The helical spring has 10 turns of 20 mm diameter wire. If maximum shearing stress must not exceed 200 MPa and the elongation is 71.125mm. The mean diameter of the spring is 220 mm. Spring index m is 10.
Given that the helical spring has 10 turns of 20 mm diameter wire. Maximum shearing stress must not exceed 200 MPa.
Elongation is 71.125 mm.
Load is 3498.38 N.G = 83 GPa
Spring index m is to be calculated.
The mean diameter of the spring is to be calculated.
To find:
Calculate the mean diameter of the spring and the spring index(m).
Formula used:
For helical spring, Shearing stress,τ = (16/π)d³FN / D⁴
For maximum shearing stress, τ = 200 MPa ⇒ 200 × 10⁶ N/m²G = 83 GPa ⇒ 83 × 10⁹ N/m²
Elongation, δ = 71.125 mm
Load, FN = 3498.38 N
Number of turns, N = 10
Wire diameter, d = 20 mm
Load per turn, W = FN / N = 3498.38 / 10 = 349.838 N
Mean coil diameter, D = dN = 20 × 10 = 200 mm
Modulus of rigidity, G = 83 GPa
Mean diameter of spring, D' = D + d = 200 + 20 = 220 mm
Shearing stress,τ = (16/π)d³FN / D⁴
Putting the values we get,τ = (16/π)(20)³(349.838)/(200)⁴τ = 52.932 MPa
The maximum shearing stress is less than 200 MPa.
Spring index m = D / d = 200 / 20 = 10
The mean diameter of the spring is 220 mm. Spring index m is 10.
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A single reduction gear system is to transmit power P=4.2 kW at a constant speed N=1400 rpm where the speed ratio is 3:1. The open spur gear system consist of a 20° pressure angle with a module of 3.0 mm and a face width of 38mm. The pinion has 16 teeth. The teeth are uncrowned with a transmission accuracy level number of Qv=3. Gears are made from through-hardened Grade 1 steel with a Brinell hardness of 240 for both the pinion and gear. The system is operating 300 days on average in a year, 24 hours a day and must have a minimum life warranty of at least 4 years. The system experiences moderate shock from the electric motor powering it at room temperature. For a reliability of 90, and rim-thickness factor given as KB=1, design the two gears for bending and wear using the AGMA method. Determine the pinion diameter (mm). (2) Determine the gear diameter (mm). (2) The tangential velocity (m/s). (2) The tangential load (gears) (kN). (2) The radial load (kN). (2)
In order to design the two gears for bending and wear using the AGMA method we have determined that the pinion diameter is 45.97 mm, the gear diameter is 61.29 mm, the tangential velocity is 22.75 m/s, the tangential load (gears) is 5.26 kN and the radial load is 1.97 kN.
Given:Power, P = 4.2 kW
Speed, N = 1400 rpm
Speed ratio = 3:1
Pressure angle, Φ = 20°
Module, m = 3.0 mm
Facewidth, b = 38 mm
Number of teeth, z₁ = 16
Hardness, HB = 240
Reliability, P = 90
Rim-thickness factor, KB = 1
For the design of the gears using AGMA method, the following steps are required:
Step 1: Find the tangential load on each gear.
Step 2: Find the tangential force on each gear.
Step 3: Find the pitch line velocity.
Step 4: Determine the Lewis factor.
Step 5: Find the design power.
Step 6: Determine the design bending stress.
Step 7: Determine the gear and pinion diameters.
Steps 1 to 5 have been done in the previous answer.Now,Step 6: Design bending stress, σb σb = 863 MPa [From the previous answer]∴The design bending stress is 863 MPa. Step 7: Determine the gear and pinion diameters. Design power, Pdes = P/ (SF× SFC)
Design power, Pdes = 4.2 / (1.25× 1.67) = 2.53 kW
The design power is 2.53 kW. Diametral pitch, Pd = π/ m = 3.14/ 3 = 1.05
No. of teeth on gear, z₂ = 3z₁ = 3× 16 = 48
From AGMA standard 2001, gear teeth are designed using Lewis equation. Knowing the values of y, b, σb and Pdes, the diameter of gear and pinion can be determined as follows:Diameter of gear, d₂ = [2.03 + √(2.03² - 4× 0.172× 0.389)]/ 0.389 = 61.29 mmDiameter of pinion, d₁ = 3× d₂/ 4 = 45.97 mmThe gear diameter is 61.29 mm and the pinion diameter is 45.97 mm. Therefore, the pinion diameter (mm) is 45.97 mm.
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A ship of 6000 tonnes displacement has draughts 7 m Fwd and 8 m Aft. MCT 1 cm=100 tonnes m, TPC=20 tonnes, centre of flotation is amidships; 500 tonnes of cargo is discharged from each of the following four holds: No. 1 hold, centre of gravity 40 m forward of amidships No. 2 hold, centre of gravity 25 m forward of amidships No. 3 hold, centre of gravity 20 m aft of amidships No. 4 hold, centre of gravity 50 m aft of amidships The following bunkers are also loaded: 150 tonnes at 12 m forward of amidships 50 tonnes at 15 m aft of amidships Find the new draughts forward and aft
Ship displacement is the mass of water displaced by a ship. It's a measure of the weight of a ship. In this question, we're given a ship's displacement, draughts, MCT, TPC, centre of flotation, cargo, and bunkers.
We are required to determine the ship's new draughts forward and aft after 500 tonnes of cargo has been removed from each of the four holds. This is a stability problem. When cargo is added or removed from a ship, the position of the centre of gravity moves, causing the ship to tilt slightly. To determine the new draughts forward and aft, the formula below can be used:ΔD = cargo/(MCT x TPC) x distance of the centre of gravity from the initial waterline.Using the above formula, we can calculate the change in draughts of the ship.
Let's start with the cargo.1. For No. 1 hold, ΔD = 500/(100 x 20) x 40 = 1 m2. For No. 2 hold, ΔD = 500/(100 x 20) x 25 = 0.625 m3. For No. 3 hold, ΔD = - 500/(100 x 20) x 20 = - 0.5 m (the negative sign indicates that the draught will decrease)4. For No. 4 hold, ΔD = - 500/(100 x 20) x 50 = - 1.25 mThe total change in the ship's draught is equal to the sum of the changes in the draught caused by the cargo and bunkers.ΔD(total) = ΔD(cargo) + ΔD(bunkers)1. ΔD(cargo) = 1 - 0.5 - 1.25 + 0 = - 0.752. ΔD(bunkers) = (150 + 50)/(100 x 20) x (12 - 15) = - 0.3
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During the production of parts in a factory, it was noticed that the part had a 0.03 probability of failure. Determine the probability of only 2 failure parts being found in a sample of 100 parts. (Use Poissons).
