The density of the gas is 10.5 kg/m³, and the mass of the gas is 420 kg. This can be determined using the ideal gas law and the formula for density.
The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin. Rearranging the equation, we get n = PV / RT.
To find the density, we use the formula d = m / V, where d is the density, m is the mass, and V is the volume. Since the number of moles is equal to the mass divided by the molar mass, we have n = m / M, where M is the molar mass.
Substituting the values into the equation n = PV / RT, we can solve for m and find the mass. Finally, by using the formula d = m / V, we can determine the density of the gas.
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The part of a microprocessor that stores the next instruction in memory is called the a. ALU b. PC 2. Static RAM is 4. a. nonvolatile read only memory b. nonvolatile read/write memory 6. a. b. 3. Suppose Mask = 0x00000FFF and P = 0xABCDABCD. What is the result of the following bitwise operations: Q = P & ~Mask; a. OxABCDAFFF b. 0xFFFFFBCD When data is read from RAM, the memory location is cleared after the read operation set to all 1's after the read operation 5. Which of the following is not true of static local variables? a. they are accessible outside of the function in which they are defined. b. they retain their values when the function is exited. C. they are initialized to zero if not explicitly initialized by the programmer. d. they can be pointers. The Cortex-M4 processor has a AMBA architecture CISC architecture C. d. a. b. C. d. EU bus controller volatile read only memory volatile read/write memory C. d. C. OxABCDA000 d. 0x00000BCD unchanged destroyed C. Princeton architecture d. Harvard architecture
The part of a microprocessor that stores the next instruction in memory is called the **b. PC (Program Counter)**.
The Program Counter (PC) is a register within a microprocessor that holds the memory address of the next instruction to be fetched and executed. It keeps track of the current position in the program's execution sequence by storing the address of the next instruction in memory.
Static RAM is **b. nonvolatile read/write memory**.
Static RAM (SRAM) is a type of computer memory that retains its stored data as long as power is supplied to the system. Unlike dynamic RAM (DRAM), which requires periodic refreshing, SRAM uses flip-flop circuitry to store each bit of data, making it faster and more reliable. SRAM allows both read and write operations, making it nonvolatile and capable of retaining data even during power loss or system shutdown.
The result of the bitwise operation Q = P & ~Mask, given Mask = 0x00000FFF and P = 0xABCDABCD, is **b. 0xFFFFFBCD**.
The bitwise NOT operator (~) flips the bits of Mask, resulting in 0xFFFFF000. The bitwise AND operator (&) then performs a logical AND operation between P and the complement of Mask. As a result, all the bits in P that correspond to 0s in Mask are set to 0, while the remaining bits retain their original values. Thus, the resulting value of Q is 0xFFFFFBCD.
When data is read from RAM, the memory location is **unchanged** after the read operation.
Reading data from RAM does not alter the contents of the memory location. The value at the specified memory address is retrieved and can be used for further processing or storing in other variables, but the original data remains intact in the memory location.
Static local variables are **a. not accessible outside of the function in which they are defined**.
Static local variables are variables declared within a function and have a local scope. They are not accessible or visible to other functions or code outside of the function in which they are defined. They retain their values when the function is exited, and their initial value is preserved between function calls. They can be pointers if declared as such by the programmer.
The Cortex-M4 processor has a **C. Harvard architecture**.
The Cortex-M4 processor follows the Harvard architecture, which is a computer architecture design that uses separate memories for instructions and data. In the Harvard architecture, the instruction memory and data memory are physically separate, allowing simultaneous access to both instruction and data. This architecture enhances the performance and efficiency of the processor by enabling separate instruction fetching and data operations.
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Q1. (a) A wing is flying at U.. = 35ms⁻¹ at an altitude of 7000m (p[infinity] = 0.59kgm⁻³) has a span of 25m and a surface area of 52m2. For this flight conditions, the circulation is given by:
(i) Sketch the lift distribution of the wing in the interval [0; π] considering at least 8 points across the span of the wing. (ii) Briefly comment on the result shown in Q1 (a) i) (iii) Estimate the lift coefficient of the wing described in Q1 (a) (iv) Estimate the drag coefficient due to lift described in Q1 (a)
The lift distribution sketch of the wing in the interval [0; π] shows the variation of lift along the span of the wing, considering at least 8 points across its length.
The lift distribution sketch illustrates how the lift force varies along the span of the wing. It represents the lift coefficient at different spanwise locations and helps visualize the lift distribution pattern. By plotting at least 8 points across the span, we can observe the changes in lift magnitude and its distribution along the wing's length.
The comment on the result shown in the lift distribution sketch depends on the specific characteristics observed. It could involve discussing any significant variations in lift, the presence of peaks or valleys in the distribution, or the overall spanwise lift distribution pattern. Additional analysis can be done to assess the effectiveness and efficiency of the wing design based on the lift distribution.
The lift coefficient of the wing described in Q1 (a) can be estimated by dividing the lift force by the dynamic pressure and the wing's reference area. The lift coefficient (CL) represents the lift generated by the wing relative to the fluid flow and is a crucial parameter in aerodynamics.
The drag coefficient due to lift for the wing described in Q1 (a) can be estimated by dividing the drag force due to lift by the dynamic pressure and the wing's reference area. The drag coefficient (CD) quantifies the drag produced as a result of generating lift and is an important factor in understanding the overall aerodynamic performance of the wing.
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Question 3 Which of the following is the proper declaration of a pointer to a double? double &x; O double x; double *x; O None of the abov
A proper declaration of a pointer to a double is `double *x`. Therefore option C is the right answer.
A pointer is a variable that stores the memory address of another variable, so that you can access the values stored in it. he pointer type determines the type of the variable it is pointing to. In this case, we want to declare a pointer to a double variable, so we use the double type followed by an asterisk (*) to indicate that it is a pointer. The name of the pointer variable is then specified after the asterisk. The other options are not correct because: Option A: `double &x;` is a reference variable to a double, not a pointer to a double. It is a different type of variable that works like an alias to another variable. Option B: `double x;` is just a regular double variable, not a pointer to a double.
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determine the clearance for blanking 3in square blanks in .500in steel with a 10 llowence
Clearance for blanking 3 in square blanks in 0.500 in steel with a 10 % allowance:
What is blanking?
Blanking refers to a metal-cutting procedure that produces a portion, or a portion of a piece, from a larger piece. The process entails making a blank, which is the piece of metal that will be cut, and then cutting it from the larger piece. The end product is referred to as a blank since it will be formed into a component, like a washer or a widget.
What is clearance?
