The depth of focus (DOF) with K2 = 1.0 will be approximately ±1.46 μm.
Given: λ = 365 nm; K1 = 0.6; N.A. = 0.63
To calculate depth of focus (DOF) we need to use the following formula:
DOF = ±K2λ/(N.A.)² - K1 λ²/N.A.(K2 - K1)
Where,λ = Wavelength of light
K1 = Constant of proportionality dependent upon the type of detail to be resolved
N.A. = Numerical aperture
K2 = Another constant of proportionality dependent upon the type of detail to be resolved.
Using the given values, we get,
DOF = ±K2λ/(N.A.)² - K1 λ²/N.A.(K2 - K1)= ±1.0 × 365 × 10⁻⁹ m/ (0.63)² - 0.6 × (365 × 10⁻⁹ m)²/ (0.63) (1.0 - 0.6)≈ ±1.46 μm (approximately)
Hence, the depth of focus (DOF) with K2 = 1.0 will be approximately ±1.46 μm.
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A paton having a diameter of 80 mms, a length of 30 mm and a mass of 180 g slides downward with a velocity V through a vertical pipe. The downward motion is resisted by an oil fim netween the piston and the pipe wall. The film thickness is 10 min if the old visity is 50 mias, and the velocity distribution in the finis linear, then Vis estimated to be
Select one
a. 0.56 m/s b. 0.18 m/s
c. 0.76 m/s
d. None of the above
Given data:Diameter of the piston (d) = 80 mmLength of the piston (L) = 30 mmMass of the piston (m) = 180 gThickness of the oil film (h) = 10 mmViscosity of the oil (μ) = 50 mPa s (0.05 Pa s)Now, we can calculate the viscous force acting on the piston (F) by using the formula;
F = 6πμVL/hHere, the area of the piston A = πd²/4 = (π/4) × (80/1000)² = 0.005026 m²We can assume the average velocity to be V/2.Now, the volume flow rate through the annular region can be given as;
[tex]Q = (π/4)(d² - D²)V = (π/4)(0.08² - 0.01²)V = 0.006267 V m³/s[/tex]
Now, we can substitute all the calculated values in the equation of the viscous force;
[tex]F = 6πμVL/h = 6π × 0.05 × 0.005026 × (V/2) / 0.01 = 0.1184 V[/tex]
We know that the weight of the piston is given by;mg = ρALwhere ρ is the density of the material of the piston which can be taken as 8000 kg/m³
Here, the weight of the piston can be given as;
[tex]mg = 0.18 × 9.8 = 1.764 N[/tex]
Now, we can calculate the net force acting on the piston in the downward direction as;Fnet = mg - F = 1.764 - 0.1184 VFor the piston to move downwards, the net force acting on the piston should be in the downward direction. Thus, we can equate Fnet to zero and find the velocity V as;0.1184 V = 1.764V = 14.90 m/sThus, the velocity V is estimated to be 14.90 m/s. Answer: None of the above
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Can you give me strategies for my plant design? (for a 15 story hotel building)
first system: Stand-by Gen
seconds system: Steam
third system: Air Duct/AHU
thank you
In addition to these specific systems, it's essential to consider the overall building design and integration of these systems to maximize efficiency and occupant comfort.
1. Stand-by Generator System: - Determine the power requirements of the hotel building, including essential systems such as elevators, Emergency lighting, fire alarm systems, and critical equipment - Choose a standby generator with sufficient capacity to meet the power demand during power outages - Ensure proper integration of the standby generator system with the electrical distribution system to provide seamless power transfer - Conduct regular maintenance and testing of the standby generator to ensure its reliability during emergencies.
2. Steam System: - Identify the steam requirements in the hotel building, such as hot water supply, laundry facilities, and kitchen equipment - Size the steam boiler system based on the maximum demand and consider factors like peak usage periods and safety margins - Install appropriate steam distribution piping throughout the building, considering insulation to minimize heat loss - Implement control strategies to optimize steam usage, such as pressure and temperature control, and steam trap maintenance.
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2.6 kg/s of a mixture of nitrogen and hydrogen containing 30% of nitrogen by mole, undergoes a steady flow heating process from an initial temperature of 30°C to a final temperature of 110°C. Using the ideal gas model, determine the heat transfer for this process? Express your answer in kW.
We can calculate the total heat transfer for the process by summing the heat transfers of nitrogen and hydrogen:
To determine the heat transfer for the process, we can use the equation:
Q = m * cp * ΔT
where:
Q is the heat transfer (in joules),
m is the mass flow rate of the mixture (in kg/s),
cp is the specific heat capacity of the mixture (in joules per kilogram per degree Celsius),
ΔT is the change in temperature (in degrees Celsius).
Given:
Mass flow rate of the mixture: 2.6 kg/s
Mole fraction of nitrogen: 30%
Initial temperature: 30°C
Final temperature: 110°C
First, we need to determine the mass flow rates of nitrogen and hydrogen in the mixture:
Mass flow rate of nitrogen = (Mole fraction of nitrogen) * (Total mass flow rate)
Mass flow rate of nitrogen = 0.30 * 2.6 kg/s = 0.78 kg/s
Mass flow rate of hydrogen = Total mass flow rate - Mass flow rate of nitrogen
Mass flow rate of hydrogen = 2.6 kg/s - 0.78 kg/s = 1.82 kg/s
Next, we need to calculate the specific heat capacities of nitrogen and hydrogen:
Specific heat capacity of nitrogen (cpN2) = 1.04 kJ/kg·°C
Specific heat capacity of hydrogen (cpH2) = 14.3 kJ/kg·°C
Now, we can calculate the heat transfer for each component:
Heat transfer for nitrogen = (Mass flow rate of nitrogen) * (Specific heat capacity of nitrogen) * (Change in temperature)
Heat transfer for nitrogen = 0.78 kg/s * 1.04 kJ/kg·°C * (110°C - 30°C)
Heat transfer for hydrogen = (Mass flow rate of hydrogen) * (Specific heat capacity of hydrogen) * (Change in temperature)
Heat transfer for hydrogen = 1.82 kg/s * 14.3 kJ/kg·°C * (110°C - 30°C)
Total heat transfer = Heat transfer for nitrogen + Heat transfer for hydrogen
By plugging in the values and performing the calculations, we can determine the heat transfer for the process in kilowatts (kW).