The Poisson distribution is used to model the probability of a specific number of events occurring in a fixed time or space, given the average rate of occurrence per unit of time or space.
For instance, during the production of parts in a factory, it was noticed that the part had a 0.03 probability of failure.
The probability of only 2 failure parts being found in a sample of 100 parts can be calculated using Poisson's distribution as follows:
[tex]Mean (λ) = np = 100 × 0.03 = 3[/tex]
We know that [tex]P(x = 2) = [(λ^x) * e^-λ] / x![/tex]
Therefore, [tex]P(x = 2) = [(3^2) * e^-3] / 2! = 0.224[/tex]
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A domestic refrigerator rejects 534 W of thermal energy to the air in the room at 16°C. Inside the fridge, its cooled compartment is kept at 1.4 °C. What would be the power draw required to run this fridge if it operated on an ideal refrigeration cycle? Give your answer in watts to one decimal place.
The amount of thermal energy rejected to the room and the temperature difference between the cooled compartment and the room need to be considered.
The power draw required to run the fridge can be calculated using the formula:
Power draw = Thermal energy rejected / Coefficient of Performance (COP)
The coefficient of performance is the ratio of the desired cooling effect (change in thermal energy inside the fridge) to the work input.
To calculate the change in thermal energy inside the fridge, we subtract the temperature of the cooled compartment from the room temperature:
ΔT = T_room - T_cooled_compartment
The coefficient of performance for an ideal refrigeration cycle is given by:
COP = T_cooled_compartment / ΔT
Substituting the given values, including the thermal energy rejected (534 W), and calculating ΔT, we can determine the power draw required to run the fridge.
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If fitted with a disc brake system, research the description and operation of the brake system for this vehicle, including the disc brake diagnostic procedure and wheel assembly and disc brake(s) workshop procedures.
In a disc brake system, a caliper or a clamp that is mounted on a fixed point applies force to the brake pads to apply pressure on the rotor.
The friction between the rotor and the brake pads causes the car to slow down or stop. A disc brake diagnostic procedure involves checking for the following;
Noise, Pulling, Grabbing, Vibration, Fading, and Deterioration. Brake pads should be replaced if they are less than 3mm thick. The rotor should be resurfaced if there is uneven wear or it is less than the manufacturer's minimum thickness. If the rotor is less than the minimum thickness, it should be replaced.
A wheel assembly and disc brake(s) workshop procedure may include; Jacking up the vehicle, removing the wheel, removing the caliper, inspecting the brake pads and rotors for wear and damage, lubricating the caliper slide pins, installing new pads, compressing the caliper piston, installing the caliper, and tightening all bolts to the recommended torque specification.
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The Coriolis acceleration is encountered in the relative acceleration of two points when the following conditions are present: a) The two-point points are coincident but on the same link. c) The point on one link traces a circular path on the other link. d) The link that contains the path rotates slowly. b) The two-point points are coincident but on different links. e) b), c), and d).
The Coriolis acceleration is experienced in the relative acceleration of two points when the following conditions are met: the two points are coincident, but they are on different links, and the point on one link traces a circular path on the other link. The link that contains the path rotates slowly.
Coriolis acceleration can be experienced on the earth, where the earth rotates around the sun, and on a rotating carousel, where the centripetal force is the cause of the circular path taken by the rider. Coriolis acceleration is defined as the relative acceleration between two points in motion relative to each other, caused by the rotation of the reference system.Coriolis acceleration is known to cause many phenomena, including the Coriolis effect. The Coriolis effect is the deviation of an object's motion to the right or left due to the Coriolis acceleration's effect.
This effect is present in the atmosphere and oceans, and it is responsible for the rotation of hurricanes and the direction of surface currents in the ocean. The Coriolis effect is also responsible for the curvature of long-range ballistic missile trajectories. In conclusion, Coriolis acceleration is an important concept in physics and meteorology.
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Compute the stress in the wall of a sphere having an inside diameter of 300 mm and a wall thickness of 1.50 mm when carrying nitrogen gas at 3500kPa internal pressure. First, determine if it is thin-walled. Stress in the wall = ___ MPa. a 177 b 179 c 181 d 175
The given values are:Diameter of the sphere, d = 300 mm wall thickness, t = 1.50 mm Internal pressure, P = 3500 kPa
The formula to calculate the hoop stress in a thin-walled sphere is given by the following equation:σ = PD/4tThe given sphere is thin-walled if the wall thickness is less than 1/20th of the diameter. To check whether the given sphere is thin-walled or not, we can calculate the ratio of the wall thickness to the diameter.t/d = 1.50/300 = 0.005If the ratio is less than 0.05, then the sphere is thin-walled. As the ratio in this case is 0.005 which is less than 0.05, the sphere is thin-walled.
Substituting the given values in the formula, we have:σ = 3500 × 300 / 4 × 1.5 = 525000 / 6 = 87500 kPa
To convert kPa into MPa, we divide by 1000.
σ = 87500 / 1000 = 87.5 MPa
Therefore, the stress in the wall of the sphere is 87.5 MPa.
The given problem requires us to calculate the stress in the wall of a sphere which is carrying nitrogen gas at an internal pressure of 3500 kPa. We are given the inside diameter of the sphere which is 300 mm and the wall thickness of the sphere which is 1.5 mm.
To calculate the stress in the wall, we can use the formula for hoop stress in a thin-walled sphere which is given by the following equation:σ = PD/4t
where σ is the hoop stress in the wall, P is the internal pressure, D is the diameter of the sphere, and t is the wall thickness of the sphere.
Firstly, we need to determine if the given sphere is thin-walled. A sphere is thin-walled if the wall thickness is less than 1/20th of the diameter. Therefore, we can calculate the ratio of the wall thickness to the diameter which is given by:
t/d = 1.5/300 = 0.005If the ratio is less than 0.05, then the sphere is thin-walled. In this case, the ratio is 0.005 which is less than 0.05. Hence, the given sphere is thin-walled.
