel with multiple cups arranged symmetrically in a circular pattern. The water is directed onto the cups using nozzles, and the high velocity of water from the nozzles impinges on the cups, causing the wheel to rotate. The rotation of the wheel is converted into electrical energy. The Kaplan turbine consists of a cylindrical turbine shell with a propeller-like blade. The blades are attached to a rotor and can be adjusted to control the flow of water. The water enters the turbine shell and moves through the blades, causing the rotor to rotate. The rotation of the rotor is converted into electrical energy.

The Pelton and Kaplan turbines are used in hydroelectric power generation because they can convert the energy from water into electrical energy. These turbines are used in power generation because they can work on the principle of hydraulic pressure. The Pelton turbine is suitable for high-head applications, and the Kaplan turbine is used for low to medium-head applications. These turbines are essential for hydroelectric power generation because they can generate large amounts of electricity.

Hydroelectric power generation plants use turbines to generate electricity from water. The Pelton and Kaplan turbines are two types of turbines that are used in hydroelectric power generation. These turbines are different in terms of their construction and applications. The Pelton turbine is used in high-head applications, and the Kaplan turbine is used in low to medium-head applications. These turbines are essential for hydroelectric power generation because they can generate large amounts of electricity. The Pelton and Kaplan turbines are used in power generation because they can work on the principle of hydraulic pressure and convert the energy from water into electrical energy.

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Question 1 (Road Map to Communication System)

1. Determine the Fourier transform of the right-sided exponential signal x(t) = e¯ªu(t) Question 2 (Matlab) 1. Plot the magnitude and phase spectrum of the results with respect to frequency

### Answers

Determine the Fourier **transform** of the right-sided exponential signal x(t) = e^(-a*t)u(t)The given signal x(t) = e^(-a*t)u(t) where u(t) is a unit step function. Now, we need to find the **Fourier** transform of x(t). The Fourier transform of x(t) is given byX(w) = ∫(-∞ to ∞)x(t)e^(-jwt)dtHere, x(t) = e^(-a*t)u(t)

Therefore, X(w) = ∫(0 to ∞)e^(-a*t)e^(-jwt)dt = ∫(0 to ∞)e^(-(a+jw)t)dt= {-1/(a+jw)}[e^(-(a+jw)t)](0 to ∞)= {-1/(a+jw)}[0 - 1] = {1/(a+jw)}Thus, the Fourier transform of x(t) = e^(-a*t)u(t) is X(w) = {1/(a+jw)} Plot the magnitude and phase spectrum of the results with **respect** to frequency Here, we have the Fourier transform of x(t) asX(w) = {1/(a+jw)}The **magnitude** of the Fourier transform of x(t) is given by |X(w)| = |1/(a+jw)|= 1/√(a^2+w^2)

The phase of the Fourier transform of x(t) is given by Φ(w) = tan^(-1)(w/a)Therefore, the magnitude and phase spectrum of the results with **respect** to frequency can be plotted as follows.

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Explain how the water saving system integrated to the locks of the Panama Canal works. of the Canal expansion.

Explain what a hydro-pneumatic water supply system is, what are its main components and what are its advantages and disadvantages components and what are its advantages and disadvantages with respect to elevated tank water supply systems. elevated tank water supply systems.

What is the Specific Speed Ns and what is its importance during the selection of Hydraulic Turbines.

### Answers

The water-saving system integrated into the locks of the Panama Canal is known as the Integrated Water **Resources **Management (IWRM) program. It aims to reduce the water consumption of the canal by using water-saving basins, water reutilization, and optimization of water flow.

Hydro-pneumatic water supply system: This is a system that combines the principles of **hydraulics **and pneumatics to ensure the safe and effective supply of water. The system is comprised of a pressure tank, a pump, and a pressure switch. When the pressure in the tank drops, the pressure switch triggers the pump to start pumping water into the tank, which then creates pressure. This pressure is used to push the water out of the tank and into the system.

Advantages:

1. Provides consistent water pressure.

2. Compact and require less space.

3. Reduced pump cycling, which reduces energy costs.

4. Easy to install and maintain.

5. Reduces water hammer.

Disadvantages:

1. Expensive.

2. Requires electricity to operate.

3. The tank may require periodic maintenance.

4. Susceptible to leaks and other mechanical failures.

5. Can be noisy.

Elevated tank water supply system:

This system stores water in an elevated tank, which then supplies water to the system by gravity. The system is comprised of a tank, a pump, and a valve. When the water level in the tank drops below a certain level, the pump starts pumping water into the tank.

Advantages:

1. Requires less electricity to operate.

2. Low maintenance.

3. Noisy operation.

Disadvantages:

1. Requires more space.

2. The tanks are susceptible to leaks.

3. The system requires careful consideration of pressure management.

4. High risk of water hammer.

Specific Speed (Ns):

The Specific Speed (Ns) is a dimensionless number that is used to describe the speed at which a hydraulic **turbine** operates. It is an important parameter in the selection of hydraulic turbines because it helps to determine the optimal design of the turbine.

The value of Ns is calculated as the speed at which a geometrically similar turbine would operate if it were one foot in diameter and had a head of one foot. By using Ns, it is possible to compare the performance of different hydraulic turbines and select the most suitable one for a specific application.

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2. The following questions deal with manipulating complex expressions. (a) (3e). (202) = AeB. Find A and B. (b) e(¹+jy)t = AejB. Find A and B, which may be functions of time. (c) 3e³e(-2+3j)t = AeB. Find A and B. (d) Write eje(-2+3j)t + e-jee-2-3j)t as a real-valued function of time. [Hint: use Euler's formula: ej + e-j¹ = 2 cos(x).

### Answers

According to the statement the **expression **can be written as a real-valued **function **of time as: [tex]e^{-2t}[/tex] 2 cos 3t.

a) The expression is (3e) (202). We can rewrite this as (3)([tex]e^{202}[/tex]).Using Euler's formula:

e^θ = cos θ + i sin θ

We have:

e^(202) = cos 202 + i sin 202

Therefore, (3) (e^202) = 3 cos 202 + i3 sin 202

Thus,

A = 3 cos 202, andB = 3 sin 202

(b) The **expression **is e^(jy)t. Using **Euler's formula**, we have:

e^jθ = cos θ + i sin θ

We have:

e^(jy)t = cos yt + i sin yt

Therefore,

A = cos yt, and

B = sin yt(c)

The expression is 3e^(3j)t e^(-2t). We can rewrite this as 3e^(3j-2)t.

Using Euler's formula: e^θ = cos θ + i sin θ

We have: e^(3j-2)

t = cos (3t - 2) + i sin (3t - 2)

Therefore, 3e^(3j-2)t = 3 cos (3t - 2) + i3 sin (3t - 2)

Thus,

A = 3 cos (3t - 2), andB = 3 sin (3t - 2)

(d) We have:

e^(j)(-2+3j)t + e^(-j)(-2-3j)t

Using Euler's formula:

e^jθ = cos θ + i sin θ

Therefore:

e^(j)(-2+3j)t = e^(-2t) (cos 3t + i sin 3t)e^(-j)(-2-3j)t = e^(-2t) (cos 3t - i sin 3t)

Thus:

e^(j)(-2+3j)t + e^(-j)(-2-3j)t= e^(-2t) (cos 3t + i sin 3t + cos 3t - i sin 3t)= e^(-2t) 2 cos 3t.

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