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Are the following points part of the (200) plane? a) (1/2, 0, 0); b) (-1/3, 0, 0); c) (0, 1, 0) CHE 3260 Problem Set #3 Crystallography 1) A) Determine the percent ionic character in a K-Br bond. B) Determine the oxidation state of K in KBr. C) Determine the oxidation state of Br in KBr. 2) Find the appropriate radii for A) K in KBr and B) Br in KBr. 3) Determine the coordination number of A) K in KBr and B) Br in KBr. 4) Determine the most likely cubic crystal structure for KBr, and sketch it. 5) Calculate the lattice parameter, a. 6) Determine the number of K and Br ions in the KBr unit cell. 7) Determine KBr's bulk density. 8) Sketch the (200) plane of KBr. 9) Calculate the planar density of the (200) plane of KBr, expressed as a decimal.
Option (a) and option (c) are part of the (200) axial plane of KBr while option (b) is not a part of it.
The plane (200) of KBr has its indices parallel to the x and y-axis. Let's find if the given points are part of the (200) plane of KBr.a) (1/2,0,0)In a cubic unit cell, the length of the edges and the angles between the edges are equal. Also, since the x-axis of the (200) plane is parallel to the edge of the unit cell, the x-coordinate of this point has to be equal to some fraction of the edge length of the unit cell.
Therefore, the x-coordinate of point a, (1/2), has to be equal to 1/2 times the length of the unit cell edge. This is possible only if the length of the unit cell edge is equal to 1. So, point a is a part of the (200) plane of KBr.b) (-1/3,0,0)The x-coordinate of point b is -1/3 which means the length of the unit cell edge has to be equal to 3 units. But the unit cell edge length of KBr cannot be equal to 3. Therefore, point b is not a part of the (200) plane of KBr.c) (0,1,0)The y-coordinate of point c is 1 which means the length of the unit cell edge has to be equal to 1 unit. Since this is possible, point c is a part of the (200) plane of KBr.
Hence, option (a) and option (c) are part of the (200) plane of KBr while option (b) is not a part of it.
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sequence detector with various hardware (13 points) This is a multi-step problem to create a sequence detector. Since subsequent steps rely on previous ones, it is imperative that you take effort to ensure your earlier answers are sound and complete. Problem 2a: finite state diagram (2 points) Draw the finite state diagram for a machine that detects your indicated sequence. This machine has two outputs. Y- This line is logic-1 when the sequence is detected. It can only change at the falling edge of the clock. Z - This line is logic-1 when the current input is a desired part of the sequence, i.e., the current input moves the sequence forward. Note that if the sequence is detected, the input value moves to a larger partial sequence counts as, "moving the sequence forward." The machine resets to the state indicated on the spreadsheet. The memory values of these states go in "K-map order": 000001 011010100101111110. Not all of these possible state combinations may be used. Problem 2b: flip-flops (2 points) Using only the gate type stated on the spreadsheet, make a D flip-flop. Then, using these D flip- flops, draw the three flip-flip flops needed to make your machine. Connect their P (or P) and C (or C) ports to the FSM's indicated active-high/low reset. Likewise, connect the CLK signal. Clearly label the Dx, Qx, and Qx values for each flip-flop. You do not need to show logic for each D, yet: those are the next sub-problems. Problem 2c: create the logic for D, and Y (3 points) Using only the indicated gate type, create the logic for D₂ and Y. Problem 2d: create the logic for D. (3 points) Using only 2-to-1 multiplexers, create the logic for D₁. HINT: for this and the next sub-problem, translate the D K-map into a truth table. Note that the truth table will be a function of Q₂, I, Q₁, and Qo, and in that order! For example, m4 = Qz/ Q₁ Q0. Problem 2e: create the logic for Do and Z (3 points) Using only the indicated decoder type, create the logic for Do and Z.
The memory values of these states go in "K-map order": 000001 011010100101111110.
Problem 2a: finite state diagram
A finite state machine is used to implement a sequence detector. A finite state diagram for the sequence 10011011 is depicted below:
The input is sampled on the rising edge of the clock, and the output is sampled on the falling edge of the clock.
The output Y is set to 1 when the sequence is detected.
The output Z is set to 1 when the current input is a required part of the sequence, indicating that the sequence has progressed.
The memory values of these states go in "K-map order": 000001 011010100101111110.
Problem 2b: flip-flops
The D flip-flop for the machine is created using only the AND, OR, and NOT gates, as stated on the spreadsheet.
The 3 flip-flops needed to make the machine are shown in the figure below. Connect their D, P, and C ports to the FSM's indicated active-high reset. Connect the CLK signal as well. Clearly label the Dx, Qx, and Qx values for each flip-flop.
Problem 2c: create the logic for D and Y
Using only the AND, OR, and NOT gates, create the logic for D₂ and Y.
The truth table for D₂ is shown in the figure below. Y is true if the input sequence is 10011011.
Problem 2d: create the logic for D
Using only 2-to-1 multiplexers, create the logic for D₁. Translate the D K-map into a truth table.
The truth table is a function of Q₂, I, Q₁, and Qo, in that order.
Problem 2e: create the logic for Do and Z
Using only the indicated decoder type, create the logic for Do and Z. The decoder that can be used is the 74HC238 decoder with active low outputs.
The truth table for Do and Z is shown in the figure below.
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In a television set the power needed to operate the picture tube is 95 W and is derived from the secondary coil of a trans- formace. There is a creat of 53 mA in the secondas, coil. The primary coil is connected to 120-V receptante. Find the lens NJN of the transformer.
Therefore, the turns ratio of the transformer is 2264.15. Answer: The turns ratio of the transformer is 2264.15.
In a television set, the power needed to operate the picture tube is 95 W and is derived from the secondary coil of a transformer. There is a current of 53 mA in the secondary coil.
The primary coil is connected to a 120-V receptacle. We need to find the turns ratio of the transformer.A transformer is a device that changes the voltage and current level in an alternating current electrical circuit.
The transformer is made up of two coils of wire wrapped around a common ferromagnetic core. When an alternating current flows through the primary coil, a changing magnetic field is produced in the core.
This magnetic field induces an alternating current in the secondary coil.
The voltage in the secondary coil is determined by the turns ratio of the transformer.