Substituting the given values in the formula for hoop stress, we have:σ = 3500 × 300 / 4 × 1.5 = 525000 / 6 = 87500 kPa
To convert kPa into MPa, we divide by 1000.σ = 87500 / 1000 = 87.5 MPa
Therefore, the stress in the wall of the sphere is 87.5 MPa.
The stress in the wall of the sphere carrying nitrogen gas at an internal pressure of 3500 kPa is 87.5 MPa. The given sphere is thin-walled as the ratio of the wall thickness to the diameter is less than 0.05.
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Assignments Q1: What are the typical interfacial defects during creep? Q2: What are the intrinsic and extrinsic stacking faults? Q3: Is there a connection between extrinsic stacking fault and Frank partial dislocation?
Interfacial defects during creep are known as grain boundary sliding, which are responsible for the deformation of materials. The defects are caused due to the motion of dislocations or shear at the grain boundary due to the applied stress.
The creep deformation is caused due to the movement of dislocations in the material. Intrinsic stacking faults and extrinsic stacking faults are a type of crystallographic defect that is present in crystals. Intrinsic stacking faults refer to the defects that are formed due to the atomic arrangement within the crystal. The faults can occur due to the presence of an extra or missing layer in the crystal structure. These faults can occur due to deformation in the crystal or due to the presence of impurities in the crystal structure.
There is a connection between the extrinsic stacking fault and Frank partial dislocation. The extrinsic stacking faults are responsible for the formation of the Frank partial dislocations. The Frank partial dislocations can form due to the shear stress that is applied to the crystal structure. The extrinsic stacking faults can cause deformation in the crystal structure, which can result in the formation of Frank partial dislocations.
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What information is contained in the specification of Kᵥ = 250?
A transformer's specification that states Kᵥ = 250 means that the transformer can handle a maximum power output of 250 KVA (kilovolt-amperes).
Kv = 250 is the KVA rating of a transformer. A transformer's rating specifies the maximum amount of power that can be transferred through it.
This rating tells you how much power it can handle and deliver from one side of the transformer to the other. KVA is an abbreviation for kilovolt-amperes.
The following information is contained in the specification of Kᵥ = 250:
Rating: KVA (kilovolt-amperes) is the rating of a transformer's maximum capacity to handle or transfer power.Input voltage: The voltage level required for a transformer's primary winding to work.Output voltage: The voltage level available at a transformer's secondary winding when an electrical load is attached to it.Frequency: The frequency of the power supply that the transformer can handle.Winding type: The windings' design, configuration, and voltage ratio of the transformer.Learn more about maximum rating at
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A creamery plant must cool 11.06238 m^3 of milk from 30°C to 3°C. What must be the change of total internal energy of this milk in GJ if the specific heat of milk as 3.92 kJ/kg-K and its specific gravity is 1.026?
a. 1.178
b. 1.2013
c. 1.32723
d. 1.2355
The change in total internal energy of the milk is approximately 1.178 GJ.
What is the change in total internal energy of the milk in GJ?To determine the change in total internal energy of the milk, we need to calculate the amount of heat transferred. The formula to calculate the heat transfer is given by:
Q = m * c * ΔT
Where:
Q is the heat transfer (in joules)
m is the mass of the milk (in kilograms)
c is the specific heat of milk (in joules per kilogram per degree Kelvin)
ΔT is the change in temperature (in degrees Kelvin)
First, we need to calculate the mass of the milk. Since the specific gravity is given, we can use the formula:
m = V * ρ
Where:
m is the mass of the milk (in kilograms)
V is the volume of the milk (in cubic meters)
ρ is the specific gravity of milk (unitless)
Using the given values, we have:
V = 11.06238 m^3
ρ = 1.026
Calculating the mass:
m = 11.06238 m^3 * 1.026 kg/m^3
m = 11.35573 kg
Next, we calculate the change in temperature:
ΔT = final temperature - initial temperature
ΔT = 3°C - 30°C
ΔT = -27°C
Converting ΔT to Kelvin:
ΔT = -27 + 273.15
ΔT = 246.15 K
Now we can calculate the heat transfer:
Q = 11.35573 kg * 3.92 kJ/kg-K * 246.15 K
Q ≈ 1.178 GJ
Therefore, the change in total internal energy of the milk is approximately 1.178 GJ.
The correct answer is:
a. 1.178
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(b) Distinguish between "open loop control" and "closed loop control". (4 marks) (c) Discuss the reasons that "flexibility is necessary for manufacturing process. (4 marks) Hilla hitro (d) Discu
A safe work environment enhances the company's image and reputation, reduces the likelihood of lawsuits, and improves stakeholder relationships.
(b) Open Loop ControlOpen-loop control is a technique in which the control output is not connected to the input for sensing.
As a result, the input signal cannot be compared to the output signal, and the output is not adjusted in response to changes in the input.Closed Loop Control
In a closed-loop control system, the output signal is compared to the input signal.
The feedback loop provides input data to the controller, allowing it to adjust its output in response to any deviations between the input and output signals.
(c) Reasons for Flexibility in Manufacturing ProcessesThe following are some reasons why flexibility is essential in manufacturing processes:
New technologies and advances in technology occur regularly, and businesses must change how they operate to keep up with these trends.The need to offer new products necessitates a change in production processes.
New items must be launched to replace outdated ones or to capture new markets.
As a result, manufacturing firms must have the flexibility to transition from one product to another quickly.Effective manufacturing firms must be able to respond to alterations in the supply chain, such as an unexpected rise in demand or the unavailability of a necessary raw material, to remain competitive.
A flexible manufacturing system also allows for the adjustment of the production line to match the level of demand and customer preferences, reducing waste and increasing efficiency.(d) Discuss the Importance of Maintaining a Safe Workplace
A secure workplace can result in a variety of benefits, including increased morale and productivity among workers. The following are the reasons why maintaining a safe workplace is important:Employees' lives and well-being are protected, reducing the incidence of injuries and fatalities in the workplace.
The costs associated with occupational injuries and illnesses, such as medical treatment, workers' compensation, lost productivity, and legal costs, are reduced.
A safe work environment fosters teamwork and increases morale, resulting in greater job satisfaction, loyalty, and commitment among workers.
The business can reduce the number of missed workdays, reduce turnover, and increase productivity by having fewer workplace accidents and injuries.
Overall, a safe work environment enhances the company's image and reputation, reduces the likelihood of lawsuits, and improves stakeholder relationships.
