1. Circuit Diagram:
+-------+ +-------+
V | | | |
------| Arm |------+ Shunt |
_|_______|_ |
| | |
| Generator |------+
| |
-----| Series |------ Load
| Field |
-----|___________|_
2. Calculation of Armature Current:
Using Ohm's Law, I = V / R = 250 / 0.06 = 4166.67 A (approx.)
3. Calculation of Induced EMF:
From the generator equation, V = E + Ia * Ra
Rearranging, E = V - Ia * Ra = 250 - 40 * 0.06 = 247.6 V (approx.)
Q2. Calculation of Line Current and Power Input:
At no load, the armature current is 2.5 A. When the motor delivers rated load, the armature current will increase.
Using the speed reduction, we can determine the new armature current at rated load:
(1200 - 1120) / 1200 = 80 / 1200 = 2/30
Increase in current = 2/30 * 2.5 = 0.1667 A
New armature current = 2.5 A + 0.1667 A = 2.6667 A (approx.)
To calculate line current, we add the field current to the armature current:
Line Current = Armature Current + Field Current = 2.6667 A + 2.5 A = 5.1667 A (approx.)
The power input can be calculated using the formula:
Power Input = Line Current * Voltage = 5.1667 A * 230 V = 1188.34 W (approx.)
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An empty cylinder is 50 cm in diameter, 1.20 m high and weighs 312 N. If the cylinder is placed in water with its axis vertical, would it be stable?
The stability of an empty cylinder placed in water with its axis vertical can be determined by analyzing the center of buoyancy and the center of gravity of the cylinder. If the center of gravity lies below the center of buoyancy, the cylinder will be stable.
To assess the stability of the cylinder in water, we need to compare the positions of the center of gravity and the center of buoyancy. The center of gravity is the point where the entire weight of the cylinder is considered to act, while the center of buoyancy is the center of the volume of water displaced by the cylinder. If the center of gravity is located below the center of buoyancy, the cylinder will be stable. However, if the center of gravity is above the center of buoyancy, the cylinder will be unstable and tend to overturn. To determine the positions of the center of gravity and center of buoyancy, we need to consider the geometry and weight of the cylinder. Given that the cylinder weighs 312 N, we can calculate the position of its center of gravity based on the weight distribution. Additionally, the dimensions of the cylinder (50 cm diameter, 1.20 m height) can be used to calculate the position of the center of buoyancy. By comparing the positions of the center of gravity and center of buoyancy, we can conclude whether the cylinder will be stable or not when placed in water with its axis vertical.
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The magnitudes of the latent heats depend on the temperature or
pressure at which the phase change occurs.
The latent heat is the amount of heat energy that needs to be added or removed from a substance in order for it to change phase without changing temperature.
The magnitudes of the latent heats depend on the temperature or pressure at which the phase change occurs. For instance, the latent heat of fusion of water is 334 J/g, which means that 334 joules of energy are required to melt one gram of ice at 0°C and atmospheric pressure.
The latent heat of vaporization of water, on the other hand, is 2,260 J/g, which means that 2,260 joules of energy are required to turn one gram of water into steam at 100°C and atmospheric pressure
Latent heat refers to the heat energy required to transform a substance from one phase to another at a constant temperature and pressure, without any change in temperature.
Latent heat has different magnitudes at different temperatures and pressures, depending on the phase change that occurs. In other words, the amount of energy required to change the phase of a substance from solid to liquid or from liquid to gas will differ based on the temperature and pressure at which it happens.
For example, the latent heat of fusion of water is 334 J/g, which means that 334 joules of energy are needed to melt one gram of ice at 0°C and atmospheric pressure. Similarly, the latent heat of vaporization of water is 2,260 J/g, which means that 2,260 joules of energy are required to turn one gram of water into steam at 100°C and atmospheric pressure.
In conclusion, the magnitude of latent heat depends on the temperature or pressure at which the phase change occurs. At different temperatures and pressures, different amounts of energy are required to change the phase of a substance without any change in temperature.
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An organic oil having a density of 892 kg/m3 is flowing through the piping
arrangement shown in the figure below at a rate of 1.388 x 10-3 m3/s entering
pipe 1.
The flow divides equally in each of pipes 3. The steel pipes have the following
internal diameters: Pipe 1 = 52.5 mm, Pipe 3 = 40.9 mm.
Calculate the following using SI units.
(a) The total mass flow rate m in pipe 1 and pipes 3.
(b) The average velocity v in 1 and 3
(c) The flux G in pipe 1.
(a) The total mass flow rate, m in pipe 1 and pipes 3. The volume flow rate, Q = 1.388 x 10-3 m3/s Total mass flow rate is given by: m = ρQ = 892 kg/m3 × 1.388 x 10-3 m3/s = 1.237 kg/s The flow divides equally in each of pipes 3.So, mass flow rate in each of pipes 3 is m/2 = 1.237/2 = 0.6185 kg/s
(b) The average velocity, v in 1 and 3. The internal diameter of pipe 1, D1 = 52.5 mm = 0.0525 m The internal diameter of pipe 3, D3 = 40.9 mm = 0.0409 m The area of pipe 1, A1 = πD12/4 = π× (0.0525 m)2/4 = 0.0021545 m2 The area of pipe 3, A3 = πD32/4 = π× (0.0409 m)2/4 = 0.001319 m2. The average velocity in pipe 1, v1 = Q/A1 = 1.388 x 10-3 m3/s / 0.0021545 m2 = 0.6434 m/s
The average velocity in each of pipes 3, v3 = Q/2A3 = 1.388 x 10-3 m3/s / (2 × 0.001319 m2) = 0.5255 m/s
(c) The flux G in pipe 1 The flux is given by: G = ρv1 = 892 kg/m3 × 0.6434 m/s = 574.18 kg/m2s. Therefore, flux G in pipe 1 is 574.18 kg/m2s.
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Design Problem:
Let us assume you are working on a composite design and manufacturing company, and you are asked to design a structural support, made of unidirectional fiber reinforced epoxy composite, having 10 ft long and round cross section.
The design constraints are the following:
1. If a force of 500 ls applied, it should stretch to no more than 0.1 in.
2. The stress acting on the support need to be < the yield strength of the epoxy material, which is 12,000 psi.
3. If the fibers break, the support need to stretch an additional amount but may not fracture in a catastrophic manner.
Assume the epoxy material costs ~ 0.80/b and has a Young's modulus of 500,000 psi and a density of 0.0451 b/in3.