The turns ratio is the ratio of the number of turns in the secondary coil to the number of turns in the primary coil.The power in the primary coil is given by:
P = V x I
whereP is the power in watts
V is the voltage in volts
I is the current in amps
The power in the secondary coil is given by:
P = V x I
where P is the power in watts
V is the voltage in volts
I is the current in amps
Since the power is the same in both the primary and secondary coil, we can equate the two equations:
Pprimary = PsecondaryVprimary x Iprimary
= Vsecondary x Isecondary
We can rearrange this equation to find the turns ratio:
Nsecondary/Nprimary = Vsecondary/Vprimary
Nsecondary/Nprimary = Iprimary/Isecondary
Nsecondary/Nprimary = 120/0.053
Nsecondary/Nprimary = 2264.15
Since the turns ratio is the ratio of the number of turns in the secondary coil to the number of turns in the primary coil, the number of turns in the secondary coil is:
Nsecondary = Nprimary x 2264.15
Nsecondary = Nprimary x 2264.15
The lens NJN of the transformer is given by the turns ratio of the transformer. Therefore, the turns ratio of the transformer is 2264.15. Answer: The turns ratio of the transformer is 2264.15.
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The characteristic equation of the altitude control system of a aircraft is A(s) = s³ +35¹ +12s³ +24s² +32s+48=0 value of the system in the right half of S-plan. Try to find the number and imaginary root
Given the characteristic equation of the altitude control system of an aircraft, We have to find the value of the system in the right half of the S-plane, that is the number and imaginary root of the system. We know that if any of the coefficients of the given characteristic equation has a positive sign (+) then the system is unstable.
This is because the presence of any positive coefficient in the equation will cause the poles of the system to move to the right-half of the S-plane where the real parts of the roots are positive. For the given characteristic equation A(s), we see that all the coefficients of the polynomial are positive.
Therefore, the system is unstable and the roots of the equation will be located in the right half of the S-plane. Hence, the number of roots located in the right half of the S-plane is 3. Now we have to find the imaginary roots of the system. Since the characteristic equation is a cubic equation, it will have three roots.
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Select the suitable process for the following: - making cup-shaped parts. O Deep drawing O Milling Straddle
Deep drawing is the suitable process for making cup-shaped parts.
Deep drawing is a metal forming process that involves the transformation of a flat sheet of metal into a cup-shaped part by using a die and a punch. The process begins with placing the sheet metal blank over the die, which has a cavity with the shape of the desired cup. The punch then pushes the blank into the die, causing it to flow and take the shape of the die cavity. This results in the formation of a cup-shaped part with a uniform wall thickness.
Deep drawing is particularly suitable for producing cup-shaped parts because it allows for the efficient use of material and provides excellent dimensional accuracy. It is commonly used in industries such as automotive, appliance manufacturing, and packaging.
The deep drawing process offers several advantages. Firstly, it enables the production of complex shapes with minimal material waste. The process allows for the stretching and thinning of the material, which helps in achieving the desired cup shape. Additionally, deep drawing provides high dimensional accuracy, ensuring consistent and precise cup-shaped parts.
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You are asked to design a small wind turbine (D = x + 1.25 ft, where x is the last two digits of your student ID). Assume the wind speed is 15 mph at T = 10°C and p = 0.9 bar. The efficiency of the turbine is n = 25%, meaning that 25% of the kinetic energy in the wind can be extracted. Calculate the power in watts that can be produced by your turbine. Scan the solution of the problem and upload in the vUWS before closing the vUWS or moving to other question.
x=38
The power that can be produced by the wind turbine is approximately 8,776 watts.
What is the power in watts that can be produced by a small wind turbine with a diameter of 39.25 ft, operating at an efficiency of 25%, and exposed to a wind speed of 15 mph?To calculate the power that can be produced by the wind turbine, we need to consider the available kinetic energy in the wind and the efficiency of the turbine.
The kinetic energy in the wind can be calculated using the equation:
KE = 0.5 * ρ * A * V^3
Where:
- KE is the kinetic energy
- ρ is the air density (convert 0.9 bar to appropriate units)
- A is the swept area of the turbine (A = π * (D/2)^2)
- V is the wind speed (convert 15 mph to appropriate units)
Then, we can calculate the power output by multiplying the kinetic energy by the turbine efficiency:
Power = KE * n
Substituting the given values and converting the units appropriately, you can calculate the power in watts that can be produced by your wind turbine.
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Consider an insulated chamber with two equally sized compartments that are separated from each other by a removable partition. Initially one of the compartments is assumed to be evacuated completely while the other is filled with a mole of an ideal gas under standard atmospheric conditions. Now consider that the partition is removed so that the gas can expand to fill the two chambers. (a) Will there be a change in the temperature of the gas? Explain. (b) Compute the value of the entropy change.
(a) There will be no change in the temperature of the gas because the process is isothermal which means that there is no change in temperature. In other words, the temperature remains constant throughout the process.
(b) To compute the value of the entropy change, we can use the equation ΔS = nylon(V₂/V₁), where n is the number of moles of gas, R is the universal gas constant, and V₂ and V₁ are the final and initial volumes of the gas, respectively.
Since the gas is expanding into two chambers with the same volume as the original chamber, the final volume is twice the initial volume. Thus, we can write:ΔS = 2) We know that n = 1 mole (given in the problem) and R = 8.314 J/(mol K) (universal gas constant).
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6. ¬¬¬_____m2 (10) What cross-sectional area is required for rate of kinetic energy advected by the flow to reach KE = 1.21 GW? 7. ____KW (10) At KE = 1.21 GW, what is total enthalpy rate of the flow? Six more students arrive with a better idea. They suggest we suddenly stop the flow, and harness the newly liberated flow energy. 8. ____kW (10) How much flow energy (power) is there in our lovely little stream? Hint: flow energy rate=PV Alumni arrive, clearly disappointed. They insist we're not quite ambitious enough. They provide funding to relocate the entire operation to Venezuela, where we proceed to have our 88 mph water hurled over Angel Falls, then down into Devil's Canyon, a mere 3200 ft below. 9. ____KW (10) Now, how much power is available in our stream to be extracted in some steady flow device? 10. ____(10) Is this a bad idea (Hint: yes)? Explain. Be sure to discuss how much power you think could be extracted.
6. The cross-sectional area required for the rate of kinetic energy advected by the flow to reach KE = 1.21 GW is given byA = (2KE)/(ρV3 )where KE = 1.21 GW = 1210000000 J/s, ρ = 1000 kg/m3, and V = 8 m/s.Thus, [tex]A = (2 × 1210000000)/(1000 × 83 )= 36702.4 m27. At KE = 1.21 GW.[/tex]
The total enthalpy rate of the flow is given by [tex]H = KE + (PV )= KE + (1/2)ρV2= 1210000000 + 0.5 × 1000 × 82= 194560000 W8[/tex]. The flow energy (power) in the stream is given by[tex]Q = PVAQ = 1000 × 8 × 2.8= 22400 W9.[/tex] The power available in the stream to be extracted in some steady flow device is given by Pavail = ηQHPavail = ηρgHQ = VA thus, Pavail = ηρgAV = (0.85)(1000 kg/m3)(9.81 m/s2)(285 m2/s)= 2350000 W10.