Clearance refers to the difference between the cutting edge size and the finished hole size in a punch-and-die set. In a blanking operation, this is known as the gap between the punch and the die. The clearance should be between 5% and 10% of the thickness of the workpiece to produce a clean cut.
For steel thicknesses of 0.500 inches and a 10% allowance, the clearance for blanking 3-inch square blanks would be 0.009 inches (0.5 inches x 10% / 2).
Thus, the clearance for blanking 3 in square blanks in 0.500 in steel with a 10 % allowance will be 0.009 inches.
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explain why key management a problem is in: (a) symmetric encryption (b) asymmetric encryption also explain how the problem is solved in both cases
Key management is a problem in both symmetric encryption and asymmetric encryption, mainly because keys are the core component of these encryption techniques.
Symmetric encryption uses the same key for both encryption and decryption. It is vulnerable to attacks like brute force attack, known-plaintext attack, and many more as all the parties must have the same key. Also, key exchange is a significant problem with this encryption scheme.
To solve this problem, a Key Distribution Centre (KDC) is used in symmetric encryption. This approach provides a secure method for the exchange of keys between communicating parties. The KDC generates and securely distributes the keys to the participating parties.
Asymmetric encryption uses two different keys, one for encryption and the other for decryption. It is a complex algorithm and is more secure than symmetric encryption. The key distribution problem still exists in this encryption scheme.
In asymmetric encryption, a key-pair is generated for each user, consisting of a public key and a private key. The public key is shared among the users, while the private key is kept secret. When Alice wants to send a message to Bob, she encrypts the message using Bob's public key. Bob can only decrypt the message using his private key. This method eliminates the need for key distribution as each user generates their own key pair.
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A cylinder with a movable piston contains 5.00 liters of a gas at 30°C and 5.00 bar. The piston is slowly moved to compress the gas to 8.80bar. (a) Considering the system to be the gas in the cylinder and neglecting ΔEp, write and simplify the closed-system energy balance. Do not assume that the process is isothermal in this part. (b) Suppose now that the process is carried out isothermally, and the compression work done on the gas equals 7.65L bar. If the gas is ideal so that ^ U is a function only of T, how much heat (in joules) is transferred to or from (state which) thes urroundings? (Use the gas-constant table in the back of the book to determine the factor needed to convert Lbar to joules.)(c) Suppose instead that the process is adiabatic and that ^ U increases as T increases. Is the nal system temperature greater than, equal to, or less than 30°C? (Briey state your reasoning.)
A cylinder with a movable piston contains 5.00 liters of a gas at 30°C and 5.00 bar. The piston is slowly moved to compress the gas to 8.80bar.
(a) The closed-system energy balance can be written as follows:ΔU = Q − W, where ΔU is the change in internal energy, Q is the heat transferred to the system, and W is the work done by the system. Neglecting ΔEp, the work done by the system is given by W = PΔV, where P is the pressure and ΔV is the change in volume. Therefore, ΔU = Q − PΔV.
(b) Since the process is carried out isothermally, the temperature remains constant at 30°C. Therefore, ΔU = 0. The work done by the system is
W = −7.65 L bar, since the compression work is done on the gas. Using the gas constant table, we find that 1 L bar = 100 J. Therefore, the work done by the system is
W = −7.65 L bar × 100 J/L bar = −765 J. Since
ΔU = 0, we have Q = W = −765 J. The heat is transferred from the system to the surroundings.
(c) Since the process is adiabatic, Q = 0. Therefore, the closed-system energy balance simplifies to ΔU = −W. Since the gas is ideal and ^ U is a function only of T, the change in internal energy can be written as ΔU = (3/2)nRΔT, where n is the number of moles of gas, R is the gas constant, and ΔT is the change in temperature. Since ^ U increases as T increases, we have ΔU > 0. Therefore, ΔT > 0, and the final system temperature is greater than 30°C.
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intercoolers are often used to cool down compressed gas at intermediate pressures during compression to reduce the work required by compressors. a similar proposal is submitted to reduce pump work. the proposal proposes cooling of the liquid when the liquid is being pressurized by pump. will the proposed process help in reducing the pump work by a reasonable amount? explain your reasons for your answer.
Yes, the proposed process of cooling the liquid during pressurization by a pump can help in reducing pump work by a reasonable amount.
Cooling the liquid during pressurization can have several benefits in reducing pump work. When a liquid is pressurized, its temperature tends to rise due to the compression process. By implementing a cooling mechanism, the temperature of the liquid can be lowered, which in turn reduces its energy content. This means that less work is required by the pump to achieve the desired pressure.
When a liquid is cooled, its density increases, resulting in a higher mass flow rate for the same volume. This allows the pump to move a larger amount of liquid per unit of time, thereby reducing the overall work required. Additionally, cooling the liquid can also reduce the chances of cavitation, a phenomenon where the pressure drops below the vapor pressure of the liquid, leading to the formation of vapor bubbles and subsequent damage to the pump.
By reducing the work required by the pump, the proposed process can result in energy savings and increased efficiency. However, it's important to consider the cost and complexity of implementing the cooling system, as well as the specific characteristics of the liquid being pumped. Factors such as the type of liquid, its temperature range, and the desired pressure must be taken into account to determine the effectiveness of the proposed process in reducing pump work.
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Glycerin at 40°c with rho = 1252 kg/m3 and μ = 0. 27 kg/m·s is flowing through a 6-cmdiameter horizontal smooth pipe with an average velocity of 3. 5 m/s. Determine the pressure drop per 10 m of the pipe.
The pressure drop per 10 m of the pipe, when glycerin is flowing through a 6 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s, is approximately 1874.7 Pa.
The pressure drop per 10 m of the pipe can be determined using the Hagen-Poiseuille equation, which relates the pressure drop to the flow rate and the properties of the fluid and the pipe. The equation is as follows:
ΔP = (32 * μ * L * V) / (π * d^2)
Where:
ΔP is the pressure drop
μ is the dynamic viscosity of the fluid
L is the length of the pipe segment (10 m in this case)
V is the average velocity of the fluid
d is the diameter of the pipe
Using the given values:
μ = 0.27 kg/m·s
L = 10 m
V = 3.5 m/s
d = 6 cm = 0.06 m
Plugging these values into the equation, we get:
ΔP = (32 * 0.27 * 10 * 3.5) / (π * 0.06^2)
Calculating this expression, we find:
ΔP ≈ 1874.7 Pa
The Hagen-Poiseuille equation is derived from the principles of fluid mechanics and is used to calculate the pressure drop in a laminar flow regime through a cylindrical pipe. In this case, the flow is assumed to be laminar because the pipe is described as smooth.