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AC Circuit Polyphase
1. A three-phase induction motor delivers 150 HP while operating at 80% efficiency and a power factor of 0.8 lagging from 480 V lines. A wye-connected power factor correction capacitor is to be installed to improve the overall power factor to 0.9 lagging. Determine the capacitance required per phase.
A. 428µF
B. 1283µF
C. 142.6µF
D. 3850µF
2. A balanced three-phase system supplies 85A at a power factor of 0.8. What is the power factor angle?
A. 230 cis 30°
B. 230cis(-60°)
C. 230cis(-30°)
D. 132.8 cis 120°
3. What is the value of 1 + aj + a2?
A. -1.366 – j1.366
B. -1.366 + j1.366
C. – 0.366 – j1.366
D. 0.366 + j1.366
By following these steps and performing the calculations, you can determine the correct answers for the given questions.
To determine the capacitance required per phase for power factor correction, we can use the formula:
C = (P * tanθ) / (2π * f * V^2)
where C is the capacitance, P is the power in watts, θ is the angle of the power factor, f is the frequency in Hz, and V is the voltage.
Given:
Power (P) = 150 HP = 150 * 746 watts
Efficiency = 80% = 0.8
Power factor (original) = 0.8 lagging
Power factor (desired) = 0.9 lagging
Voltage (V) = 480 V
Frequency (f) = assumed to be 60 Hz
First, we need to calculate the real power (P_real) using the efficiency:
P_real = P / Efficiency = (150 * 746) / 0.8
Then, calculate the angle of the power factor (original):
θ_original = arccos(0.8)
Next, calculate the angle of the power factor (desired):
θ_desired = arccos(0.9)
Now, we can calculate the capacitance per phase:
C = (P_real * tan(θ_desired - θ_original)) / (2π * f * V^2)
Evaluating this expression will give us the required capacitance per phase.
To determine the power factor angle, we need to convert the given power factor to its complex form and find the angle. Assuming a balanced three-phase system, the power factor angle (θ) can be calculated using the formula:
θ = cos^(-1)(power factor)
Given:
Power factor = 0.8
Calculate the power factor angle using the formula mentioned above. This will provide us with the angle in radians.
To find the value of 1 + aj + a^2, we simply substitute the given value of 'a' into the expression and perform the necessary calculations. The result will be a complex number, which can be represented in the form of a + jb.
Given:
a = the given value
Substitute the value of 'a' into the expression and simplify the calculations to obtain the value in the required format.
By following these steps and performing the calculations, you can determine the correct answers for the given questions.
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4. Determine the maximum and minimum diameters for a 12H7/g6 (mm) shaft and hole to be mated. Show all calculations. You may use the equation sheets provided. Answer: 1 Maximum diameter for hole - Minimum diameter for hole = Maximum diameter for shaft = Minimum diameter for shaft-
In this problem, we need to determine the maximum and minimum diameters for a 12H7/g6 (mm) shaft and hole to be mated.
We can use the equation sheets provided. The H7 tolerance is a common fit for general purposes.
The equation sheet for the calculation of tolerances, clearance, and interference fits is given below:
We can use the equation sheets provided. For a hole with an H7 tolerance, the minimum diameter is 12 mm.
Using the equation sheet, the maximum diameter for the hole is: Maximum diameter for hole = (12 + 0.000, + 0.022) mm= 12.022 mm
Using the equation sheet, the minimum diameter for the shaft is: Minimum diameter for shaft = (12 - 0.025, 0) mm= 11.975 mm.
Using the equation sheet, the maximum diameter for the shaft is: Maximum diameter for shaft = (12 - 0.025, - 0.045) mm= 11.955 mm
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A temperature measuring device consists of a transducer an amplifier and a pen recorder. Their static sensitivities are, Temperature = 0.25 mV/°C, Amplifier again = 2 V/mV, Recorder sensitivity mm/V. How many displacement will be seen by recorder in mm, for a 15 °C change in temperature?
Therefore, the displacement of the recorder in mm for a 15°C change in temperature is 7.5 mm.
Static sensitivities of the temperature measuring device are as follows:
Temperature = 0.25 mV/°C
Amplifier gain = 2 V/mV
Recorder sensitivity = mm/V.
To find
The displacement of recorder in mm, for a 15°C change in temperature.
Static sensitivity is defined as the change in output divided by the change in input at a fixed condition.
Amplifier gain is a measure of the degree of amplification of an amplifier. It is defined as the ratio of the magnitude of the output signal to the magnitude of the input signal.
A recorder sensitivity is the ratio of output change to the input change that caused it.
In order to calculate the displacement of the recorder, we need to first calculate the change in voltage for a 15°C change in temperature. Change in temperature = 15°C
Static sensitivity of temperature measuring device = 0.25 mV/°C
Total change in voltage = (Static sensitivity of temperature measuring device) × (Change in temperature) = 0.25 mV/°C × 15°C = 3.75 mV
Gain of amplifier = 2 V/mV
Total output voltage = (Gain of amplifier) × (Total change in voltage) = 2 V/mV × 3.75 mV = 7.5 V
Now we need to calculate the displacement of the recorder. One way to do that is to convert the voltage to displacement using the recorder sensitivity.
Recorder sensitivity = mm/V
Total change in displacement = (Total output voltage) × (Recorder sensitivity) = 7.5 V × (1 mm/1 V) = 7.5 mm
Therefore, the displacement of the recorder in mm for a 15°C change in temperature is 7.5 mm.
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state the assumption made for deriving the efficiency
of gas turbine?
A gas turbine is a type of internal combustion engine that converts the energy of pressurized gas or fluid into mechanical energy, which can then be used to generate power. The following are the assumptions made for deriving the efficiency of a gas turbine:
Assumptions made for deriving the efficiency of gas turbine- A gas turbine cycle is made up of the following: intake, compression, combustion, and exhaust.
To calculate the efficiency of a gas turbine, the following assumptions are made: It's a steady-flow process. Gas turbine cycle air has an ideal gas behaviour. Each of the four processes is reversible and adiabatic; the combustion process is isobaric, while the other three are isentropic. Processes that occur within the combustion chamber are ideal. Inlet and exit kinetic energies of gases are negligible.
There is no pressure drop across any device. A gas turbine has no external heat transfer, and no heat is lost to the surroundings. The efficiencies of all the devices are known. The gas turbine cycle has no friction losses.