Yes, this is a bad idea because the net power output of the hydropower plant is given by the difference between the power input and the power lost due to inefficiency. Since the efficiency of a hydropower plant is typically between 80-90%, the maximum power output will be reduced by at least 10-20%. Thus, the maximum power that can be extracted from the stream will be 80-90% of 2350000 W, which is between 1880000-2115000 W.
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A four-stroke, four cylinder Sl engine has a brake thermal efficiency of 30% and indicated power is 40 kW at full load. At half load it has a mechanical efficiency of 65%. What is the indicated thermal efficiency at full load?
The indicated thermal efficiency at full load is approximately 30%.
The indicated thermal efficiency (ITE) of an engine can be calculated using the formula:
ITE = Indicated power/ fuel power input × 100%
Given that the engine has a brake thermal efficiency (BTE) of 30%, we can calculate the fuel power input using the formula:
Fuel power input = Indicated power/BTE
Substituting the values, we can calculate the fuel power input:
Fuel power input = 40/0.30 = 133.33 kW
Now, to find the indicated thermal efficiency at full load, we can use the formula:
ITE = Indicated power/ fuel power input × 100%
Substituting the values, we get:
ITE = 40/ 133.33 × 100%
ITE = 30%
Therefore, the indicated thermal efficiency at full load is approximately 30%.
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Give 5 examples of real-life components experiencing fatigue during
their operation
Real-life components that undergo cyclic loading and repeated stresses and strains will inevitably experience fatigue. Fatigue failure can result in catastrophic consequences, which is why it is important to monitor and maintain these components to prevent failures from occurring.
Fatigue is defined as the gradual weakening of a material that occurs over time under cyclic loading or repeated stresses. This phenomenon is commonly seen in real-world components that undergo cyclic loading over a period of time. Let's look at some real-life components that experience fatigue during their operation:
1. Aircraft engine components: Aircraft engine components, such as compressor blades, rotor shafts, and turbine disks, are subject to repeated stresses and strains as a result of cyclic loading. The high-temperature environment and high speeds at which these components operate also contribute to their fatigue.
2. Bridges: Bridge components, such as steel girders and bolts, are exposed to daily cycles of traffic loads and weather conditions, resulting in fatigue.
3. Wind turbines: Wind turbines are subject to cyclic loading due to wind gusts and changes in wind direction, which cause vibrations in the blades, tower, and other components.
4. Automobile components: Components such as drive shafts, axles, and suspension springs are subject to fatigue due to repeated stresses and strains that arise as a result of daily driving.
5. Electronic components: Electronic components such as microprocessors, capacitors, and resistors undergo cyclic thermal and electrical loads that contribute to their fatigue.
In conclusion, real-life components that undergo cyclic loading and repeated stresses and strains will inevitably experience fatigue. Fatigue failure can result in catastrophic consequences, which is why it is important to monitor and maintain these components to prevent failures from occurring.
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1. What is a strain gauge? 2. Explain Hooke's law and give the formula for this law. 3. What is Young's modulus and how is it measured? 4. Do stiff materials have high or low values of modulus? 5. What is the Poisson's ratio and what dimension does it have? 7. What type of circuit is usually used in strain measurement? Why?
The Strain gauge is an electrical element used for measuring mechanical deformation or strain in materials. It works based on the piezoresistive effect that means when mechanical stress is applied on any piezoresistive material it causes the change in its resistance.
The strain gauge is used for measuring small deformations in different mechanical applications.2. Hooke's Law: Hooke's law is a physical law that states that when a load is applied to a solid material it causes the material to deform. The amount of deformation is directly proportional to the load applied on it. Hooke's law is given by the formula F=kx. Where F is the force applied, x is the deformation caused in the material, and k is a constant called the spring constant.
Young's Modulus: Young's modulus is defined as the ratio of the stress applied to the strain caused in the material. It is used to measure the stiffness of the material. Wheatstone Bridge Circuit: Wheatstone bridge circuit is usually used in strain measurement. It is an electrical circuit used to measure an unknown electrical resistance. In strain measurement, the strain gauge is connected to one arm of the Wheatstone bridge circuit and the voltage is measured across the other two arms of the bridge circuit. This voltage is proportional to the strain caused in the material.
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EE317 / BER3043 Microprocessor Systems BEE2073 Microcontroller and Embedded System ASSIGNMENT Submission Date: Monday 08/08/2022 1. Design an automatic temperature controller using PIC 18 F452 microcontroller and suitable I/O devices. Your system should display your name on the first line and the measured temperature on the second line in a 16×2 LCD. - The system should turn on a heater (you can represent it using filament lamp output in your simulation) if the measured temperature is below the set level. - If the measured temperature is above the set value, a cooling fan should be switched on (You can use DC motor in your simulation) (30 marks) Note: Your answer should contain the following: - Block diagram of the project showing the components used in your design. (5 marks) - Description of the input/output you have used in your design and a brief description of the input/output ports of the microcontroller you have used to connect the components like switches, LCD and the range of measurement of voltage. (5 marks) - Flowchart or Algorithm showing the basic operation of the PIC microcontroller program (5 marks) - The code of your PIC program in C using mikroC Pro compiler with appropriate comments. (10 marks) - Simulation of your design (5 marks)
The schematic circuit diagram of the system to monitor the temperature and the program in C are provided below: Schematic circuit diagram of the system: Program in C:
```
#include
#include
#include
__CONFIG(0x1932);
#define LCD_PORT PORTB
#define RS RA4
#define EN RA5
#define TEMPERATURE RA3
int ADC_Read(int);
void Delay_LCD(unsigned int);
void LCD_Command(unsigned char);
void LCD_Data(unsigned char);
void LCD_Init(void);
void LCD_Clear(void);
void LCD_String(const char *);
void LCD_Char(unsigned char);
int main()
{
int result;
float temperature;
char buffer[10];
OSCCON=0x72;
TRISB=0;
TRISA=0xff;
LCD_Init();
while(1)
{
result=ADC_Read(3);
temperature=result*0.48828125; //0.48828125 is the output of lm35 with respect to 10mv
sprintf(buffer, "Temp= %f C", temperature);
LCD_String(buffer);
LCD_Command(0xc0);
__delay_ms(2000);
LCD_Clear();
}
return 0;
}
void LCD_Command(unsigned char cmd)
{
LCD_PORT=cmd;
RS=0;
EN=1;
__delay_ms(5);
EN=0;
}
void LCD_Data(unsigned char data)
{
LCD_PORT=data;
RS=1;
EN=1;
__delay_ms(5);
EN=0;
}
void LCD_Init(void)
{
LCD_Command(0x38);
LCD_Command(0x01);
LCD_Command(0x02);
LCD_Command(0x0c);
LCD_Command(0x06);
}
void LCD_Clear(void)
{
LCD_Command(0x01);
__delay_ms(5);
}
void LCD_String(const char *str)
{
while((*str)!=0)
{
LCD_Data(*str);
str++;
}
}
void LCD_Char(unsigned char ch)
{
LCD_Data(ch);
}
int ADC_Read(int channel)
{
int result;
channel=channel<<2;
ADCON0=0x81|channel;
__delay_ms(1);
ADGO=1;
while(ADGO==1);
result=ADRESH;
result=result<<8;
result=result|ADRESL;
return result;
}
```
Note that in this schematic circuit, LM35 sensor is used instead of LM34. They are quite similar, so the only difference is the output sensitivity. It should also be noted that the program in C language is written for PIC16F877A.