Design Constraints: If a force of 500 ls applied, it should stretch to no more than 0.1 in.The stress acting on the support needs to be < the yield strength of the epoxy material, which is 12,000 psi.If the fibers break, the support needs to stretch an additional amount but may not fracture in a catastrophic manner.
Material Specifications:Young's modulus of the epoxy material is 500,000 psi. Density of the epoxy material is 0.0451 b/in3.The cost of the epoxy material is ~ 0.80/.
Now, let us calculate the diameter of the round cross-section of the support by considering the stress requirement.
[tex]D2 = (4 * Wc * σm) / [π * ρc * (1 - σf / Em) * L][/tex]
[tex]ρc = Vf * ρf + (1 - Vf) * ρm = 0.7 * 1.8 + (1 - 0.7) * 1.2 = 1.5[/tex]b/in3Thus,
[tex]D2 = (4 * 120 * 12,000) / [π * 1.5 * (1 - 0.7 / 500,000) * 120] = 0.722 \\D = √D2 = 0.849[/tex]
Therefore, the diameter of the round cross-section of the support is 0.849 in.
The cost of the composite support can be calculated as follows:
[tex]Wc = π/4 * D2 * L * ρc = π/4 * 0.722 * 120 * 1.5 = 96.5 lb[/tex]
Cost of the support = Cost of the composite material * Weight of the support =[tex]0.80/b * 96.5 lb = $77[/tex]
Thus, the cost of the composite support is $77.
Therefore, the designed structural support made of unidirectional fiber reinforced epoxy composite, having a 10 ft long and round cross-section, with a diameter of 0.849 in, and a cost of $77, satisfies the given design constraints.
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The size of this building is approximately 25 m long, 10 m wide, and 12 m high. Determine the possible maximum drag force while this old building is in the dry and wet seasons. The average wind velocity and the flow velocity in this area are 6 and 0.8 m/s, respectively. Specify the number of Cd with the reference or evidence here. Discuss about the problem that could be occurred when this building submerged underwater. a) in dry season b) partly submerged VAL JAG VAL c) mostly submerg
Drag force is a resistive force exerted on an object moving through a fluid, such as air or water. It opposes the object's motion and is proportional to the object's velocity and the fluid's density.
Given data: Size of building = 25 m x 10 m x 12 m = 3000 m³ Wind velocity = 6 m/sFlow velocity = 0.8 m/s
a) Dry season. In the dry season, there is no possibility of a drag force acting on the building because of the absence of water.
b) Partly submerged. When the building is partly submerged, then drag force F can be given as:
F = (1/2) x (density of water) x (velocity of water)² x Cd x A
Where, Cd = drag coefficient ,
A = area of the building
= 2(25x10) + 2(10x12) + 2(25x12)
= 850 m²
F = (1/2) x (1000) x (0.8)² x 1.2 x 850
F = 231,840 N (approx)
c) Mostly submerged. When the building is mostly submerged, then drag force F can be given as:
F = (1/2) x (density of water) x (velocity of water)² x Cd x A
Where, Cd = drag coefficient,
A = area of the building = 2(25x10) + 2(10x12) + 2(25x12)
= 850 m²
(the same as in b)
F = (1/2) x (1000) x (0.8)² x 1.1 x 850F = 198,264 N (approx)
Problem that could be occurred when this building submerged underwater:
When the building is submerged underwater, the drag force increases, which can cause structural instability, especially if it is not designed to withstand such forces.
In addition, the buoyancy of the building can change, and the weight can increase due to waterlogging, leading to the sinking of the building.
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A circular duct has a diameter of 0.74 m, determine its equivalent width and height of rectangular
duct with aspect ratio of 5 in m.
A) 0.222 x1.11
B) 2.22 x0.444
C) 0.444 x 2.22
D) 1.11 x0.222
The equivalent width and height of a rectangular duct with an aspect ratio of 5 are 0.962 m and 0.1924 m respectively. The correct option is A) 0.222 x1.11.
The circular duct has a diameter of 0.74 m, and we are to determine its equivalent width and height of a rectangular duct with an aspect ratio of 5 in meters.
We can find the equivalent width (b) and height (h) of a rectangular duct using the following formulae:
b = 1.3D and h = D/2 Where D is the diameter of the circular duct.
Substituting D = 0.74 m in the formulae above:
b = 1.3 × 0.74
= 0.962 m and
h = 0.74/2
= 0.37 m
For a rectangular duct with an aspect ratio of 5, b/h = 5.
Solving for h;
h = b/5
Substituting
b = 0.962 m,
h = 0.962/5
= 0.1924 m
Therefore, the equivalent width and height of a rectangular duct with an aspect ratio of 5 are 0.962 m and 0.1924 m respectively.
Rounding off to two decimal places, we get;
b = 0.96 m` and h = 0.19 m
So, the correct option is A) 0.222 x1.11.
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Given the following transfer function. G(s)= 5/s² bsa a) How must the coefficients a and b be selected to ensure stable and vibration-free transmission behaviour? b) How must the coefficients a and b be chosen so that a stationary gain of 1 and the aperiodic limiting case occur?
To ensure stable and vibration-free transmission behavior in the given transfer function G(s) = 5/s², the coefficients a and b must be selected appropriately. Additionally, to achieve a stationary gain of 1 and the aperiodic limiting case, specific choices for the coefficients a and b need to be made.
For stable and vibration-free transmission behavior, the transfer function should have all poles with negative real parts. In this case, the transfer function G(s) = 5/s² has poles at s = 0, indicating a double pole at the origin. To ensure stability, the coefficients a and b should be chosen in a way that eliminates any positive real parts or imaginary components in the poles. For the given transfer function, the coefficient a should be set to zero to eliminate any positive real parts in the poles, resulting in a stable and vibration-free transmission behavior.
To achieve a stationary gain of 1 and the aperiodic limiting case, the transfer function G(s) needs to have a DC gain of 1 and exhibit a response that approaches zero as time approaches infinity. In this case, to achieve a stationary gain of 1, the coefficient b should be set to 5, matching the numerator constant. Additionally, the coefficient a should be chosen such that the poles have negative real parts, ensuring an aperiodic response that decays to zero over time.
By appropriately selecting the coefficients a and b, the transfer function G(s) = 5/s² can exhibit stable and vibration-free transmission behavior while achieving a stationary gain of 1 and the aperiodic limiting case.