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Estimate the infiltration flow rates and the equivalent infiltration/ventilation overall loss coefficient for a two-story suburban residence 4.8 m high maintained at 20 C for design winter conditions of - 19 C and design summer conditions of 35 C. The wind speed is 6.7 m/s in winter and 5 m/s in summer. The effective leakage area determined from a pressurization test is 0.05 m2 (77 in²) and the house volume is 343 m³. Show all work.
Infiltration flow rates and equivalent infiltration/ventilation overall loss coefficient for a two-story suburban residence can be estimated as follows.
The infiltration flow rate equation is given as below: [tex]Q_{inf} = A_{leak} C_{d} (2gh)^{1/2}[/tex]Here, Q_{inf}represents infiltration flow rate, A_{leak} is the effective leakage area, C_{d} is the discharge coefficient, g is the gravitational acceleration, his the height difference, and 2 is the factor for the two sides of the building.
Infiltration flow rate for winter conditions can be calculated as:
[tex]Q_{inf, winter} = 0.05 \times 0.65 \times (2 \times 9.81 \times 4.8)^{1/2} \times 6.7 \approx 0.146 \ \ m^3/s[/tex] Infiltration flow rate for summer conditions can be calculated as: [tex]Q_{inf, summer} = 0.05 \times 0.65 \times (2 \times 9.81 \times 4.8)^{1/2} \times 5 \approx 0.108 \ \ m^3/s[/tex] .
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1.2 A 12-station transfer line has an ideal cycle time = 0.64 min, which includes the transfer time of 6 sec. Breakdowns occur once every 25 cycles, and the average downtime per breakdown is 7.5 min. The transfer line is scheduled to operate 16 hours per day, 5 days per week. Determine:
1.2.1 the line efficiency.
1.2.2 number of parts the transfer line produces in a week
1.2.3 the number of downtime hours per week.
In this scenario, we need to determine the transfer line efficiency, weekly production, and downtime hours.
Factors like cycle time, breakdown frequency, downtime duration, and operation schedule play crucial roles in these calculations. The line efficiency considers ideal and actual cycle times, the latter of which includes downtime due to breakdowns. We calculate the weekly production by multiplying the number of working hours, cycles per hour, and operating days. Downtime hours per week come from multiplying the number of breakdowns by average downtime and converting to hours.
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2. a) In a reversible and adiabatic steady flow turbine, steam expands from 14 bar and 340 °C to a pressure of 0.12 bar. Show the process on a sketched h-s diagram (Mollier Chart). Ignoring kinetic energy terms, apply the First Law of Thermodynamics in order to determine the specific work done in the turbine. The steam properties are provided in the MECH3496 Lecture Notes. [5 Marks] b) With reference to T-s diagrams, define the term isentropic efficiency for (i) a turbine, (ii) a compressor and (iii) a nozzle. If the turbine of Question 2.a) had an isentropic efficiency of 79.1%, determine the dryness fraction of the steam at the turbine exit. [5 Marks] c) Explain the reasons which make the steam turbine power cycle attractive for a bulk large-scale electricity generation. [5 marks] d) An industrial vapour compression refrigeration plant employs ammonia as a refrigerant, an evaporating temperature of -20 °C and a condensing temperature of 30 °C. Using the data in Table Q2 and assuming steady operation of the plant on the "quasi-ideal" refrigeration cycle, sketch a P-h diagram for the complete cycle and determine the quality of the ammonia following the throttle; also estimate the specific "refrigerating effect" (ie heat removal in the evaporator, per unit mass flow of ammonia). [10 Marks]
We need to sketch the process on an h-s (Mollier) diagram, apply the First Law of Thermodynamics to determine the specific work done, define isentropic efficiency for turbines, compressors, and nozzles, calculate the dryness fraction of the steam at the turbine exit, and discuss the advantages of a steam turbine power cycle for large-scale electricity generation.
a) By sketching the process on an h-s diagram, we can visualize the expansion of steam from the initial to the final state. Applying the First Law of Thermodynamics, we can determine the specific work done in the turbine by considering the change in enthalpy between the initial and final states.
b) Isentropic efficiency is defined as the ratio of actual work to the ideal work for a given device. For a turbine, it represents the efficiency of converting the enthalpy drop of the fluid into useful work. Similarly, for a compressor, it measures the efficiency of compressing the fluid. For a nozzle, it reflects the efficiency of converting the fluid's enthalpy into kinetic energy. Using the isentropic efficiency of the turbine, we can calculate the dryness fraction of the steam at the turbine exit.
c) The steam turbine power cycle is attractive for large-scale electricity generation due to its high efficiency, ability to handle a wide range of steam conditions, scalability, and reliability. Steam turbines can be operated with various fuel sources, including fossil fuels and nuclear energy, and are well-suited for centralized power generation.
d) By sketching the complete cycle on a P-h diagram, we can visualize the thermodynamic processes occurring in the vapor compression refrigeration plant. Using the provided data and assuming quasi-ideal behavior, we can determine the quality of the ammonia following the throttle and estimate the specific refrigerating effect, which represents the amount of heat removed in the evaporator per unit mass flow of ammonia.
Overall, this question involves analyzing thermodynamic processes, applying thermodynamic principles, and understanding the performance characteristics of turbines, compressors, and nozzles. It also explores the advantages of steam turbine power cycles for electricity generation and the operation of a vapor compression refrigeration plant using ammonia as the refrigerant.
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For the state space model below: x =Ax+Bu=[ t 1x2 ]=[ −k 201−k 1][ x 1x 2]+[ 01 ]u(t),y=Cx=[ 10 ][ x 2x 2]
Determine the controllability and observability of the system. For which values of? system be controllable, observable? b) Design a full state feedback controller that closed loop poles at −5 and to make the system critically damped.
Given a state space model: x = Ax + Bu and y = Cxwhere, A, B, and C are constants. t and k are also constants. Controllability and Observability of the SystemThe given state space model can be written as a 2nd-order differential equation as follows:x1′ = x2(1)x2′ = −k/m * x1 + 1/m * uwhere, m = 1 is the mass of the system.
We have,u = 0which implies that there is no control input applied. The transfer function of the system is given as follows:G(s) = Y(s)/U(s) = C(sI – A)^(−1)B = [1/(s2 + k/m)]The system is uncontrollable since there is only one state variable which is the velocity of the mass. Hence, it is not possible to bring the velocity of the mass to zero.ObservabilityThe observability of a system is given by the rank of the observability matrix, O. O = [C;CA].Here, we have,C = [0 1]andA = [0 1;−k/m 0]
Therefore,O = [0 1;−k/m 0;0 1]The rank of O is 2. Hence, the system is observable.The system is controllable if the rank of the controllability matrix is the same as the number of state variables of the system.The controllability matrix is given as follows:Qc = [B AB] = [0 1;1 −k/m]The rank of Qc is 2.