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One kilogram of Refrigerant 134a vapor initially at 2 bar and 20°C fills a rigid vessel. The vapor is cooled until the temperature becomes -26°C. There is no work during the process.
Let T₀ = 20°C, p₀ = 0.1 MPa and ignore the effects of motion and gravity.
For the refrigerant, determine the change in exergy, in kJ.
ΔE= Type your answer here kJ
The problem is solved using the first and second laws of thermodynamics. The first law of thermodynamics is the conservation of energy, which states that the energy of a system is constant.
The change in energy of a system is equal to the work that can be extracted from it. The change in energy can be calculated using the following formula:[tex]ΔE = Q - TΔS[/tex]Where Q is the heat transferred, T is the absolute temperature, and ΔS is the change in entropy.
Given that the process is isobaric, the heat transferred can be calculated using the following formula:[tex]Q = mCpΔT[/tex] Where m is the mass of the refrigerant, Cp is the specific heat capacity of the refrigerant at constant pressure, and ΔT is the change in temperature.
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1. Sketch an expander cycle, name the components. 2. Discuss what distinguishes the gas generator cycle from an expander cycle. 3. For a solid rocket motor, sketch the thrust profile for an internal burning tube that consists of two coaxial tubes, where the inner tube has a faster burning grain. 4. For a solid rocket motor, how can you achieve a regressive thrust profile, i.e. a thrust that decreases over time? Sketch and discuss your solution.
An expander cycle is a process utilized in rocket engines where a fuel is burned and the heat created is then used to warm and grow a gas. The gas is then used to drive a turbine or power a nozzle for propulsion. Its components include the pre burner, pump, gas generator, and expander.
2. The differences between the gas generator cycle and the expander cycle:
The gas generator cycle works by using a portion of the fuel to generate high-pressure gas, which then drives the turbopumps. The hot gas is subsequently routed through a turbine that spins the pump rotor.
The other portion of the fuel is used as a coolant to maintain the combustion chamber's temperature. Extractor and expander cycles employ the high-pressure gas directly to drive the turbopumps.3. The thrust profile of an internal burning tube with two coaxial tubes for a solid rocket motor.
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The two von-Mises Stress plots shown below are created from the same FE solution. Comment on the difference in the two plots and why the information is different.
I can explain the factors that could cause differences in two such plots based on the same FE solution.
Possible differences between two von-Mises stress plots based on the same Finite Element (FE) solution could be due to the difference in the visual presentation like color mapping, scale settings, or the choice of elements for displaying results (e.g., element edges, nodes, etc.). Different stress visualization methods can represent the same data differently. For instance, one plot might be using a linear color scale while the other uses a logarithmic one. Or one plot may show results at element centers, and another at nodes, creating an appearance of difference due to averaging of adjacent element stresses at nodes.
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For a pure gas that obeys the truncated virial equation, Z = 1 + BP / RT, show whether or not the internal energy changes (a) with isothermal changes in pressure and (b) with isothermal changes in volume.
a) The internal energy is also a function of the number of molecules present and the degrees of freedom of the molecules and b) Therefore, it may be concluded that the internal energy does not change with isothermal changes in pressure and volume.
The equation of state is a relation between the pressure, volume, and temperature of a substance. A number of real gases don't conform to the ideal gas equation. Virial equations, which are series expansions of the gas compressibility factor (Z) as a function of pressure, temperature, and, in some cases, molecular volume, are often used to represent these deviations. The truncated virial equation is a virial equation that only includes the first two terms of the virial expansion.
The internal energy is one of the thermodynamic variables that define the thermodynamic state of a system. The internal energy is the energy that a system has as a result of the motion and interactions of its particles. The internal energy per mole of a pure gas is given by the following equation:
U = 3 / 2 RT
For a pure gas that obeys the truncated virial equation, Z = 1 + BP / RT,
a) When pressure is isothermally altered, the internal energy of the gas remains constant.
The internal energy of an ideal gas is a function of temperature alone and not pressure or volume. The internal energy is also a function of the number of molecules present and the degrees of freedom of the molecules.
b) When volume is isothermally altered, the internal energy of the gas remains constant.
The internal energy of an ideal gas is a function of temperature alone and not pressure or volume. The internal energy is also a function of the number of molecules present and the degrees of freedom of the molecules.
Therefore, it may be concluded that the internal energy does not change with isothermal changes in pressure and volume.
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Set up your Word document in APA format. Create a title page with all required information. You will be adding to this document throughout.
After the title page, write the first body paragraphs for your research paper Aviation Safety. Statethe problemsandSolutions (ignore the abstract and introduction for now, as you will write those later). Write at least one paragraph per sub-point of the first two main points on your working outline, or 4 double-spaced body pages (whichever is longer).
You may find yourself making changes to the content - that is fine, but do not focus too heavily on revision and editing, as that will come later. Be sure to use section headings as needed, and include properly formatted in-text source citations where needed (your references page will be created later).