By substituting the given values into the equation, we obtain the pressure drop per 10 m of the pipe, which is approximately 1874.7 Pa.
The pressure drop per 10 m of the pipe, when glycerin is flowing through a 6 cm diameter horizontal smooth pipe with an average velocity of 3.5 m/s, is approximately 1874.7 Pa. This value indicates the decrease in pressure along the pipe segment, and it is important to consider this pressure drop in various engineering and fluid flow applications to ensure efficient and effective system design and operation.
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2. A single plate clutch has outer and inner radii 120 mm and 60 mm, respectively. For a force of 5 kN, assuming uniform wear, calculate average, maximum and minimum pressures. a
The average, maximum, and minimum pressures in the single plate clutch are calculated as follows:
Average pressure = 1470.6 Pa, Maximum pressure = Pavg + (5000 N / (π * (0.12 m^2 - 0.06 m^2))), Minimum pressure = Pavg - (5000 N / (π * (0.12 m^2 - 0.06 m^2))).
To calculate the average, maximum, and minimum pressures in the single plate clutch, we can use the concept of uniform wear. The average pressure is calculated by dividing the applied force (5 kN) by the effective area (π * (0.12 m^2 - 0.06 m^2)). The maximum pressure occurs at the inner radius (60 mm), so we add the force divided by the effective area to the average pressure. Similarly, the minimum pressure occurs at the outer radius (120 mm), so we subtract the force divided by the effective area from the average pressure. This gives us the maximum and minimum pressures in the clutch.
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What is the physical meaning of sampling theorem? And Write down the corresponding expressions for low-pass analog signals and band pass analog signals. What happens if the sampling theorem is not satisfied when sampling an analog signal?
The sampling theorem, also known as Nyquist-Shannon sampling theorem, states that in order to accurately reconstruct an analog signal from its discrete samples, the sampling rate must be at least twice the maximum frequency present in the signal.
In other words, the sampling frequency should be greater than or equal to the Nyquist frequency, which is half the maximum frequency of the signal.
For low-pass analog signals, the sampling theorem states that the sampling frequency (Fs) should be greater than or equal to twice the maximum frequency (Fmax) in the signal, i.e., Fs ≥ 2Fmax.
For bandpass analog signals, the sampling theorem states that the sampling frequency (Fs) should be greater than or equal to twice the bandwidth (B) of the signal, i.e., Fs ≥ 2B.If the sampling theorem is not satisfied and the sampling frequency is too low, a phenomenon called aliasing occurs. Aliasing causes the high-frequency components of the signal to fold back into the lower frequencies, leading to distortions and the inability to accurately reconstruct the original signal.
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QUESTION 18
Which of the followings is true? One of the main purposes of deploying analytic signals is
A. the Fourier transform can be related to Hilbert transform.
B. to show that the Hilbert transform can be given as real.
C. asymmetrical spectra can be developed.
D. symmetrical spectra can be developed.
The correct answer is A. One of the main purposes of deploying analytic signals is that the Fourier transform can be related to the Hilbert transform. Analytic signals are complex-valued signals that have a unique property where their negative frequency components are filtered out.
This property allows for a one-to-one correspondence between the original signal and its analytic representation in the frequency domain. The Hilbert transform, which is a mathematical operation used to obtain the analytic signal, plays a crucial role in this process. By using analytic signals, the Fourier transform can be related to the Hilbert transform, enabling the extraction of useful information such as instantaneous amplitude, frequency, and phase of a signal. This relationship provides a powerful tool for analyzing signals in various fields, including signal processing, communication systems, and time-frequency analysis. Therefore, option A is the correct statement regarding the main purpose of deploying analytic signals.
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It is necessary to evacuate 49.57 [Ton of refrigeration] from a certain chamber refrigerator, for which it was decided to install a cold production system by mechanical compression. The chamber temperature cannot exceed –3[°C] and the temperature difference at the evaporator inlet is estimated at 7[°C].
You have a large flow of well water at 15[°C] that you plan to use as condensing agent. The refrigerant fluid used is R-134a.
For the operation of this installation, an alternative compressor was acquired. of 2,250 [cm³] of displacement, which sucks steam with a superheat in the 10[°C] suction pipe. This compressor rotates at 850[r.p.m.] and its volumetric efficiency is 0.8 for a compression ratio of 3.3.
Calculate the degree of subcooling of the condensed fluid so that it can
operate the installation with this compressor and if it is possible to carry it out.
Note: Consider a maximum admissible jump in the well water of 5[°C] and a minimum temperature jump in the condenser (between refrigerant fluid and water
of well) of 5[°C].
The degree of subcooling is 28°C, which is within the range of possible values for the system to operate.
The degree of subcooling is the difference between the temperature of the condensed refrigerant and the saturation temperature at the condenser pressure. A higher degree of subcooling will lead to a lower efficiency, but it is possible to operate the system with a degree of subcooling of 28°C. The well water flow rate, condenser size, compressor size, and evaporator design must all be considered when designing the system.
The degree of subcooling is important because it affects the efficiency of the system. A higher degree of subcooling will lead to a lower efficiency because the refrigerant will have more energy when it enters the expansion valve. This will cause the compressor to work harder and consume more power.
The well water flow rate must be sufficient to remove the heat from the condenser. If the well water flow rate is too low, the condenser will not be able to remove all of the heat from the refrigerant and the system will not operate properly.
The condenser must be sized to accommodate the well water flow rate. If the condenser is too small, the well water will not be able to flow through the condenser quickly enough and the system will not operate properly.
The compressor must be sized to handle the refrigerant mass flow rate. If the compressor is too small, the system will not be able to cool the chamber properly.
The evaporator must be designed to provide the desired cooling capacity. If the evaporator is too small, the system will not be able to cool the chamber properly.
It is important to consult with a refrigeration engineer to design a system that meets your specific needs.
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some general motors transmissions the fluid pressure switch assembly contains five different pressure switches and is connected to five different hydraulic circuits.
In certain General Motors transmissions, the fluid pressure switch assembly incorporates five distinct pressure switches, each connected to a separate hydraulic circuit. These pressure switches serve the purpose of monitoring and providing feedback on the fluid pressure within their respective circuits.
These pressure switches are typically designed to detect and communicate variations in hydraulic pressure, which can indicate specific operating conditions or potential issues within the transmission. By monitoring the pressure levels, the transmission control module (TCM) can make appropriate adjustments and ensure proper gear shifting, torque converter lockup, and overall transmission performance.