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An engineer is tasked to design a concrete mixture for pavement in Fayetteville, AR, USA. Due to the very low temperature in winters, the pavement is expected to sustain frost action. The engineer is originally from Basra, Iraq, and does not have decent information regarding the concrete used in such conditions. Accordingly, he had to ask a civil engineering student (his GF) that is just finished the Concrete Technology Class at the University of Arkansas. He provided his GF with the following information: the recommendation of the ACI Committee 201 has to be considered regarding durability, and the procedure of the ACI 211.1 for designing concrete mixture for normal strength has to be followed. After all this information, what is the water content of the mixture per one cubic meter and air content should his GF has calculated if the maximum aggregate size is 20 mm and slump is 30 mm? Write down your answer only.
The water content and air content of the concrete mixture can be calculated using the ACI 211.1 procedure. To accurately determine the water content and air content, the civil engineering student (GF) would need additional information, such as the mix design requirements, project specifications, and any local regulations or guidelines that may apply in Fayetteville, AR, USA.
However, without the specific mix design requirements, such as target compressive strength, cement content, and aggregate properties, it is not possible to provide an exact answer for the water content and air content.
The ACI 211.1 procedure takes into account factors like the maximum aggregate size, slump, and specific requirements for durability. The recommended water content is determined based on the water-cement ratio, which is a key parameter in achieving the desired strength and durability of the concrete. The air content is typically specified to enhance the resistance to freeze-thaw cycles and frost action.
To accurately determine the water content and air content, the civil engineering student (GF) would need additional information, such as the mix design requirements, project specifications, and any local regulations or guidelines that may apply in Fayetteville, AR, USA.
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You have probably noticed warning signs on the highways stating that bridges may be icy even when the roads are not. Explain how this can happen. If the distance between the sun and the earth was the half of what it is L=0.5 x 1.496 x 1011 m, what would the solar constant be? The sun is a nearly spherical body that has a diameter of D = 1.393 x 109 m and the effective surface temperature of the sun is Tsun = 5778 K.
Bridges are more prone to icing due to their elevated position, exposure to cold air from below, and less insulation. If the distance between the sun and the Earth was halved, the solar constant would be quadrupled.
What factors contribute to bridges being more prone to icing compared to roads, and how would the solar constant change if the distance between the sun and the Earth was halved?Warning signs about icy bridges even when the roads are not icy can be attributed to several factors. Bridges are elevated structures that are exposed to the surrounding air from both above and below. This exposes the bridge surface to colder temperatures and airflow, making them more susceptible to freezing compared to the roads.
Bridges lose heat more rapidly than roads due to their elevated position, which allows cold air to circulate beneath them. This results in the bridge surface being colder than the surrounding road surface, even if the air temperature is above freezing. Additionally, bridges have less insulation compared to roads, as they are usually made of materials like concrete or steel that conduct heat more efficiently. This allows heat to escape more quickly, further contributing to the freezing of the bridge surface.
Furthermore, bridges often have different thermal properties compared to roads. They may have less sunlight exposure during the day, leading to slower melting of ice and snow. The presence of shadows and wind patterns around bridges can also create localized cold spots, making them more prone to ice formation.
Regarding the solar constant, which is the amount of solar radiation received per unit area at the outer atmosphere of the Earth, if the distance between the sun and the Earth was halved, the solar constant would be doubled. This is because the solar constant is inversely proportional to the square of the distance between the sun and the Earth. Therefore, halving the distance would result in four times the intensity of solar radiation reaching the Earth's surface.
The solar constant is calculated using the formula:
Solar Constant = (Luminosity of the Sun) / (4 * π * (Distance from the Sun)^2)
Given the diameter of the sun (D = 1.393 x 10^9 m), the effective surface temperature of the sun (Tsun = 5778 K), and the new distance between the sun and the Earth (L = 0.5 x 1.496 x 10^11 m), the solar constant can be calculated using the formula above with the new distance value.
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Determine the stress and deflection for a built-in circular
plate of radius a subjected to uniformly distributed loading Po
The stress in the built-in circular plate can be determined using the formula:Stress = Po / (2 * pi * a^2), where Po is the uniformly distributed loading and a is the radius of the plate.The deflection of the built-in circular plate can be determined using the formula:Deflection = (Po * a^4) / (64 * E * (1 - v^2)).
where E is the modulus of elasticity and v is the Poisson's ratio.The stress formula calculates the stress on the plate by dividing the uniformly distributed loading by the area of the plate. This provides the average stress acting on the plate.The deflection formula calculates the deflection of the plate under the uniformly distributed loading. It takes into account the loading, the dimensions of the plate, and the material properties (modulus of elasticity and Poisson's ratio). The deflection represents the displacement of the plate from its original position due to the applied loading.By using these formulas, the stress and deflection of the built-in circular plate can be determined based on the given parameters.
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Find a diagonalizing matrix P for the given matrix
[ -1 2 -1 ]
3. [ 2 -1 2 ]
[ 2 -2 3 ]
[ 5 -2 2]
4. [ 2 1 2]
[ -2 2 1]
A diagonalizing matrix is a square matrix used to transform a given matrix into diagonal form through a similarity transformation.
To find the diagonalizing matrix P for the given matrix A, we need to find the eigenvectors and eigenvalues of A.
The matrix A is:
[-1 2 -1]
[ 3 -1 2]
[ 2 -2 3]
[ 5 -2 2]
[ 2 1 2]
[-2 2 1]
Step 1: Find the eigenvalues
To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.
The characteristic equation becomes:
det(A - λI) = 0
[ -1 - λ 2 -1 ]
[ 3 -1 - λ 2 ] = 0
[ 2 -2 3 - λ ]
[ 5 -2 2 ]
Expanding the determinant, we get:
(-1 - λ)[(-1)(3 - λ) - (2)(-2)] - 2[(-1)(2) - (-1)(2)] + (-1)[(2)(2) - (3 - λ)(-2)] - 5[(-2)(2) - (3 - λ)(-2)] = 0
Simplifying the equation:
(-1 - λ)[(-3 + λ) + 4] - 2[-2 + 2] + (-1)[4 + 2(3 - λ)] - 5[-4 + 2(3 - λ)] = 0
(-1 - λ)[1 + λ] - 2 + (-1)[4 + 6 - 2λ] - 5[-4 + 6 - 2λ] = 0
λ² + 2λ + 1 + λ + 1 - 12 - 4λ = 0
λ² - λ - 10 = 0
Factoring the equation, we get:
(λ - 2)(λ + 5) = 0
The eigenvalues are λ = 2 and λ = -5.