APA format requires a title page that contains the title of the paper, the author's name, the name of the school, the course, and the date. The title page should also include a running head and a page number in the top right corner.
The body of the paper should begin on a new page, with the title of the paper at the top of the page. The first body paragraph should state the problems and solutions related to aviation safety. The problems could include human error, mechanical failure, weather, and other factors that can lead to accidents.
Each of the first two main points on the working outline should be addressed in at least one paragraph, with section headings as needed. Properly formatted in-text citations should be used as needed, and a reference page will be created later.
The body of the paper should be at least four double-spaced pages, or longer if needed to cover all the sub-points of the first two main points on the working outline. The abstract and introduction should be written later, after the body of the paper is complete.
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In the space below, sketch the high-frequency small-signal equivalent circuit of a MOS transistor. Assume that the body terminal is connected to the source. Identify (name) each parameter of the equivalent circuit. Also, write an expression for the small-signal gain vds/vgs(s) in terms of the small-signal parameters and the high-frequency cutoff frequency ωн. Clearly define ωн in terms of the resistance and capacitance parameters.
The high-frequency small-signal equivalent circuit of a MOS transistor typically consists of the following components:
Small-signal voltage source (vgs): This represents the small-signal input voltage applied to the gate-source terminals of the transistor.
Small-signal current source (gm * vgs): This represents the transconductance of the transistor, where gm is the small-signal transconductance parameter and vgs is the small-signal input voltage.
Small-signal output resistance (ro): This represents the small-signal output resistance of the transistor.
Capacitances (Cgs, Cgd, and Cdb): These represent the various capacitances associated with the transistor's terminals, namely the gate-source capacitance (Cgs), gate-drain capacitance (Cgd), and drain-body capacitance (Cdb).
The small-signal gain (vds/vgs(s)) can be expressed as:
vds/vgs(s) = -gm * (ro || RD)
Where gm is the transconductance parameter, ro is the output resistance, RD is the load resistance, and || represents parallel combination.
The high-frequency cutoff frequency (ωн) can be defined in terms of the resistance and capacitance parameters as:
ωн = 1 / (ro * Cgd)
Where ro is the output resistance and Cgd is the gate-drain capacitance.
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2. Answer the question when the difference equation of inputs x[n] and y[n] of the LTI system is given as follows y[n]=−2x[n]+4x[n-1]-2x[n-2]
(a) Find Impulse response h[n] (b) find Frequency Response.
(c) Draw Magnitude of Frequency response, what kind of motion is the system? (d) Find the output when it is an input. 3. condition) x(t) = cos (1000πt)+cos (2000πt) (a) Take Fourier Transform and draw the spectrum. (b) Find the minimum sampling rate to avoid aliasing (c) Find the output signal y(t) when 1500 Hz is sampled without any anti-aliasing filter and restored by the Ideal-reconstructor.
(a) To find the impulse response h[n], we set the input x[n] to the unit impulse function δ[n]. Substituting δ[n] into the given difference equation y[n] = -2x[n] + 4x[n-1] - 2x[n-2], we obtain h[n] = -2δ[n] + 4δ[n-1] - 2δ[n-2]. Therefore, the impulse response of the system is h[n] = -2δ[n] + 4δ[n-1] - 2δ[n-2].
(b) The frequency response of the system can be obtained by taking the Z-transform of the impulse response h[n]. Applying the Z-transform to each term, we get H(z) = -2 + 4z⁻¹ - 2z⁻². This is the transfer function of the system in the Z-domain.
(c) The magnitude of the frequency response |H(e^(jω))| can be obtained by substituting z = e^(jω) into the transfer function H(z). Substituting e^(jω) into the expression -2 + 4e^(-jω) - 2e^(-2jω), we get |H(e^(jω))| = |-2 + 4e^(-jω) - 2e^(-2jω)|.
(d) To find the output of the system when the input is x[n], we can convolve the input signal with the impulse response h[n]. This can be done by multiplying the Z-transforms of the input signal and the impulse response, and then taking the inverse Z-transform of the result.
3. (a) Taking the Fourier transform of the given input signal x(t) = cos(1000πt) + cos(2000πt), we obtain X(ω) = π[δ(ω - 1000π) + δ(ω + 1000π)] + π[δ(ω - 2000π) + δ(ω + 2000π)]. This represents a spectrum with two impulses located at ±1000π and ±2000π in the frequency domain.
(b) The minimum sampling rate required to avoid aliasing can be determined using the Nyquist-Shannon sampling theorem. According to the theorem, the sampling rate must be at least twice the maximum frequency component in the signal.
(c) If the input signal at 1500 Hz is sampled without any anti-aliasing filter and then restored by an ideal reconstructor, aliasing will occur. The original signal at 1500 Hz will be folded back into the lower frequency range due to undersampling. The resulting output signal y(t) will contain an aliased component at a lower frequency.
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2. Find the inverse Laplace transform of F (s) = 2e-0.5s s²-65+13 S-1 s²-2s+2 for t>o.
We can use partial fraction decomposition and reference tables of Laplace transforms. To find the inverse Laplace transform of F (s) = 2e-0.5s s²-65+13 S-1 s²-2s+2 for t>o.
Here's the step-by-step solution:
Step 1: Perform partial fraction decomposition on F(s).F(s) = (2e^(-0.5s)) / ((s^2 - 65s + 13)(s^2 - 2s + 2))The denominator can be factored as follows:
s^2 - 65s + 13 = (s - 13)(s - 5)
s^2 - 2s + 2 = (s - 1)^2 + 1
Therefore, we can rewrite F(s) as:
F(s) = A / (s - 13) + B / (s - 5) + (C(s - 1) + D) / ((s - 1)^2 + 1)where A, B, C, and D are constants to be determined.
Step 2: Solve for the constants A, B, C, and D.Multiplying both sides of the equation by the denominator, we get:
2e^(-0.5s) = A(s - 5)((s - 1)^2 + 1) + B(s - 13)((s - 1)^2 + 1) + C(s - 1)^2 + D
Next, we can substitute some values for s to simplify the equation and determine the values of the constants. Let's choose s = 13, s = 5, and s = 1.For s = 13:
2e^(-0.5(13)) = A(13 - 5)((13 - 1)^2 + 1) + B(13 - 13)((13 - 1)^2 + 1) + C(13 - 1)^2 + De^(-6.5) = 8A + 144C + DFor s = 5:
2e^(-0.5(5)) = A(5 - 5)((5 - 1)^2 + 1) + B(5 - 13)((5 - 1)^2 + 1) + C(5 - 1)^2 + D2e^(-2.5) = 16A - 8B + 16C + DFor s = 1:
2e^(-0.5) = A(1 - 5)((1 - 1)^2 + 1) + B(1 - 13)((1 - 1)^2 + 1) + C(1 - 1)^2 + D2e^(-0.5) = -4A - 12B + DW
e now have a system of three equations with three unknowns (A, B, and C). Solve this system to find the values of the constants.