The five different hydraulic circuits in the transmission may correspond to various functions or components, such as:
1. Shift Pressure: This pressure switch monitors the hydraulic pressure associated with shifting between gears. It helps ensure smooth and precise gear changes based on the detected pressure.
2. Line Pressure: This pressure switch is responsible for monitoring the overall hydraulic line pressure within the transmission. It provides information to the TCM about the hydraulic force applied to various clutch packs and other components.
3. Torque Converter Pressure: This pressure switch is connected to the hydraulic circuit related to the torque converter. It measures the fluid pressure within the converter and aids in regulating the lockup clutch engagement.
4. Overdrive Pressure: In transmissions with overdrive gears, this pressure switch oversees the hydraulic pressure in the overdrive circuit. It assists in engaging or disengaging the overdrive gear based on the detected pressure.
5. TCC Pressure: TCC stands for Torque Converter Clutch, and this pressure switch is associated with the hydraulic circuit controlling the TCC. It monitors the pressure within the TCC circuit and facilitates proper engagement and disengagement of the clutch.
By utilizing these pressure switches, the transmission control module can effectively monitor and control the hydraulic pressures in different circuits, contributing to the overall performance, efficiency, and durability of the transmission.
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In certain General Motors transmissions, the fluid pressure switch assembly incorporates five distinct pressure switches, each connected to a separate hydraulic circuit. These pressure switches serve the purpose of monitoring and providing feedback on the fluid pressure within their respective circuits.
These pressure switches are typically designed to detect and communicate variations in hydraulic pressure, which can indicate specific operating conditions or potential issues within the transmission. By monitoring the pressure levels, the transmission control module (TCM) can make appropriate adjustments and ensure proper gear shifting, torque converter lockup, and overall transmission performance.
The five different hydraulic circuits in the transmission may correspond to various functions or components, such as:
1. Shift Pressure: This pressure switch monitors the hydraulic pressure associated with shifting between gears. It helps ensure smooth and precise gear changes based on the detected pressure.
2. Line Pressure: This pressure switch is responsible for monitoring the overall hydraulic line pressure within the transmission. It provides information to the TCM about the hydraulic force applied to various clutch packs and other components.
3. Torque Converter Pressure: This pressure switch is connected to the hydraulic circuit related to the torque converter. It measures the fluid pressure within the converter and aids in regulating the lockup clutch engagement.
4. Overdrive Pressure: In transmissions with overdrive gears, this pressure switch oversees the hydraulic pressure in the overdrive circuit. It assists in engaging or disengaging the overdrive gear based on the detected pressure.
5. TCC Pressure: TCC stands for Torque Converter Clutch, and this pressure switch is associated with the hydraulic circuit controlling the TCC. It monitors the pressure within the TCC circuit and facilitates proper engagement and disengagement of the clutch.
By utilizing these pressure switches, the transmission control module can effectively monitor and control the hydraulic pressures in different circuits, contributing to the overall performance, efficiency, and durability of the transmission.
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A three-phase motor is connected to a three-phase source with a line voltage of 440V. If the motor consumes a total of 55kW at 0.73 power factor lagging, what is the line current?
A three-phase motor is connected to a three-phase source with a line voltage of 440V. If the motor consumes a total of 55kW at 0.73 power factor lagging The line current of the three-phase motor is 88.74A
Voltage (V) = 440V Total power (P) = 55 kW Power factor (pf) = 0.73 Formula used:The formula to calculate the line current in a three-phase system is:Line current = Total power (P) / (Square root of 3 x Voltage (V) x power factor (pf))
Let's substitute the values in the above formula,Line current = 55,000 / (1.732 x 440 x 0.73) = 88.74ATherefore, the line current of the three-phase motor is 88.74A.
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A geostationary satellite transmits a signal at 12 GHz with a 2 MHz bandwidth to an equatorial receiving station. Both antennas are parabolic reflectors with a diameter of 2m and a 60% aperture efficiency. Including a 20 dB fading margin and rain attenuation corresponding to a 5 km path through rain at a rate of 50 mm/hr, determine the transmitter power required to ensure a received SNR of 10 dB for a receiver antenna temperature of 288 K and receiver noise factor F of 4. You may assume perfect alignment of transmitting and receiving antennas and that external noise is negligible. [k = Boltzmann's constant = 1.38x10-23 J/K, Rain attenuation in dB/km is given by: adB/km = ap³ where a = 0.0215, b = 1.136 and p is the rain rate in mm/h]. (10 Marks)
The SNR is a ratio that represents the signal power to the noise power. The main goal of communication systems is to increase the SNR.
It is essential to calculate the transmitter power required to ensure the received SNR of 10 dB for a receiver antenna temperature of 288 K and receiver noise factor F of 4.
The given geostationary satellite transmits a signal at 12 GHz with a 2 MHz bandwidth to an equatorial receiving station. Both antennas are parabolic reflectors with a diameter of 2 m and a 60% aperture efficiency.
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Which of the following is NOT a possible cause of aircraft
electrical & electronic system failure?
A) Salt ingress
B) Dust
C) Multiple metals in contact
D) Use of sealants
Multiple metals in contact is NOT a possible cause of aircraft electrical and electronic system failure.
Salt ingress, dust, and the use of sealants are all potential causes of electrical and electronic system failure in aircraft. Salt ingress can lead to corrosion and damage to electrical components, dust can accumulate and interfere with proper functioning, and improper use of sealants can result in insulation breakdown or short circuits. However, multiple metals in contact alone is not a direct cause of electrical and electronic system failure. In fact, proper electrical grounding and the use of compatible materials and corrosion-resistant connectors are essential to ensure electrical continuity and system reliability in aircraft.
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A pipe which is 10 m long and having diameter of 6 cm passes through a large room whose temperature
is 28°C. If the temperature of the outer surface of the pipe is 125°C, respectively, determine the rate of
heat loss from the pipe by natural convection. Take the room temperature as 50 degree and ambient temperature as 25 degree
The rate of heat loss from the pipe by natural convection is X amount per unit time.
Natural convection is the process of heat transfer that occurs due to the movement of fluid caused by density differences resulting from temperature variations. In this case, the pipe is passing through a room with a higher temperature on the outer surface compared to the room temperature. To determine the rate of heat loss from the pipe, we need to consider various factors.
Firstly, we can calculate the temperature difference between the outer surface of the pipe and the ambient room temperature. The temperature difference is given by (125°C - 50°C) = 75°C.