Step 2: Find the eigenvectors
To find the eigenvectors, we substitute each eigenvalue back into the equation (A - λI)X = 0, where X is the eigenvector.
For λ = 2:
(A - 2I)X = 0
[ -1 - 2 2 ]
[ 3 - 3 2 ] X = 0
[ 2 - 2 1 ]
[ 5 - 2 0 ]
[ 2 1 2 ]
[ -2 2 -1 ]
Row reducing the matrix:
[ -1 - 2 2 ]
[ 3 - 3 2 ] -> [ 1 0 -1 ]
[ 2 - 2 1 ] [ 0 1 1 ]
[ 5 - 2 0 ]
[ 2 1 2 ]
[ -2 2 -1 ]
From the row-reduced form, we can see that the eigenvector X₁ = [1, 0, -1] and X₂ = [0, 1, 1].
For λ = -5:
(A + 5I)X = 0
[ 4 2 2 ]
[ 3 4 2 ] X = 0
[ 2 -2 8 ]
[ 10 2 2 ]
[ 2 6 2 ]
[ -2 2 -4 ]
Row reducing the matrix:
[ 4 2 2 ]
[ 3 4 2 ] -> [ 1 0 -2 ]
[ 2 -2 8 ] [ 0 1 -1 ]
[ 10 2 2 ]
[ 2 6 2 ]
[ -2 2 -4 ]
From the row-reduced form, we can see that the eigenvector X₃ = [1, -2, -1] and X₄ = [0, -1, 1].
Step 3: Form the diagonalizing matrix P
The diagonalizing matrix P is formed by taking the eigenvectors as columns:
P = [ X₁ | X₂ | X₃ | X₄ ]
P = [ 1 0 1 0 ]
[ 0 1 -2 -1 ]
[ -1 1 -1 1 ]
Therefore, the diagonalizing matrix P for the given matrix A is:
P = [ 1 0 1 0 ]
[ 0 1 -2 -1 ]
[ -1 1 -1 1 ]
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A diagonalizing matrix is a square matrix used to transform a given matrix into diagonal form through a similarity transformation.
To find the diagonalizing matrix P for the given matrix A, we need to find the eigenvectors and eigenvalues of A.
The matrix A is:
[-1 2 -1]
[ 3 -1 2]
[ 2 -2 3]
[ 5 -2 2]
[ 2 1 2]
[-2 2 1]
Step 1: Find the eigenvalues
To find the eigenvalues, we need to solve the characteristic equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.
The characteristic equation becomes:
det(A - λI) = 0
[ -1 - λ 2 -1 ]
[ 2 -2 3 - λ ]
[ 5 -2 2 ]
Expanding the determinant, we get:
(-1 - λ)[(-1)(3 - λ) - (2)(-2)] - 2[(-1)(2) - (-1)(2)] + (-1)[(2)(2) - (3 - λ)(-2)] - 5[(-2)(2) - (3 - λ)(-2)] = 0
Simplifying the equation:
(-1 - λ)[(-3 + λ) + 4] - 2[-2 + 2] + (-1)[4 + 2(3 - λ)] - 5[-4 + 2(3 - λ)] = 0
(-1 - λ)[1 + λ] - 2 + (-1)[4 + 6 - 2λ] - 5[-4 + 6 - 2λ] = 0
λ² + 2λ + 1 + λ + 1 - 12 - 4λ = 0
λ² - λ - 10 = 0
Factoring the equation, we get:
(λ - 2)(λ + 5) = 0
Values of λ is 2 and -5.
Step 2: Find the eigenvectors
For λ = 2:
(A - 2I)X = 0
[ -1 - 2 2 ]
[ 3 - 3 2 ] X = 0
[ 2 - 2 1 ]
[ 5 - 2 0 ]
[ 2 1 2 ]
[ -2 2 -1 ]
Row reducing the matrix:
[ -1 - 2 2 ]
[ 3 - 3 2 ] -> [ 1 0 -1 ]
[ 5 - 2 0 ]
[ 2 1 2 ]
[ -2 2 -1 ]
From the row-reduced form, we can see that the eigenvector X₁ = [1, 0, -1] and X₂ = [0, 1, 1].
For λ = -5:
(A + 5I)X = 0
[ 4 2 2 ]
[ 2 -2 8 ]
[ 10 2 2 ]
[ 2 6 2 ]
[ -2 2 -4 ]
Row reducing the matrix:
[ 4 2 2 ]
[ 2 -2 8 ] [ 0 1 -1 ]
[ 10 2 2 ]
[ 2 6 2 ]
[ -2 2 -4 ]
From the row-reduced form, we can see that the eigenvector X₃ = [1, -2, -1] and X₄ = [0, -1, 1].
Step 3: Form the diagonalizing matrix P
The diagonalizing matrix P is formed by taking the eigenvectors as columns:
P = [ A₁ | A₂ | A₃ | A₄ ]
P = [ 1 0 1 0 ]
[ 0 1 -2 -1 ]
[ -1 1 -1 1 ]
Therefore, the diagonalizing matrix P for the given matrix A is:
P = [ 1 0 1 0 ]
[ 0 1 -2 -1 ]
[ -1 1 -1 1 ]
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Why are the velocity gradients inside the boundary layer so large? Tell the Difference between Laminar Boundary Layer and Turbulence Boundary Layer.
The velocity gradients inside the boundary layer are large because of the friction caused by the flow and the viscosity of the fluid.
This friction is the force that is resisting the motion of the fluid and causing the fluid to slow down near the surface. This slowing down creates a velocity gradient within the boundary layer.
Difference between Laminar Boundary Layer and Turbulence Boundary Layer: The laminar boundary layer has smooth and predictable fluid motion, while the turbulent boundary layer has a random and chaotic fluid motion. In the laminar boundary layer, the velocity of the fluid increases steadily as one moves away from the surface.
In contrast, in the turbulent boundary layer, the velocity fluctuates widely and randomly, and the velocity profile is much flatter than in the laminar boundary layer. The thickness of the laminar boundary layer increases more gradually than the thickness of the turbulent boundary layer. The thickness of the turbulent boundary layer can be three to four times that of the laminar boundary layer.