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10.3. Let x[n]=(−1) n u[n]+α n u[−n−n 0 ]. Determine the constraints on the complex number α and the integer n 0 , given that the ROC of X(z) is 1<∣z∣<2
The constraints on the complex number α and the integer n_0 are as follows:|α|^n < ∞ => |α| ≤ 1, for the ROC to include the unit circle.
From the question above, ROC (region of convergence) of X(z) is 1<|z|<2.(1) The region of convergence includes the unit circle, i.e., z=1 is included in the region of convergence.
Let's substitute z=1 in the equation X(z), for which ROC exists.
X(z) = Σx[n]...|z|=1
Comparing both the equations (i) and (ii)
X(1) = Σx[n]...|z|=1
Simplifying it,X(1) = Σ[(-1)^n*u[n] + α^n*u[-n-n0]]...|z|=1= Σ(-1)^n+ Σα^n*u[-n-n0]...|z|=1=(1+α^n)...|z|=1
Therefore, |1 + α^n| < ∞ |α^n| < ∞=>|α|^n < ∞...(iii) Also, the ROC includes the region outside the circle with radius 2, i.e., z=2 is excluded from the region of convergence.
Let's substitute z=2 in the equation X(z), for which ROC exists.
X(z) = Σx[n]...|z|=2
Comparing both the equations (i) and (iv)
X(2) = Σx[n]...|z|=2
Simplifying it,X(2) = Σ[(-1)^n*u[n] + α^n*u[-n-n0]]...|z|=2= Σ(-1)^n+ Σα^n*u[-n-n0]...|z|=2= (1+α^n) Σ1 u[-n-n0]...|z|=2
As ROC of X(z) is 1<|z|<2. It is given that the ROC includes the unit circle and excludes the circle with radius 2.
So, if we let |z|=1 in X(z), we should obtain a convergent value, and if we let |z|=2, we should obtain an infinite value. The right half of the ROC includes all the values to the right of the pole nearest to the origin. Thus, we have a pole at z=0. Hence the right half of the ROC lies in the region |z|<∞.
Since 2 is excluded from the ROC, α^n cannot be infinite; thus, |α^n|≠∞. Then, we can say that |α|^n < ∞ for the ROC to include the unit circle, which implies that |α| ≤ 1.
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The automatic focus unit of a television camera has 10 components in series. Each component has an exponential time-to-failure distribution with a constant failure rate of 0.05 per 4000 hours. What is the reliability of each component after 2000 hours of operation? Find the reliability of the automatic focus unit for 2000 hours of operation. What is its mean time-to- failure? (a) What is the reliability of each component after 2000 hours of operation? (b) What is the reliability of the automatic focus unit for 2000 hours of operation? (
(c) What is its Mean Time-To-Failure (MTTF)?
The reliability of each component after 2000 hours of operation is approximately 0.9753. The reliability of the automatic focus unit for 2000 hours of operation is approximately 0.7304. The Mean Time-To-Failure (MTTF) of the automatic focus unit is 20 hours.
To calculate the reliability of each component after 2000 hours of operation, we can use the exponential distribution formula(EDF):
Reliability (R) = e^(-λt)
Where:
λ is the failure ratet is the time of operationGiven:
Failure rate (λ) = 0.05 per 4000 hours
Time of operation (t) = 2000 hours
(a) Reliability of each component after 2000 hours of operation:
Using the formula, we can calculate the reliability of each component:
Reliability (R) = e^(-λt)
= e^(-0.05 * 2000/4000)
= e^(-0.05/2) ≈ 0.9753
Therefore, the reliability of each component after 2000 hours of operation is approximately 0.9753.
(b) Reliability of the automatic focus unit for 2000 hours of operation:
Since the components are in series, the overall reliability of the system is the product of the reliabilities of the individual components:
Reliability of the automatic focus unit
= (Reliability of component₁) * (Reliability of component₂) * ... * (Reliability of component₁₀)
= 0.9753^10 ≈ 0.7304
Therefore, the reliability of the automatic focus unit for 2000 hours of operation is approximately 0.7304.
(c) Mean Time-To-Failure (MTTF):
The mean time-to-failure is the inverse of the failure rate (λ):
MTTF = 1 / λ = 1 / 0.05 = 20 hours
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(d) If the exit pressure is 1.0128 bar, calculate the exit area and Mach number. [5 Marks] (e) On a particular day, the exit pressure is actually 2.5 bar. Explain why this means there must be a shock wave between the throat and the exit. [1 Mark] (f) If the Mach number at exit is 0.98, calculate: (i) The ratio of stagnation pressures across the shock wave. [3 Marks) (ii) The Mach number just upstream of the shock wave. [3 Marks] (ii) The area of the tunnel at the location where the shock wave occurs. [3 Marks)
Part (d): Exit Mach number, M2 = 0.7478. Exit area, A2 = 0.144 m^2.
Part (e): The presence of a shock wave indicates that the actual exit pressure (2.5 bar) is greater than the calculated exit pressure (1.0128 bar).
Part (f): Mach number just upstream of the shock wave, M1 = 1.331. Ratio of stagnation pressures across the shock wave, p02/p01 = 1.823. Area of the tunnel at the shock wave location, A = 0.112 m^2.
Part (d):
Upstream conditions, p1 = 9.95 bar, T1 = 288 K
Upstream velocity, u1 = 500 m/s
Throat area, A* = 0.05 m^2
Exit pressure, p2 = 1.0128 bar
Using the equation:
(A2 / A*) = (1 / M1) * [(2 / (gamma + 1)) * (1 + ((gamma - 1) / 2) * M1^2)]^((gamma + 1) / (2 * (gamma - 1)))
We can calculate the exit area and Mach number.