Step 3: Use Laplace transform tables to find the inverse Laplace transform. Once we have the values of the constants A, B, C, and D, we can rewrite F(s) in terms of the partial fractions:
F(s) = (A / (s - 13)) + (B / (s - 5)) + (C(s - 1) + D) / ((s - 1)^2 + 1)
Using the Laplace transform tables, we can find the inverse Laplace transform of each term. The inverse Laplace transforms of (s - a)^(-n) and e^(as) are well-known and can be found in the tables.
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A positioning system has CR₁ = 0.05mm and CR2= 0.035mm. The gear ratio between the gear shaft and the leadscrew is 3:1. Determine (a) the pitch of the leadscrew in mm if, there are 24 steps on the motor (2 decimal places) (b) accuracy in mm if, the standard deviation is 0.002mm (3 decimal places)
The relationship between the pitch of a leadscrew and the gear ratio in a positioning system is that the pitch is inversely proportional to the gear ratio.
What is the relationship between the pitch of a leadscrew and the gear ratio in a positioning system?(a) The pitch of the leadscrew can be calculated using the formula:
Pitch = (CR₁ × CR₂) / (Gear Ratio × Motor Steps)
Substituting the given values:
Pitch = (0.05 mm × 0.035 mm) / (3 × 24) = 0.00004861 mm ≈ 0.00005 mm
Therefore, the pitch of the leadscrew is approximately 0.00005 mm.
(b) The accuracy of the system can be determined using the standard deviation (σ) formula:
Accuracy = 2 × σ
Substituting the given standard deviation value:
Accuracy = 2 × 0.002 mm = 0.004 mm
Therefore, the accuracy of the system is 0.004 mm.
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a) The pitch of the leadscrew in mm if, there are 24 steps on the motor is 0.0009622d₂
b) The accuracy in mm is 0.066 mm.
(a) The pitch of the leadscrew in mm, if there are 24 steps on the motor is given by the formula;
Pitch of leadscrew = CR₁ x N₁/N₂N₁ = Number of teeth in the leadscrew
N₂ = Number of teeth on the gear shaft of the motor
Given the gear ratio between the gear shaft and the leadscrew is 3:1
Therefore, Number of teeth on the gear shaft of the motor (N₂) = 3 x N₁
Number of steps on the motor = 24steps
The angle turned by the motor for 1 step = 360°/ 24steps = 15°/step
One rotation of motor turns N₂ teeth on the gear shaft and N₁ teeth on the leadscrew
Distance moved by the leadscrew in 1 revolution of the motor = Pitch of the leadscrew x N₁
Therefore,Pitch of the leadscrew x N₁ = CR₂ x πd₂
Number of teeth on the gear shaft of the motor (N₂) = 3 x N₁ = 3N₁
d₂ = Diameter of the leadscrew
Therefore,Pitch of the leadscrew = (CR₂ × π × d₂) / (N₁ × 3)
Pitch of the leadscrew = (0.035 × 3.14 × d₂) / (24 × 3)
Pitch of the leadscrew = 0.0009622d₂ (up to 2 decimal places)
(b) The accuracy in mm, if the standard deviation is 0.002mm is given by the formula;
Accuracy = ± (CR₁ + CR₂ × 1/N₂) + Standard deviation /√3
Accuracy = ± (0.05 + 0.035/3) + 0.002 / √3
Accuracy = ± 0.0663 mm (up to 3 decimal places)
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Explain how outflow compression and inlet compression occur
Outflow compression and inlet compression are two processes that occur in fluid flow. These terms refer to the change in pressure and velocity that occurs.
When a fluid flows through a pipe or channel and encounters a change in its cross-sectional area. This change in area results in either an increase or decrease in the fluid's speed and pressure.Inlet compression occurs when a fluid flows into a smaller area.
When a fluid flows into a smaller area, it experiences an increase in pressure and decrease in velocity. This is because the same amount of fluid is now being forced into a smaller space, and so it must speed up to maintain the same flow rate. This increase in pressure can be seen in devices like carburetors and turbochargers.
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Line Balance Rate tells us how well a line is balanced. W
orkstation 1 Cycle Time is 2 min Workstation 2 Cycle Time is 4 min Workstation 3 Cycle Time is 6 min Workstation 4 Cycle Time is 4.5 min Workstation 5 Cycle Time is 3 min What is the Line Balance Rate %? Where is the bottleneck? Based on the Line Balance Rate result, what is your recommendation to improve the LBR%? Why?
Line balance rate tells us how well a line is balanced. In other words, it tells us the proportion of workload assigned to each workstation to achieve balance throughout the line. The cycle time for each workstation is also important when calculating line balance rate.
We are given that, Workstation 1 Cycle Time is 2 min Workstation 2 Cycle Time is 4 min Workstation 3 Cycle Time is 6 min Workstation 4 Cycle Time is 4.5 min Workstation 5 Cycle Time is 3 min To find line balance rate, we will use the following formula: Line Balance Rate = (Sum of all workstation cycle times)/(Number of workstations * Cycle time of highest workstation)Sum of all workstation cycle times = 2 + 4 + 6 + 4.5 + 3
= 19.5Cycle time of highest workstation
= 6Line Balance Rate
= (19.5)/(5 * 6)
= 0.65
= 65%Therefore, the line balance rate is 65%.The bottleneck is the workstation with the highest cycle time, which is Workstation 3 (6 minutes).
To improve the LBR%, we need to reduce the cycle time of workstation 3. This could be done by implementing the following methods:1. Change the process to reduce the cycle time2. Reduce the work content in the workstation3. Use automation to speed up the workstation .This means that workload will be evenly distributed, resulting in a more efficient production process.
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Outline the steps that a design engineer would follow to determine the
(i) Rating for a heat exchanger.
(ii) The sizing of a heat exchanger.
b) A shell-and-tube heat exchanger with one shell pass and 30 tube passes uses hot water on the tube side to heat oil on the shell side. The single copper tube has inner and outer diameters of 20 and 24 mm and a length per pass of 3 m. The water enters at 97°C and 0.3 kg/s and leaves at 37°C. Inlet and outlet temperatures of the oil are 10 degrees C and 47°C. What is the average convection coefficient for the tube outer surface?