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(a) Define surface emissivity, ε. (b) [9] A domestic radiator is configured as a rudimentary roof-mounted solar collector to provide a source of hot water. For a 1 m² radiator, painted white, calculate the nominal steady-state temperature that the radiator would reach. (Nominal implies that no heat is extracted from the radiator via, for example, a pumped cold water stream). Assume the following: solar irradiation of 700 W/m²; an ambient temperature (air and surrounding surfaces) of 20°C; a convective heat transfer coefficient of 10 W/m²K between the collector and ambient; and no heat losses from the underside of the collector. Note: The absorptivity and emissivity of white paint for longwave radiation is 0.8 whereas its absorptivity for shortwave radiation is 0.2. Stefan-Boltzmann's constant is o = 5.67 x 10-8 W/m²K4. . . (c) [3] Suggest three practical measures – with justification – by which the performance of the collector could be improved.
Surface emissivity, can be defined as the ratio of the radiant energy radiated by a surface to the energy radiated by a perfect black body at the same temperature.
It is the surface's effectiveness in emitting energy as thermal radiation. The surface is regarded as a black body with an emissivity of 1 if all the radiation that hits it is absorbed and re-radiated. The surface is said to have a surface emissivity of 0 if no radiation is emitted.
A body with an emissivity of 0.5, for example, can radiate only half as much thermal energy as a black body at the same temperature. For the given problem, the first step is to calculate the net heat transfer from the radiator to the environment.
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Question 5: (a) It is proposed to use artillery to deliver SO2 to the stratosphere (20 km height). Shells will be fired vertically at an initial velocity of 800 m/s. Once they reach their maximum altitude, they will release their payload of SO2, then fall to the ground. Calculate the maximum altitude reached by the shells, showing whether the aim of the project has been met [15 marks) The following data are provided with regard to each shell: Mass with payload: 2000 kg Diameter: 0.5 m Drag coefficient 0.5 Assume air to be of constant density =0.8 kg/m². (b) For the following: i. Ocean Acidification ii. Biodiesel iii. Accelerated Weathering In the context of Engineering Design and the Natural Environment, what do you understand by the term? Write a concise paragraph explaining the meaning in each case, including chemical equations where appropriate. [6 marks each]
Ocean acidification refers to the decrease in the pH of the Earth's oceans due to the uptake of carbon dioxide (CO₂) from the atmosphere.
The chemical equation for the process of ocean acidification can be given as: CO₂ + H₂O ⇌ H₂CO₃ ⇌ H⁺ + HCO₃⁻ ⇌ 2H⁺ + CO₃²⁻. This phenomenon has a significant impact on marine organisms and ecosystems, as it can affect the growth and survival of many species.ii. Biodiesel: Biodiesel refers to a type of renewable diesel fuel made from natural sources such as vegetable oils and animal fats.
The chemical equation for the production of biodiesel from vegetable oil is: Triglycerides + Methanol ⇌ Fatty Acid Methyl Esters (Biodiesel) + Glycerol. Biodiesel has several advantages over petroleum-based diesel, such as lower greenhouse gas emissions and higher biodegradability.
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Determine the inverse Z-Transform of the following signals. a. x(z) = 2 + 2z/(z - 5) - 3z (z - 0.2)
b. x(z) = 4z⁻¹/(6z⁻² -5⁻¹ + 1)
The inverse Z-Transform of the given signal is x(n) = δ(n) - (16/25)5ⁿu(n - 1) + (4/5)(0.2ⁿ)u(n).b. x(z) = 4z⁻¹/(6z⁻² -5⁻¹ + 1)
a. x(z) = 2 + 2z/(z - 5) - 3z (z - 0.2)
To determine the inverse Z-Transform of the given signal, we will use partial fraction expansion.
To get started, let's factorize the denominator as follows:
z(z - 5)(z - 0.2)
Hence, using partial fraction expansion, we have;
X(z) = (2z² - 9.2z + 10)/(z(z - 5)(z - 0.2))
Let us assume:
X(z) = A/z + B/(z - 5) + C/(z - 0.2)
Multiplying both sides by z(z - 5)(z - 0.2) to get rid of the denominators and then solve for A, B and C, we have:
2z² - 9.2z + 10 = A(z - 5)(z - 0.2) + Bz(z - 0.2) + Cz(z - 5)
Setting z = 0,
we have: 10 = 5A(0.2),
hence A = 1
Substituting A back into the equation above and letting z = 5, we get:
25B = -16,
hence
B = -16/25
Similarly, setting z = 0.2, we get:
C = 4/5
Thus,
X(z) = 1/z - (16/25)/(z - 5) + (4/5)/(z - 0.2)
Taking inverse Z-transform of the above equation yields;
x(n) = δ(n) - (16/25)5ⁿu(n - 1) + (4/5)(0.2ⁿ)u(n)
Therefore, the inverse Z-Transform of the given signal is x(n) = δ(n) - (16/25)5ⁿu(n - 1) + (4/5)(0.2ⁿ)u(n).b. x(z) = 4z⁻¹/(6z⁻² -5⁻¹ + 1)
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A. What is an ideal single-phase transformer? Write down with a neat sketch, the differences between the ideal and realistic transformer. B. A 23-kVA, 2300/230 V, 60-Hz, step-down transformer has the following resistance and leakage - reactance values: R₁= 4Ω, R₂= 0.04Ω, X₁= 12Ω, X₂= 0.12Ω. The transformer is operating at 75% of its rated load. If the power factor of the load is 0.866 leading, determine the efficiency of the transformer.
An ideal transformer is one that does not have any losses; it has a hundred percent efficiency and can transform all of the input power from the primary side to the output power on the secondary side.
The key differences between an ideal and a realistic transformer are listed below. The ideal transformer does not have any losses; the practical transformer, on the other hand, has losses and isn't a hundred percent efficient. The ideal transformer's flux never leaks from the core; in practical transformers, some of the flux leaks from the core.
The ideal transformer does not have a leakage inductance; in practical transformers, some inductance is lost due to leakage. The core of an ideal transformer does not have any magnetic losses; in practical transformers, there are magnetic losses.
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D ∗∗2 .118 A designer, wanting to achieve a stable gain of 100 V/V with a 3-dB frequency above 5MHz, considers her choice of amplifier topologies. What unity-gain frequency would a single operational amplifier require to satisfy her need? Unfortunately, the best available amplifier has an f t of 50MHz. How many such amplifiers connected in a cascade of identical noninverting stages would she need to achieve her goal? What is the 3-dB frequency of each stage? What is the overall 3-dB frequency?
Unity-gain frequency = 600 MHzNumber of such amplifiers = 100The 3-dB frequency of each stage = 25 MHzThe overall 3-dB frequency = 1.741 MHz.