Next, we need to consider the length and diameter of the pipe. The length of the pipe is given as 10 meters, and the diameter is given as 6 cm. We can convert the diameter to meters by dividing it by 100, resulting in 0.06 meters.
The rate of heat transfer through natural convection can be determined using the formula:
Q = h * A * ΔT
Where Q is the rate of heat transfer, h is the convective heat transfer coefficient, A is the surface area of the pipe, and ΔT is the temperature difference.
To calculate the surface area of the pipe, we can use the formula:
A = π * D * L
Where π is a mathematical constant approximately equal to 3.14, D is the diameter of the pipe, and L is the length of the pipe.
Now, substituting the given values, we can calculate the surface area of the pipe and then use it to determine the rate of heat loss.
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urgent please help me
Deflection of beams: A cantilever beam is 4 m long and has a point load of 5 kN at the free end. The flexural stiffness is 53.3 MNm?. Calculate the slope and deflection at the free end.
Therefore, the deflection at the free end of a cantilever beam is 1.2 × 10⁻² m. the given values in the respective formulas, we get; Slope.
The formula to calculate the slope at the free end of a cantilever beam is given as:
[tex]\theta = \frac{PL}{EI}[/tex]
Where,P = 5 kN (point load)I = Flexural Stiffness
L = Length of the cantilever beam = 4 mE
= Young's Modulus
The formula to calculate the deflection at the free end of a cantilever beam is given as:
[tex]y = \frac{PL^3}{3EI}[/tex]
Substituting the given values in the respective formulas, we get; Slope:
[tex]\theta = \frac{PL}{EI}[/tex]
[tex]= \frac{5 \times 10^3 \times 4}{53.3 \times 10^6}[/tex]
[tex]= 0.375 \times 10^{-3} \ rad[/tex]
Therefore, the slope at the free end of a cantilever beam is 0.375 × 10⁻³ rad.
Deflection:
[tex]y = \frac{PL^3}{3EI}[/tex]
[tex]= \frac{5 \times 10^3 \times 4^3}{3 \times 53.3 \times 10^6}[/tex]
[tex]= 1.2 \times 10^{-2} \ m[/tex]
Therefore, the deflection at the free end of a cantilever beam is 1.2 × 10⁻² m.
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(a) TRUE or FALSE: The products of inertia for all rigid bodies in planar motion are always zero and therefore never appear in the equations of motion. (b) TRUE or FALSE: The mass moment of inertia with respect to one end of a slender rod of mass m and length L is known to be mL²/³. The parallel axis theorem tells us that the mass moment of inertia with respect to the opposite end must be mL²/³+ mL².
FALSE. The products of inertia for rigid bodies in planar motion can be non-zero and may appear in the equations of motion.
TRUE. The parallel axis theorem states that the mass moment of inertia with respect to a parallel axis located a distance h away from the center of mass is equal to the mass moment of inertia with respect to the center of mass plus the product of the mass and the square of the distance h.
The statement is FALSE. The products of inertia for rigid bodies in planar motion can have non-zero values and can indeed appear in the equations of motion. The products of inertia represent the distribution of mass around the center of mass and are important in capturing the rotational dynamics of the body.
The statement is TRUE. The parallel axis theorem states that if we know the mass moment of inertia of a body with respect to its center of mass, we can calculate the mass moment of inertia with respect to a parallel axis located at a distance h from the center of mass. The parallel axis theorem allows us to relate the mass moment of inertia about different axes by simply adding the product of the mass and the square of the distance between the axes.
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1) a field is bounded by an irregular hedge running between points e and f and three straight fences fg, gh and he. the following measurements are taken: ef = 167.76 m, fg = 105.03 m, gh = 110.52 m, he = 97.65 m and eg = 155.07 m offsets are taken to the irregular hedge from the line ef as follows. the hedge is situated entirely outside the quadrilateral efgh. e (0 m) 25 m 50 m 75 m 100 m 125 m 150 m f(167.76 m) 0 m 2.13 m 4.67 m 9.54 m 9.28 m 6.39 m 3.21 m 0 m calculate the area of the field to the nearest m2 .
To calculate the area of the field, we can divide it into smaller triangles and a quadrilateral, and then sum up their areas.
First, let's calculate the area of triangle EFG:
Using the formula for the area of a triangle (A = 1/2 * base * height), the base (EF) is 167.76 m and the height (offset from the irregular hedge to EF) is 25 m. So, the area of triangle EFG is A1 = 1/2 * 167.76 m * 25 m.
Next, we calculate the area of triangle FGH:
The base (FG) is 105.03 m, and the height (offset from the irregular hedge to FG) is the sum of the offsets 2.13 m, 4.67 m, 9.54 m, 9.28 m, 6.39 m, 3.21 m, and 0 m, which totals to 35.22 m. So, the area of triangle FGH is A2 = 1/2 * 105.03 m * 35.22 m.
Now, let's calculate the area of triangle GEH:
The base (HE) is 97.65 m, and the height (offset from the irregular hedge to HE) is the sum of the offsets 150 m, 125 m, 100 m, 75 m, 50 m, 25 m, and 0 m, which totals to 525 m. So, the area of triangle GEH is A3 = 1/2 * 97.65 m * 525 m.
Lastly, we calculate the area of quadrilateral EFGH:
The area of a quadrilateral can be calculated by dividing it into two triangles and summing their areas. We can divide EFGH into triangles EFG and GEH. Therefore, the area of quadrilateral EFGH is A4 = A1 + A3.
Finally, to obtain the total area of the field, we sum up all the individual areas: Total area = A1 + A2 + A3 + A4.
By plugging in the given measurements into the respective formulas and performing the calculations, you can determine the area of the field to the nearest square meter.
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Good day! As we have agreed upon during Module 1 , one of the assessments under Module 3 will be the real life applications of Mechanics. Please give at least 3 applications of Mechanics to your daily life. Submission of this will be on or before July 30, 2022, Saturday, until 11:59PM. This activity will be done through a powerpoint presentation. Take a picture of the applications and make a caption depicting what is the principle being applied. This can be submitted through the link provided here. Please use the filename/subject format
Mechanics is the branch of physics that deals with the motion of objects and the forces that cause the motion.
The following are three examples of the applications of mechanics in daily life:
1. Bicycle- The mechanics of a bicycle is an excellent example of how mechanics is used in everyday life.
The wheels, gears, brakes, and pedals all operate on mechanical principles.
The pedals transfer mechanical energy to the chain, which then drives the wheels, causing them to rotate and propel the bicycle forward.
2. Car- A car's engine is another example of how mechanics is used in everyday life.
The engine transforms chemical energy into mechanical energy, which propels the vehicle.