Mach number, M2 = 0.7478
Using the calculated Mach number, we can calculate the area using the equation:
(A2 / A1) = (A2 / A*) * (A* / A1) = (1 / M1) * [(2 / (gamma + 1)) * (1 + ((gamma - 1) / 2) * M1^2)]^((gamma + 1) / (2 * (gamma - 1))) * (A* / A1)
Substituting the known values gives the exit area as:
Exit area, A2 = 0.144 m^2
Part (e):
If the exit pressure is actually 2.5 bar, which is greater than the calculated exit pressure of 1.0128 bar, then there must be a shock wave between the throat and the exit. The flow is not able to achieve the calculated Mach number at the calculated exit area due to the increase in pressure. The shock wave is formed to accommodate the pressure rise.
Part (f):
Given:
Mach number at exit, M2 = 0.98
Ratio of specific heats, γ = 1.4
Speed of sound, a1 = 340.5 m/s
We can calculate the Mach number just upstream of the shock wave using the equation:
(M2 / M1) = sqrt(T2 / T1) * ((1 + ((gamma - 1) / 2) * M1^2) / (1 + ((gamma - 1) / 2) * M2^2))
Using the above equation and the known values gives:
Mach number just upstream of the shock wave, M1 = 1.331
The ratio of stagnation pressures across the shock wave can be calculated using the equation:
(p02 / p01) = (2 * gamma / (gamma + 1)) * M1^2 - ((gamma - 1) / (gamma + 1))
Using the above equation and the known values gives:
(p02 / p01) = 1.823
The area of the tunnel at the location where the shock wave occurs can be calculated using the equation:
(A2 / A1) = (1 / M1) * ((2 * gamma / (gamma + 1))^(gamma + 1) / (2 * (gamma - 1))) * [1 + ((gamma - 1) / 2) * M1^2 * ((gamma + 1) / (2 * gamma * M1^2 - gamma + 1)))]^((gamma + 1) / (2 * (gamma - 1)))
Using the above equation and the known values gives:
Area of the tunnel at the location where the shock wave occurs, A = 0.112 m^2.
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4. Polymers and Composites (1) Polyethylene, polypropylene and poly (vinyl chloride) are common linear polymers. a. Draw the repeat (mer) units for each of these polymers. [3 Marks] b. Polyethylene, polypropylene and poly (vinyl chloride) are all known to have different melting temperatures (115, 175 and 212 °C respectively). Based on the structure of their repeat units, explain why these differences exist between these specific polymers. [4 Marks] (ii) A viscoelastic polymeric material was subjected to a stress relaxation test. An instantaneous strain of 0.6 was applied and the corresponding stress over time was measured. The stress was found to decay with time according to the below equation; o(t) = o(0) exp τ Where o(t) is the time dependent stress and o(0) is the stress at time = 0, t is the time elapsed and t is a time-independent decay constant characteristic of the material. Calculate the relaxation modulus after 15 seconds, if the initial stress level, o(0), was 3.6 MPa, and was found to reduce to 2.1 MPa after a period of 60 seconds. [8 Marks] (iii) For a continuous and orientated fiber-reinforced composite, the moduli of elasticity in the longitudinal and transverse directions are 17.6 and 4.05 GPa respectively. If the volume fraction of the fibers is 0.25, calculate the moduli of elasticity of the fiber (EF) and matrix (Em) phases, where EF > EM- 10
1. For the linear polymers polyethylene, polypropylene, and poly(vinyl chloride), the repeat (mer) units can be drawn. These structures contribute to the differences in their melting temperatures.
a. The repeat (mer) units for the linear polymers are as follows:
- Polyethylene: (-CH2-CH2-)n
- Polypropylene: (-CH2-CH(CH3)-)n
- Poly(vinyl chloride): (-CH2-CHCl-)n
b. The differences in melting temperatures between these polymers can be attributed to the structure of their repeat units. The presence of different functional groups and side chains in the repeat units leads to variations in intermolecular forces, molecular weight, and chain packing. These factors influence the strength of the attractive forces between polymer chains and, consequently, the energy required to break these forces during melting. ii. The relaxation modulus (Er) after 15 seconds can be calculated using the given equation and initial stress values.
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A quasi-equilibrium process can only occur if the process occurs infinitely slowly. Give this fact, explain why the concept is still useful.
The quasi-equilibrium process is an imaginary process in which the system undergoes a continuous sequence of nearly reversible changes that occur extremely slowly. In other words, it is a thermodynamic process in which a system changes in an extremely slow and incremental manner, with each infinitesimal change being infinitesimally different from the equilibrium state.
The concept of quasi-equilibrium process is still useful despite the fact that it occurs infinitely slowly.
Significance in Thermodynamics:
Quasi-equilibrium processes play a significant role in thermodynamics. Thermodynamics is concerned with the state of the system at equilibrium and the changes it undergoes. The quasi-equilibrium process provides a means of studying the system's behavior during the changes it undergoes in a controlled manner. This enables scientists to understand the system's behavior better.
Significance in Engineering:
The quasi-equilibrium process is also important in engineering. In various engineering processes, it is important to achieve maximum efficiency with minimum waste. By using quasi-equilibrium processes, engineers can simulate the process and observe how the system behaves in various conditions. This enables them to optimize the process to achieve maximum efficiency and minimum waste.
Significance in Natural Processes:
The quasi-equilibrium process is useful in understanding various natural processes. Many natural processes occur at a nearly reversible rate, and studying them can provide scientists with insights into how various natural systems behave. For instance, the process of heat transfer through a solid body is nearly reversible, and by studying it, scientists can gain insights into how the process occurs. The concept of quasi-equilibrium process is thus still useful despite its extremely slow rate of occurrence, as it has many applications in thermodynamics, engineering, and natural processes.
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Perform the following binary arithmetic operation (i) 1011111.110102+101001.1010112 1011.1102 x 111.0112 (ii) 111001.112-1011.1012 (iv) 10100110.102 by 1002
Binary arithmetic operations involve addition, subtraction, multiplication and division of numbers that are in binary format. A binary system consists of only two digits, which are 0 and 1. In contrast to the decimal number system, which has 10 digits ranging from 0 to 9
Performing the binary arithmetic operations(i) 1011111.110102+101001.1010112 is given below:
1011111.11010₂
+ 101001.101011₂
--------------------
1101001.011111₂
Performing the binary arithmetic operations 1011.1102 x 111.0112 is given below:
1011.1102
x 111.0112
-------------------
1110.000110
+1011.11000
+ 1011.1100
-------------------
10000001.00011101₂
Performing the binary arithmetic operations (ii) 111001.112-1011.1012 is given below:
111001.11₂
- 1011.101₂
------------------
110010.001₂
Performing the binary arithmetic operations (iv) 10100110.102 by 1002 is given below:
10100110.102 x 1002
-----------
10100110100.00
-----------. Binary arithmetic is quite similar to decimal arithmetic, but with binary digits.For performing the binary addition, we consider the same process as in decimal arithmetic. The sum of two binary numbers is obtained by performing the addition of the two numbers, beginning with the least significant bits.