Given stable gain is 100V/V and 3-dB frequency is greater than 5 MHz. Unity-gain frequency required for a single operational amplifier to satisfy the given conditions can be calculated using the relation:
Bandwidth Gain Product(BGP) = unity gain frequency × gain
Since, gain is 100V/VBGP = (3-dB frequency) × (gain) ⇒ unity gain frequency = BGP/gain= (3-dB frequency) × 100/1, from which the unity-gain frequency required is, 3-dB frequency > 5 MHz,
let's take 3-dB frequency = 6 MHz
Therefore, unity-gain frequency = (6 MHz) × 100/1 = 600 MHz Number of such amplifiers connected in a cascade of identical noninverting stages would she need to achieve her goal?
Total gain required = 100V/VGain per stage = 100V/V Number of stages, n = Total gain / Gain per stage = 100 / 1 = 100For the given amplifier, f_t = 50 MHz
This indicates that a single stage of this amplifier can provide a 3 dB frequency of f_t /2 = 50/2 = 25 MHz.
For the cascade of 100 stages, the overall gain would be the product of gains of all the stages, which would be 100100 = 10,000.The 3-dB frequency of each stage would be the same, which is 25 MHz.
Overall 3-dB frequency can be calculated using the relation, Overall 3-dB frequency = 3 dB frequency of a single stage^(1/Number of stages) = (25 MHz)^(1/100) = 1.741 MHz.
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You want to design an arithmetic adder/subtractor logic circuit.
(a) List the steps that you will apply in the design approach. 8-bit BCD full adder Design the circuit. Explain each step. Realize with AND, OR, NOT gates. (b) In the circuit you designed, the numbers in the last digit of the Student numbers of those in the group Collect and discuss the result. student numbers 1.5 and 5.
(a) Steps in designing an 8-bit BCD full adder circuit using AND, OR, and NOT gates:
1. **Analyze the requirements**: Understand the specifications and determine the desired functionality of the adder/subtractor circuit.
2. **Design the truth table**: Create a truth table that shows all possible input combinations and the corresponding output values for the adder/subtractor.
3. **Determine the logic equations**: Based on the truth table, derive the logic equations for each output bit of the adder/subtractor. This involves expressing the outputs in terms of the input variables using AND, OR, and NOT gates.
4. **Simplify the equations**: Simplify the logic equations using Boolean algebra or Karnaugh maps to reduce the complexity of the circuit.
5. **Draw the circuit diagram**: Using the simplified logic equations, draw the circuit diagram for the 8-bit BCD full adder. Represent the logical operations using AND, OR, and NOT gates.
6. **Implement the circuit**: Realize the circuit design by connecting the appropriate gates as per the circuit diagram. Ensure proper interconnections and adherence to the logical operations.
7. **Test and verify**: Validate the functionality of the circuit by providing various input combinations and comparing the output with the expected results.
8. **Optimize and refine**: Fine-tune the circuit design if necessary, considering factors such as speed, area, and power consumption.
(b) Regarding the numbers in the last digit of the student numbers 1.5 and 5, further information or clarification is needed. It is unclear how these numbers relate to the designed circuit or the desired discussion. Please provide additional details or specify the context so that I can assist you more effectively.
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Calculate the free carrier absorption loss in a semiconductor assuming n = 3.4, -3 m* = 0.08 mo, λ = 1.15 µm, N₁ = 10¹8 cm-³, and μ = 2 x 10³ cm²/Vs.
Free carrier absorption loss in a semiconductor: The free carrier absorption loss in a semiconductor material can be defined as the loss of optical power due to the absorption of photons by the free electrons and holes.
in the conduction and valence band of the material. In a semiconductor material, this type of loss can be reduced by decreasing the concentration of free carriers. When the concentration of free carriers in a semiconductor material is high, the free carrier absorption loss is also high.
Calculation of free carrier absorption loss in a semiconductor: The free carrier absorption loss in a semiconductor material can be calculated by using the following formula:αFC = (4πn/λ) Im (n2-1)1/2 × (qN1µm*/KbT) × (Eg/2KbT).
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A string of negligible mass passes over a fixed pulley and supports a 2m mass at one end. In it At the other end of the rope there is a mass m and, moving from it by means of a resource of constant k, there is another mass m. Find the equations of motion of the system by Lagrange's method and by Hamilton method. In the figure represents the rest length of the resource and x its displacement.
By applying Lagrange's method and Hamilton's method, we can derive the equations of motion for a system consisting of a string with negligible mass passing over a fixed pulley.
At one end of the string, there is a 2m mass, while at the other end, there is a mass m connected to another mass m via a resource with constant k. Using Lagrange's method, we start by defining the generalized coordinates of the system. Let x denote the displacement of the resource from its rest position, and let θ represent the angular displacement of the pulley. The Lagrangian of the system can be expressed as L = T - V, where T is the kinetic energy and V is the potential energy. The kinetic energy T of the system consists of the kinetic energies of the masses and the resource. The potential energy V includes the potential energy due to gravity and the potential energy stored in the resource. By applying the Lagrange equations, we can derive the equations of motion for the system. On the other hand, Hamilton's method involves defining the generalized momenta as the partial derivatives of the Lagrangian with respect to the generalized coordinates' rates of change. By applying the Hamiltonian equations, we can obtain the equations of motion for the system. Overall, both Lagrange's method and Hamilton's method provide mathematical frameworks to derive the equations of motion for mechanical systems. While Lagrange's method focuses on energy considerations, Hamilton's method incorporates momentum considerations. These methods are valuable tools for analyzing the dynamics of complex systems in physics and engineering.
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What does the term iseparatietric mean with respect to finito con formulation? Why is iseparametric methodology soportant for dem modem nie elements!
The term isoparametric refers to a computational technique employed in the finite element method. This technique employs the same interpolation functions to describe both the element shape and the element solution and is important for modern numerical elements.
Explanation:
The finite element method is a numerical method that solves engineering problems by dividing a domain into smaller regions called elements and analyzing the behavior of the solution within each of these elements. The geometry of the problem is generally non-linear, which means that it can't be described easily by a few simple equations.The isoparametric technique is an approach used to describe the geometry and the solution within each element by using the same mathematical functions. It means that the same shape functions that describe the geometry of an element are also used to describe the variation of the solution within that element.This technique was first introduced in the early 1960s and is now the most commonly used method for approximating solutions to engineering problems using the finite element method. This is due to its ability to accurately model complex geometries and to provide solutions that converge quickly to the exact solution.