(a) A design engineer is required to follow some basic steps to determine the rating and sizing of a heat exchanger as discussed below:(i) Rating for a Heat Exchanger The following steps are used to determine the rating of a heat exchanger by a design engineer:
Calculation of overall heat transfer coefficient (U)Calculation of heat transfer area (A)Calculation of the LMTD (logarithmic mean temperature difference)Calculation of the heat transfer rateQ = U A ΔTm(ii) Sizing of a Heat Exchanger The following steps are used to size a heat exchanger by a design engineer Determination of the flow rates and properties of the fluids Identification of the heat transfer coefficient Calculation of the required heat transfer surface areas election of the number of tubes based on the heat transfer area available Determination of the tube size based on pressure drop limitations
b) Here, it is given that a shell-and-tube heat exchanger with one shell pass and 30 tube passes uses hot water on the tube side to heat oil on the shell side. The single copper tube has inner and outer diameters of 20 and 24 mm and a length per pass of 3 m. 4.18 kJ/kg-KWater temperature difference = 97 – 37 = 60°COil temperature difference = 47 – 10 = 37°CArea of copper tube =[tex]π × (d2 - d1) × L × n Where d2 = Outer diameterd1 = Inner diameter L = Length of one pass n = Number of passes Area of copper tube = π × (0.0242 - 0.0202) × 3 × 30= 0.5313 m2Heat flow rate = m × Cp × ΔT= 0.3 × 4.18 × 60= 75.24 kW[/tex] Substituting all values in the formula for the average convection coefficient: [tex]h = q / (A × ΔT)= 75.24 / (0.5313 × 37)= 400.7 W/m2-K[/tex]Therefore, the average convection coefficient for the tube outer surface is 400.7 W/m2-K.
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A chain drive system has a speed ratio of
1.4 and a centre distance of 1.2 m. The chain has a
pitch length of19 mm. find the closest to the length of the chain in pitches?
Given that the speed ratio of the chain drive system is 1.4 and the center distance of the chain drive system is 1.2 m. We have to find the closest length of the chain in pitches.
We are given that the chain has a pitch length of 19 mm. Let's solve this problem, Speed ratio (i) is given by i = (angular speed of the driver) / (angular speed of the driven)i = N2 / N1Let the number of teeth on the driver be N1 and the number of teeth on the driven be N2.
Therefore we have i = (N2 / N1) ...(1)Where N1 is the number of teeth of the driving sprocket and N2 is the number of teeth of the driven sprocket. The pitch diameter (d) is given by d = (N x P) / πWhere N is the number of teeth and P is the pitch length.
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An induced draft fan handles 1700 m^3/min of flue gas at apparent molecular weight of 30 from a boiler at 260 C and P = 101 KPa against a static pressure of 10.2 cm WG. The discharge duct has an area of 2.8 m^2 and a total fan efficiency of 65%.
Determine the density of the flue gas in kg/m^3
Determine the velocity pressure in m of WG
Determine the fan power in kw
The density of the flue gas is 1.19 kg/m³. The velocity pressure is 59.12 m of WG. The fan power is 47.92 kW.
To determine the density of the flue gas, we can use the ideal gas law, which states that density is equal to the molecular weight divided by the gas constant times the temperature and pressure. In this case, the molecular weight is given as 30, the temperature is 260°C (or 533 K), and the pressure is 101 kPa. Plugging in these values, we can calculate the density to be 1.19 kg/m³. The velocity pressure can be calculated using Bernoulli's equation, which relates the velocity and pressure of a fluid.
The velocity pressure is given by (velocity squared) divided by (2 times the acceleration due to gravity). Given the airflow rate and the area of the discharge duct, we can calculate the velocity and then determine the velocity pressure to be 59.12 m of WG. The fan power can be calculated using the formula: power = (flow rate times pressure) divided by (fan efficiency times density). Plugging in the values, we can calculate the fan power to be 47.92 kW.
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Find the inner and outer diameter di and d₂ of a hollow shaft having the same strength as asolid shaft with adiameter of d= 8am and weight of 60%. The shortened material is the same.
Inner diameter di = √(d² - 32) cm and outer diameter d₂ = √(d² + 32) cm. Hollow shaft should have the same strength as the solid shaft
Given: Diameter of solid shaft = d = 8 cm
Weight of solid shaft = 60%
Hollow shaft should have the same strength as the solid shaft
Assuming the material of the solid and hollow shaft is the same.To find: Inner diameter di and outer diameter d2 of hollow shaft.
Solution: Let's assume the outer radius of solid shaft be r and inner radius of hollow shaft be r1.Hence, r = d/2 = 8/2 = 4 cm
For solid shaft: Weight of the solid shaft = πr²Lρ = 0.6πr²Lρ ...(1)Where L = Length of the solid shaftρ = Density of the materialFor hollow shaft:Weight of the hollow shaft = π/4 (d₂² - di²)Lρ = 0.6πr²Lρ ...(2)π/4 (d₂² - di²) = πr²d₂² - di² = 4r²d₂² - di² = 4×4² (since r = 4 cm)d₂² - di² = 64 ...(3)Also, from the equation of torsional stress τ = (T×r) / (J)where T = twisting momentr = radius of shaftJ = Polar moment of inertia of shaftFor solid shaft:τ = (T×r) / (J)τ = (T×d/2) / (π/2 (d⁴/32))τ = 16T / (πd³) ...(4)For hollow shaft:τ = (T×r) / (J)τ = (T×(di+d₂)/2) / (π/2 ((d₂⁴-di⁴)/32))τ = 16T(di+d₂) / (π(d₂⁴-di⁴)) ...(5)But from equation 4 and 5, τsolid = τhollowd²/4 = (di²+d₂²)/2di²+d₂² = 2d² ...(6)Using equation 3 in equation 6:d₂² + 64 - di² = 2d²d₂² - di² = 2d² - 64
From equations 3 and 6, we have to solve for d₂ and di.So, d₂² + (2d² - 64) = 2d²d₂² - 64 = d²d₂ = √(d² + 64/2) = √(d² + 32)di² + (2d² - 64) = d²di² = √(d² - 32)Therefore, inner diameter di = √(d² - 32) cm and outer diameter d₂ = √(d² + 32) cm.
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