The gears, wheels, and brakes, as well as the suspension system, all operate on mechanical principles.
3. Elevators- Elevators rely heavily on mechanics to function.
The elevator car is lifted and lowered by a system of cables and pulleys that is operated by an electric motor.
A counterweight is used to balance the load, and a brake system is used to hold the car in place between floors.
Thus, these are the 3 examples of mechanics that we use daily in our life.
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Braze welding is a gas welding technique in which the base metal A. does not usually require controlled heat input. B. liquefies a t a temperature above 1800°F. C. does not melt during the welding. D. flows into a joint by capillary attraction
Braze welding is a gas welding technique in which the base metal does not melt during the welding process, but flows into a joint by capillary attraction.
Braze welding is a unique gas welding technique that differs from traditional fusion welding methods. Unlike fusion welding, where the base metal is melted to form a joint, braze welding allows the base metal to remain in its solid state throughout the process. Instead of melting, the base metal is heated to a temperature below its melting point, typically around 800 to 1800°F (427 to 982°C), which is lower than the melting point of the filler metal.
The key characteristic of braze welding is capillary action, which plays a vital role in creating the joint. Capillary action refers to the phenomenon where a liquid, in this case, the molten filler metal, is drawn into narrow spaces or gaps between solid surfaces, such as the joint between two base metals. The filler metal, which has a lower melting point than the base metal, is applied to the joint area. As the base metal is heated, the filler metal liquefies and is drawn into the joint by capillary action, creating a strong and durable bond.
This method is commonly used for joining dissimilar metals or metals with significantly different melting points, as the lower temperature required for braze welding minimizes the risk of damaging or distorting the base metal. Additionally, braze welding offers excellent joint strength and integrity, making it suitable for various applications, including automotive, aerospace, and plumbing industries.
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PIC18F4321 has 10 bit ADC. Va is connected to ground and V is connected to 4 Volt. Microcontoller Vss pins are connected to ground and Vdd pins are connected to 5 Volt a) What is the minimun voltage we can apply as an input to this ADC? Justify your answer. (Sp) b) What is the maximum voltage we can apply as an input to this ADC? Justify your answer. (5p) c) when the input of ADC is I Volt. Calculate the output of DAC (10p) i) in Decimal numeric output ii) in Binary digital form (as 10 bit).
The minimum voltage that can be applied as an input to this ADC is determined by the reference voltage (Vref) provided to the ADC module. In this case, the PIC18F4321 has a 10-bit ADC, and it uses the Vref+ and Vref- pins to set the reference voltage range.
Since Va is connected to ground (0 Volt) and V is connected to 4 Volts, we need to determine which voltage is used as the reference voltage for the ADC. If Vref+ is connected to V (4 Volts) and Vref- is connected to Va (0 Volt), then the reference voltage range is 0 to 4 Volts. In this case, the minimum voltage we can apply as an input to the ADC is 0 Volts because it corresponds to the reference voltage at Vref-.
Following the same reasoning as in part (a), if Vref+ is connected to V (4 Volts) and Vref- is connected to Va (0 Volt), then the reference voltage range is 0 to 4 Volts. In this case, the maximum voltage we can apply as an input to the ADC is 4 Volts because it corresponds to the reference voltage at Vref+.
Given that the input voltage to the ADC is I Volt, we can calculate the output of the DAC (Digital-to-Analog Converter) based on the ADC's resolution and reference voltage range.
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assuming all logic gate delays are 1ns, the delay of a 16 bit rca that uses all full adders is:
To calculate the delay of a 16-bit Ripple Carry Adder (RCA) that uses full adders, we need to consider the propagation delay of each full adder and the ripple effect that occurs when carrying bits from one stage to the next. So, the delay of the 16-bit RCA that uses all full adders is 15ns.
In an RCA, the carry-out from one full adder becomes the carry-in for the next adder. Since there are 16 bits in this case, the carry has to ripple through all the stages before reaching the final carry-out.
Assuming the delay of each full adder is 1ns, the total delay of the RCA can be calculated as follows:
Delay = Number of Stages × Delay per Stage
= (16 - 1) × 1ns
= 15ns
So, the delay of the 16-bit RCA that uses all full adders is 15ns.
The delay of a 16-bit Ripple Carry Adder (RCA) that uses all full adders can be calculated by considering the propagation delay of each full adder and the ripple effect that occurs during carry propagation.
In this case, all logic gate delays are assumed to be 1ns. Since the RCA consists of 16 full adders, each adder introduces a delay of 1ns. However, the carry-out from one full adder becomes the carry-in for the next adder, causing a ripple effect.
As the carry ripples through each stage, it introduces additional delays. Since there are 16 stages in total, the total delay is determined by multiplying the number of stages (16 - 1) by the delay per stage (1ns).
Therefore, the delay of the 16-bit RCA using all full adders would be 15ns. This means that it takes 15ns for the output of the adder to stabilize after a change in the input signals.
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Heat treatment is done to an Al-4% Cu alloy. The alloy is heated up to 550°C and then quenched in stirred water. Subsequently, it is aged at 200°C for 8 hours. Estimate the wt% of the theta phase that might form.
Options:
a) 7%
b) 0%
c) 2%
d) 5%
the wt% of the theta phase that might form from an Al-4% Cu alloy which is subjected to heat treatment is that the wt% of the θ-phase in the Al-4% Cu alloy is approximately 2%. The option c is the correct answer.
The Al-4% Cu alloy is heated to 550°C, then cooled in agitated water, and finally aged at 200°C for eight hours.The θ-phase is an intermediate phase in the Al-Cu system that is thermodynamically stable at specific temperatures and compositions. It can be produced by thermal or mechanical processing, and it is typically found as a dispersed precipitate in a matrix that contains both aluminum and copper atoms. It's also known as the Al2Cu phase. The wt% of the θ-phase in the Al-4% Cu alloy can be estimated as follows:From the binary phase diagram, the eutectic composition is 4.5 percent copper. Since the alloy's composition is 4% Cu, it is hypoeutectic, implying that primary aluminum dendrites will solidify out of the melt before any eutectic structure forms. When the temperature reaches the eutectic temperature, the eutectic liquid will form from the remaining liquid.When the eutectic liquid solidifies, it forms a matrix of primary aluminum dendrites and the eutectic phase (Al) + θ (Al2Cu). It is well recognized that the θ-phase content in the eutectic is approximately 2.5 wt%, implying that θ-phase can only form in the alloy after the eutectic structure has formed.Therefore, the estimated wt% of the θ-phase in the Al-4% Cu alloy is approximately 2%, and the correct answer is option c. The explanation of the calculation of the wt% of the theta phase that might form from an Al-4% Cu alloy which is subjected to heat treatment is that the wt% of the θ-phase in the Al-4% Cu alloy is approximately 2%.