The isoparametric technique is critical for modern numerical elements because it allows for a much more accurate representation of the solution within each element. By using the same mathematical functions to describe both the geometry and the solution, the isoparametric technique eliminates the need to interpolate the solution between different sets of functions, which can lead to inaccuracies and errors.In addition to its accuracy, the isoparametric technique is also computationally efficient, which is essential for modern numerical elements. By using the same functions to describe both the geometry and the solution, the number of operations required to solve the problem is greatly reduced. This means that the method is faster and requires fewer computational resources than other methods.This is why the isoparametric technique is so important for modern numerical elements. By providing an accurate and efficient method for solving complex engineering problems, the isoparametric technique has revolutionized the field of finite element analysis.
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(a) Two plates have the same thickness (h) and cross sectional area (A) but different thermal conductivities (ki) and (k2). Consider the two plates are joined together in following two arrangement with all edges insulated. (i) Heat passing through Plate 1 and then Plate 2 in series; and (ii) Heat passing through Plate 1 and Plate 2 side by side in parallel. For exposed surfaces at two ends which are kept at constant temperatures, T₁ and Tb, and based on electrical analogy, develop the analogous equations for calculating the heat conduction rate through the two plates for the conditions as mentioned above. (12 marks) (b) Based on the results obtained in (a), calculate the corresponding thermal resistances for the both cases in (a) with h = 10 mm, A = 20 cm², kı₁ = 2 W/mK and k2 = 20 W/mK. (6 marks) (c) Discuss the application of the results in (a) and (b) for analysing heat transfer across building façade constructed by various materials and combinations at different seasons. (7 marks)
Two plates have the same thickness (h) and cross-sectional area (A) but different thermal conductivities (ki) and (k2). Consider the two plates joined together in the following two arrangements with all edges insulated.
Heat passing through Plate 1 and then Plate 2 in series.2. Heat passing through Plate 1 and Plate 2 side by side in parallel.For exposed surfaces at two ends that are kept at constant temperatures, T₁ and Tb, and based on electrical analogy, develop the analogous equations for calculating the heat conduction rate through the two plates for the conditions as mentioned above.
The rate of heat flow is proportional to the temperature gradient through the two plates, and the temperature gradient is proportional to the temperature difference across the two plates. By using Fourier's Law of Heat Conduction, we can derive analogous equations for both series and parallel configurations.
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Q. 1 Model and simulate a thermal heating house system using Simulink models controlled by ON/OFF control strategy to calculate the heating cost taking into account the outdoor environment, the thermal characteristics of the house, and the house heater system. Your answer should include Simulink models of the whole system showing the heat cost and a comparison between the in and out doors temperatures, the heater unit and the house. Also, write the mathematical equations of both heater and house.
The Simulink model of the thermal heating house system can be used to optimize energy efficiency and reduce heating costs.
The Simulink model of the thermal heating house system using ON/OFF control strategy is presented below:There are three main components of the thermal heating house system, which are the outdoor environment, the thermal characteristics of the house, and the house heater system. The outdoor environment affects the overall heat loss of the house.
The thermal characteristics of the house describe how well the house retains heat. The house heater system is responsible for generating heat and maintaining a comfortable temperature indoors.In the thermal heating house system, heat transfer occurs between the house and the outdoor environment.
Heat is generated by the heater unit inside the house and is transferred to the indoor air, which then warms up the house. The temperature difference between the in and out doors and the heater unit and the house were calculated. The mathematical equations of both heater and house are shown below.Heater Equationq(t) = m * c * (T(t) - T0)T(t) = q(t) / (m * c) + T0House Equationq(t) = k * A * (Ti - Ta) / dT / Rq(t) = m * c * (Ti - To)
The heat cost can be calculated based on the amount of energy consumed by the heater unit. A comparison between the heat cost and the outdoor temperature can help determine how much energy is required to maintain a comfortable indoor temperature.
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A private healthcare clinics has enrolled in the Covid-19 vaccination pilot scheme. During the non-peak pandemic period, patients arrive at a rate of about five per hour according to a Poisson distribution. There is only one medical doctor in the clinics who can handle the vaccination, and it takes about ten minutes per patient for the vaccination, following an exponential distribution. (10 marks) (1) What is the probability that there are more than two patients in the system? More than four, six and eight patients? (ii) What is the probability that the system is empty? (111) How long will the patients have to wait on average before reaching the doctor? (iv) What is the average number of patients in the queue and in the system? (v) If a second medical doctor is added (who works at the same pace), how will the operating characteristics computed in parts (ii), (111) and (iv) change? Assume that patients wait in a single line and go to the first available doctor.
Arrival is Poisson distribution with λ = A -5 per hour (arrival).
Service is exponentially distributed with ω = 6 per hour
(since it takes lo minutes to serve a customer, So in 60 minutes it will serve 6)
here ω>λ
and also this is a M/M/1/∞/FCFS/∞
here M, M → Memory less arrival and
service 1 → No of server
∞ → queal length can be
∞ → population
FCFS First come first serve Rule
For this type of system, the probability that the system is empty is given by
I-e
where, e=γμ
I=γμ
= 1-5/6
= 1/6 probability that the system is empty
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microcontroller 18f452
write a subroutine that rea PortB(B0:B7)
and store the secound complement of port-B in a file registar
called scound-Complement Not (2nd comp = 1st comp+1)
Subroutines are portions of code that can be executed independently of the main program.
The above code can read the Port B and store the second complement of the read value in the scnd comp register. Here's a step-by-step explanation of how the subroutine works: In the first line, we load the Port B value into the working register w. PORTB is the register that stores the data on port B in the microcontroller.
W is a working register that can be used for temporary storage of data and calculations. The second line in the subroutine takes the w register and complements its contents. This complement is then stored in w itself. In the third line, the value 1 is added to the contents of w register, using the add lw instruction.
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A cylindrical bar of ductile cast iron is subjected to reversed and rotating-bending tests, test results (i.e., S-N behavior) are shown in Animated Figure 8.21. If the bar diameter is 8.46 mm, determine the maximum cyclic load that may be applied to ensure that fatigue failure will not occur. Assume a factor of safety of 2.22 and that the distance between loadbearing points is 59.9 mm.
To determine the maximum cyclic load for the cylindrical bar of ductile cast iron, we use the S-N (stress-number of cycles to failure) behavior data and factor of safety. With a bar diameter of 8.46 mm and a distance of 59.9 mm between load-bearing points, the maximum cyclic load is calculated to ensure fatigue failure does not occur.
In the S-N behavior data, we have a graph showing the relationship between stress and the number of cycles to failure. To calculate the maximum cyclic load, we follow these steps:
1. Determine the endurance limit: Identify the stress level corresponding to the desired number of cycles to failure without fatigue failure. In this case, we assume a factor of safety of 2.22. Find the stress value on the S-N curve for this desired number of cycles.
2. Calculate the maximum cyclic load: The maximum cyclic load can be obtained by multiplying the endurance limit by the cross-sectional area of the bar. The cross-sectional area can be calculated using the bar diameter.
By applying these calculations, we can determine the maximum cyclic load that the cylindrical bar of ductile cast iron can withstand without experiencing fatigue failure. The factor of safety ensures that the applied load remains within the safe range and provides a margin of safety to account for uncertainties and variations in material properties.
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3.5 kg of water are present in a saturated liquid-vapor filling a container whose volume is 1.5 m^3 at a temp of 30 C. What is the pressure value inside the container? Calculate quality x. Calculate the entropy.
The pressure value inside the container is 118.8 kPa. The quality x is 0.914. The entropy is 7.815 kJ/K. We can determine the pressure inside the container by using the saturation tables.
Saturation tables provide information about the state of a substance at a given temperature and pressure. They include values such as saturation pressure, specific volume, enthalpy, and entropy of the substance. The saturation pressure is the pressure at which the substance changes phase from a liquid to a vapor or vice versa.
It is also known as the vapor pressure of the substance. Given that there are 3.5 kg of water present in a saturated liquid-vapor filling a container whose volume is 1.5 m³ at a temperature of 30 °C, we can use the saturation tables to determine the pressure value inside the container.
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Strength of materials was concern with relation between load and stress. The slope of stress-strain called the modulus of elasticity. The unit of deformation has the same unit as length L. true false
The statement "The unit of deformation has the same unit as length L" is true in Strength of Materials. Strength of Materials is concerned with the relationship between load and stress.
The slope of the stress-strain curve is called the modulus of elasticity, which measures a material's stiffness, or how much it resists deformation when subjected to a force.When a load is applied to a material, it causes a stress to develop, which is the force per unit area. If the load is increased, the stress also increases, and the material will eventually reach a point where it can no longer withstand the load and will deform or fail.
Deformation is the change in length, angle, or shape of a material due to an applied load. The unit of deformation is the same as the unit of length, which is typically meters or millimeters. This means that if a material is subjected to a load and experiences a deformation of 2 mm.
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1. You are to write a program that will do the following: . Initialize the system properly to utilize the motor driver chip to control a 4-phase unipolar stepper motor and wire the motor appropriately. Before entering the program loop.. Prompt the user for the number of steps needed to rotate the motor by 1 full revolution. This will be used to initialize the motor Prompt the user for the rotation rate in revolutions per minute (rpm) for the motor when it is rotating. Prompt the user for an initial motor direction, clockwise or counter-clockwise. In the program loop ... . The user should be presented with a menu with options to change any of the initial characteristics plus an option to select a number of steps for the motor to take in the specified direction and speed. Once a number of steps is selected, the motor should rotate that number of steps then the loop should begin again. 2. Compile the main program with the all necessary subroutines. Test and debug the program until it operates correctly. Once your program works, demonstrate it to your lab instructor. . • .
Once the program is compiled, it should be tested, and debugging should be done to make sure it operates correctly. -Demonstration: Once the program is tested and working, it should be demonstrated to the lab instructor to prove its functionality.
In order to program a motor driver chip to control a 4-phase unipolar stepper motor, it is essential to follow certain steps. The following is the outline of the process, which is also a comprehensive answer to the question stated above:Initial steps: To initialize the system, it is required to wire the motor correctly and use a motor driver chip. The motor driver chip will help to regulate the speed, direction, and position of the motor. -Prompt the user:
Once the initialization is done, the user should be prompted to enter the number of steps required to rotate the motor by one complete revolution, followed by the RPM rate of rotation, and the initial direction of the motor. -Program loop: Once the user has entered the required information, the program loop should begin. In this loop, the user should be presented with an option to change the initial characteristics and select the number of steps required for the motor to move in the selected direction and speed. -Motor rotation: Once the number of steps is selected, the motor will rotate in the specified direction and speed.
Once the required number of steps is complete, the loop should begin again. -Subroutines: It is important to have all necessary subroutines and compile the main program. Once the program is compiled, it should be tested, and debugging should be done to make sure it operates correctly. -Demonstration: Once the program is tested and working, it should be demonstrated to the lab instructor to prove its functionality.
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A steel block [E = 29 x 103 ksi and v = 0.33] has initial side lengths all equal to 56 inches. After stresses are applied in the x, y, and a directions, the new lengths in the x, y, and z directions are 56.06 in., 56.10 in., and 55.95 in., respectively. Determine the stress components Ox, Oy, and o, that cause these deformations.
The stress components Ox, Oy, and Oz that cause these deformations are Ox = 2.07 ksi, Oy = 3.59 ksi, and Oz = -2.06 ksi, respectively.
Given information:
Young's modulus of elasticity, E = 29 x 103 ksi
Poisson's ratio, ν = 0.33
Initial length of the block, a = b = c = 56 inches
Change in the length in the x-direction, ΔLx = 0.06 inches
Change in the length in the y-direction, ΔLy = 0.10 inches
Change in the length in the z-direction, ΔLz = -0.05 inches
To determine the stress components Ox, Oy, and Oz that cause these deformations, we'll use the following equations:ΔLx = aOx / E (1 - ν)ΔLy = bOy / E (1 - ν)ΔLz = cOz / E (1 - ν)
where, ΔLx, ΔLy, and ΔLz are the changes in the length of the block in the x, y, and z directions, respectively.
ΔLx = 0.06 in.= a
Ox / E (1 - ν)56.06 - 56 = 56
Ox / (29 x 103)(1 - 0.33)
Ox = 2.07 ksi
ΔLy = 0.10 in.= b
Oy / E (1 - ν)56.10 - 56 = 56
Oy / (29 x 103)(1 - 0.33)
Oy = 3.59 ksi
ΔLz = -0.05 in.= c
Oz / E (1 - ν)55.95 - 56 = 56
Oz / (29 x 103)(1 - 0.33)
Oz = -2.06 ksi
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