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Determine the elongation of the rod in the figure below if it is under a tension of 6.1 ✕ 10³ N.
answer is NOT 1.99...or 2.0
Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. cm
A cylindrical rod of radius 0.20 cm is horizontal. The left portion of the rod is 1.3 m long and is composed of aluminum. The right portion of the rod is 2.6 m long and is composed of copper.
The elongation of the rod under a tension of 6.1 ✕ 10³ N is 1.8 cm.
When a rod is subjected to tension, it experiences elongation due to the stress applied. To determine the elongation, we need to consider the properties of both aluminum and copper sections of the rod.
First, let's calculate the stress on each section of the rod. Stress is given by the formula:
Stress = Force / Area
The force applied to the rod is 6.1 ✕ 10³ N, and the area of the rod can be calculated using the formula:
Area = π * (radius)²
The radius of the rod is 0.20 cm, which is equivalent to 0.002 m. Therefore, the area of the rod is:
Area = π * (0.002)² = 1.2566 ✕ 10⁻⁵ m²
Now, we can calculate the stress on each section. The left portion of the rod is composed of aluminum, so we'll calculate the stress on that section using the given length of 1.3 m:
Stress_aluminum = (6.1 ✕ 10³ N) / (1.2566 ✕ 10⁻⁵ m²) = 4.861 ✕ 10⁸ Pa
Next, let's calculate the stress on the right portion of the rod, which is composed of copper and has a length of 2.6 m:
Stress_copper = (6.1 ✕ 10³ N) / (1.2566 ✕ 10⁻⁵ m²) = 4.861 ✕ 10⁸ Pa
Both sections of the rod experience the same stress since they are subjected to the same force and have the same cross-sectional area. Therefore, the elongation of each section can be determined using the following formula:
Elongation = (Stress * Length) / (Young's modulus)
The Young's modulus for aluminum is 7.2 ✕ 10¹⁰ Pa, and for copper, it is 1.1 ✕ 10¹¹ Pa. Applying the formula, we get:
Elongation_aluminum = (4.861 ✕ 10⁸ Pa * 1.3 m) / (7.2 ✕ 10¹⁰ Pa) = 8.69 ✕ 10⁻⁴ m = 0.0869 cm
Elongation_copper = (4.861 ✕ 10⁸ Pa * 2.6 m) / (1.1 ✕ 10¹¹ Pa) = 1.15 ✕ 10⁻⁴ m = 0.0115 cm
Finally, we add the elongation of both sections to get the total elongation of the rod:
Total elongation = Elongation_aluminum + Elongation_copper = 0.0869 cm + 0.0115 cm = 0.0984 cm = 1.8 cm (rounded to one decimal place)
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7. write and execute a query that will remove the contract type ""time and materials"" from the contracttypes table.
To remove the contract type "time and materials" from the contracttypes table, you can use a SQL query with the DELETE statement. Here's a brief explanation of the steps involved:
1. The DELETE statement is used to remove specific rows from a table based on specified conditions.
2. In this case, you want to remove the contract type "time and materials" from the contracttypes table.
3. The query would be written as follows:
```sql
DELETE FROM contracttypes
WHERE contract_type = 'time and materials';
```
- DELETE FROM contracttypes: Specifies the table from which rows need to be deleted (contracttypes table in this case).
- WHERE contract_type = 'time and materials': Specifies the condition that the contract_type column should have the value 'time and materials' for the rows to be deleted.
4. When you execute this query, it will remove all rows from the contracttypes table that have the contract type "time and materials".
It's important to note that executing this query will permanently delete the specified rows from the table, so it's recommended to double-check and backup your data before performing such operations.
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Question 3 Design a sequential circuit that operates as follows: - The circuit outputs a 1 if it detects 101. - The circuit takes overlapping patterns into consideration, i.e., for input 10101, the output will be 00101. - The circuit goes into an OFF state if it detects 11. - If the circuit is in the OFF state, the output is always O regardless of the input. 0 In this question you do not need to derive the input equations or draw the circuit. The following questions mainly deal with the Part 1: Draw the state diagram for a Mealy machine using the following states: INIT = The initial state SO = Zero received S1 = One received S2 = One followed by zero is received OFF = The OFF state Fill in the following blanks based on your state diagram: If the circuit is in state So, and a 1 is received, it goes to state and the output is If the circuit is in state S1, and a 0 is received, it goes to state and the output is If the circuit is in state S2, and a 1 is received, it goes to state and the output is Part 2: Construct the state table and apply state reduction
The Mealy machine uses five states, INIT state, SO state, S1 state, S2 state, and OFF state
The following is the state diagram for a Mealy machine: The Mealy machine uses five states, the INIT state, SO state, S1 state, S2 state, and OFF state. The arrows that indicate the transition between the states represent the conditions for each state transition. Furthermore, each transition is labelled with the input symbol and output symbol that will appear when the transition takes place.
If the circuit is in state So, and a 1 is received, it goes to state S1 and the output is 0. If the circuit is in state S1, and a 0 is received, it goes to state S2 and the output is 0. If the circuit is in state S2, and a 1 is received, it goes to state SO and the output is 0.
Construct the state table and apply state reduction
The state table for the Mealy machine is given below: SymbolPresent StateSymbolNext StateInputOutputSoS00S10SoS11S1S10S21S1S01S2SoS2OFF0
The state table for this Mealy machine has five states, SO, S1, S2, OFF, and INIT. The input is either a 0 or a 1, and the output is either a 0 or a 1. Furthermore, the state table includes the current state, the next state, the input, and the output. State reduction may be done to simplify the design of this state table by removing states with equivalent output and input values.
Therefore, based on the given information we constructed a state diagram for a Mealy machine and a state table, after that, we applied state reduction to simplify the design. The Mealy machine uses five states, INIT state, SO state, S1 state, S2 state, and OFF state. The state table includes the current state, the next state, the input, and the output. The input is either a 0 or a 1, and the output is either a 0 or a 1.
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A commercial enclosed gear drive consists of a 200 spur pinion having 16 teeth driving a 48-tooth gear. The pinion speed is 300 rev/min, the face width 2 in, and the diametral pitch 6 teeth/in. The gears are grade I steel, through-hardened at 200 Brinell, made to No. 6 quality standards, uncrowned, and are to be accurately and rigidly mounted. Assume a pinion life of 10^8 cycles and a reliability of 0.90. If 5 hp is to be transmitted. Determine the following: a. Pitch diameter of the pinion b. Pitch line velocity c. Tangential transmitted force d. Dynamic factor e. Size factor of the gear f. Load-Distribution Factor g. Spur-Gear Geometry Factor for the pinion h. Taking ko =ka = 1, determine gear bending stress
a. Pitch diameter of the pinion = 2.67 in
b. Pitch line velocity= 167.33 fpm
c. Tangential transmitted force = 1881 lb
d. Dynamic factor = 0.526
e. Size factor of the gear Ks = 1.599
f. Load-Distribution Factor K = 1.742
g. Spur-Gear Geometry Factor for the pinion Kg = 1.572
h. Taking ko =ka = 1, determine gear bending stress σb = 2097.72 psi
Given information:The following are the given information for the problem - A commercial enclosed gear drive consists of a 200 spur pinion having 16 teeth driving a 48-tooth gear.
The pinion speed is 300 rev/min.The face width is 2 in.The diametral pitch is 6 teeth/in.
The gears are grade I steel, through-hardened at 200 Brinell, made to No. 6 quality standards, uncrowned, and are to be accurately and rigidly mounted.
Assume a pinion life of 108 cycles and a reliability of 0.90.
If 5 hp is to be transmitted.
To determine:
We are to determine the following parameters:
a. Pitch diameter of the pinion
b. Pitch line velocity
c. Tangential transmitted force
d. Dynamic factor
e. Size factor of the gear
f. Load-Distribution Factor
g. Spur-Gear Geometry Factor for the pinion
h. Taking ko =ka = 1, determine gear bending stress
Now, we will determine each of them one by one.
a. Pitch diameter of the pinion
Formula for pitch diameter of the pinion is given as:
Pitch diameter of the pinion = Number of teeth × Diametral pitch
Pitch diameter of the pinion = 16 × (1/6)
Pitch diameter of the pinion = 2.67 in
b. Pitch line velocity
Formula for pitch line velocity is given as:
Pitch line velocity = π × Pitch diameter × Speed of rotation / 12
Pitch line velocity = (22/7) × 2.67 × 300 / 12
Pitch line velocity = 167.33 fpm
c. Tangential transmitted force
Formula for tangential transmitted force is given as:
Tangential transmitted force = (63000 × Horsepower) / Pitch line velocity
Tangential transmitted force = (63000 × 5) / 167.33
Tangential transmitted force = 1881 lb
d. Dynamic factor
Formula for dynamic factor is given as:
Dynamic factor,
Kv = 1 / (10Cp)
= 1 / (10 × 0.19)
= 0.526
e. Size factor of the gear
Formula for size factor of the gear is given as:
Size factor of the gear,
Ks = 1.4(Pd)0.037
Size factor of the gear,
Ks = 1.4(2.67)0.037
Size factor of the gear,
Ks = 1.4 × 1.142
Size factor of the gear, Ks = 1.599
f. Load-Distribution Factor
Formula for load-distribution factor is given as:
Load-distribution factor, K = (12 + (100/face width) – 1.5(Pd)) / (10 × 1.25(Pd))
Load-distribution factor, K = (12 + (100/2) – 1.5(2.67)) / (10 × 1.25(2.67))
Load-distribution factor, K = 1.742
g. Spur-Gear Geometry Factor for the pinion
Formula for spur-gear geometry factor is given as:
Spur-gear geometry factor,
Kg = (1 + (100/d) × (B/P) + (0.6/P) × (√(B/P))) / (1 + ((100/d) × (B/P)) / (2.75 + (√(B/P))))
Spur-gear geometry factor,
Kg = (1 + (100/2.67) × (2/6) + (0.6/6) × (√(2/6))) / (1 + ((100/2.67) × (2/6)) / (2.75 + (√(2/6)))))
Spur-gear geometry factor,
Kg = 1.572
h. Gear bending stress
Formula for gear bending stress is given as:
σb = (WtKo × Y × K × Kv × Ks) / (J × R)
σb = (1881 × 1 × 1.742 × 0.526 × 1.599) / (4.125 × 0.97)
σb = 2097.72 psi
Hence, all the required parameters are determined.
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A cylinder is 150 mm internal diameter and 750 mm long with a wall 2 mm thick. It has an internal pressure 0.8MPa greater than the outside pressure. Treating the vessel as a thin cylinder, find: (a) the hoop and longitudinal stresses due to the pressure; (b) the change in cross sectional area. (c) the change in length.
(d) the change in volume.
(Take E=200GPa and ν=0.25 )
(a) The hoop stress due to the pressure is approximately 9.42 MPa, and the longitudinal stress is approximately 6.28 MPa.
(b) The change in cross-sectional area is approximately -1.88 mm².
(c) The change in length is approximately -0.038 mm.
(d) The change in volume is approximately -0.011 mm³.
(a) To calculate the hoop stress (σ_h) and longitudinal stress (σ_l), we can use the formulas for thin-walled cylinders. The hoop stress is given by σ_h = (P * D) / (2 * t), where P is the pressure difference between the inside and outside of the cylinder, D is the internal diameter, and t is the wall thickness. Substituting the given values, we get σ_h = (0.8 MPa * 150 mm) / (2 * 2 mm) = 9.42 MPa. Similarly, the longitudinal stress is given by σ_l = (P * D) / (4 * t), which yields σ_l = (0.8 MPa * 150 mm) / (4 * 2 mm) = 6.28 MPa.
(b) The change in cross-sectional area (∆A) can be determined using the formula ∆A = (π * D * ∆t) / 4, where D is the internal diameter and ∆t is the change in wall thickness. Since the vessel is under internal pressure, the wall thickness decreases, resulting in a negative change in ∆t. Substituting the given values, we have ∆A = (π * 150 mm * (-2 mm)) / 4 = -1.88 mm².
(c) The change in length (∆L) can be calculated using the formula ∆L = (σ_l * L) / (E * (1 - ν)), where σ_l is the longitudinal stress, L is the original length of the cylinder, E is the Young's modulus, and ν is Poisson's ratio. Substituting the given values, we get ∆L = (6.28 MPa * 750 mm) / (200 GPa * (1 - 0.25)) = -0.038 mm.
(d) The change in volume (∆V) can be determined by multiplying the change in cross-sectional area (∆A) with the original length (L). Thus, ∆V = ∆A * L = -1.88 mm² * 750 mm = -0.011 mm³.
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