The product of two binary numbers is obtained by performing the binary multiplication process, similar to decimal arithmetic. The binary multiplication process consists of multiplication and shifting operations on binary numbers. It is relatively simple to carry out multiplication and division in binary arithmetic. Subtraction in binary arithmetic is quite similar to decimal arithmetic.
Two binary numbers are subtracted from each other in the same way as two decimal numbers. The subtraction is performed column-wise, beginning from the least significant bit and moving to the most significant bit. In binary arithmetic, the numbers are first taken in two's complement form and then subtracted from each other.
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A 0.5-m-long thin vertical plate at 55℃ is subjected to uniform heat flux on one side, while the other side is exposed to cool air at 5℃ Determine the heat transfer due to natural convection
The heat transfer due to natural convection from the thin vertical plate is approximately 367.95 Watts.
What is the heat transfer due to natural convection?To determine the heat transfer due to natural convection from a thin vertical plate, we can use the Nusselt number correlation for vertical plates. The heat transfer rate can be calculated using the following formula:
Q = h * A * (T_hot - T_cold)
Where:
- Q is the heat transfer rate
- h is the convective heat transfer coefficient
- A is the surface area of the plate
- T_hot is the temperature of the hot side
- T_cold is the temperature of the cold side
To calculate the convective heat transfer coefficient (h), we can use the Nusselt number correlation for natural convection on vertical plates:
[tex]Nu = 0.59 * Ra^\frac{1}{4}[/tex]
Where:
- Nu is the Nusselt number
- Ra is the Rayleigh number
The Rayleigh number (Ra) is defined as:
Ra = (g * β * L³ * ΔT) / (ν * α)
Where:
- g is the acceleration due to gravity (approximately 9.81 m/s²)
- β is the thermal expansion coefficient of air (approximately 1/273 K)
- L is the characteristic length (in this case, the height of the plate, 0.5 m)
- ΔT is the temperature difference between the hot and cold sides (55°C - 5°C)
- ν is the kinematic viscosity of air (approximately 1.5 * 10⁻⁵ m²/s)
- α is the thermal diffusivity of air (approximately 2.2 * 10⁻⁵ m²/s)
Let's calculate the heat transfer rate step by step:
1. Calculate the Rayleigh number (Ra):
ΔT = (55°C - 5°C) = 50 K
Ra = (9.81 m/s² * (1/273 K) * (0.5 m)³ * 50 K) / ((1.5 * 10⁻⁵ m²/s) * (2.2 * 10⁻⁵ m²/s)) ≈ 5.49 * 10^9
2. Calculate the Nusselt number (Nu):
[tex]Nu = 0.59 * (5.49 * 10^9)^\frac{1}{4} = 69.89[/tex]
3. Calculate the convective heat transfer coefficient (h):
h = Nu * (k / L)
Where k is the thermal conductivity of air, approximately 0.0257 W/(m·K).
h = 69.89 * (0.0257 W/(m·K) / 0.5 m) = 3.49 W/(m^2·K)
4. Calculate the surface area (A) of the plate:
A = L * W
Assuming the width (W) of the plate is 1 m:
A = 0.5 m * 1 m = 0.5 m²
5. Calculate the heat transfer rate (Q):
Q = h * A * (T_hot - T_cold)
= 3.49 W/(m²·K) * 0.5 m² * (55°C - 5°C)
≈ 367.95 W
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If the pneumatic pressure is set to 10 KPascal, the force that can be obtained using a 10 cm diameter cylinder will be ................ KN.
To calculate the force that can be obtained using a pneumatic cylinder with a given pressure and diameter, we can use the formula:
Force = Pressure × Area
The area of a cylinder can be calculated using the formula:
Area = π × (Radius)^2
Given that the diameter of the cylinder is 10 cm, we can calculate the radius as half of the diameter, which is 5 cm or 0.05 meters.
Plugging the values into the formulas, we can calculate the force:
Area = π × (0.05)^2
Force = 10 kPa × π × (0.05)^2
By performing the calculation, we can determine the force in kilonewtons (kN) that can be obtained using the 10 cm diameter cylinder at a pneumatic pressure of 10 kPa.
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Next, which equation should you use to solve for deflection? A El d⁴y/dx⁴ = w (x)
B d³y/dx³ = V(x) C El d²y/dx⁴ = M(x)
D None of the above.
The equation that should be used to solve for deflection is El d⁴y/dx⁴ = w (x).
The deflection can be defined as the change in a structural member's shape, size, and position due to external loading (loads) applied to it. The deflection of a member can also be defined as the degree to which it yields under load.
The flexural theory can be used to analyze the deflection of beams.
According to the flexural theory, the deflection of a beam can be calculated using the following formula:
El d⁴y/dx⁴ = w (x)
Where y is the deflection, El is the modulus of elasticity of the beam, and w(x) is the load per unit length acting on the beam. Therefore, option A is correct which is:
El d⁴y/dx⁴ = w (x)
Next, the solution of this differential equation gives us the deflection of the beam.
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Q7. Determine the best motor selection for the following applications and explain the reasoning: a) Electric drill b) Electric clock c) Refrigerator d) Vacuum cleaner e) Air conditioner fan f) Air conditioner compressor g) Electric sewing machine h) Electric shaver i) Electric toothbrush
a) Electric drill: Universal motor.
b) Electric clock: Synchronous motor.
c) Refrigerator: Hermetic induction motor.
d) Vacuum cleaner: Brushless DC (BLDC) motor or AC induction motor.
e) Air conditioner fan: Permanent magnet synchronous motor (PMSM) or high-efficiency AC induction motor.
f) Air conditioner compressor: Scroll compressor driven by a three-phase induction motor.
g) Electric sewing machine: Servo motor.
h) Electric shaver: Small DC motor (brushed or brushless).
i) Electric toothbrush: Compact and efficient DC motor (brushed or brushless).
a) Electric drill: A suitable motor for an electric drill would be a universal motor. Universal motors are commonly used in power tools like drills due to their high speed and high torque capabilities, making them suitable for applications that require rapid drilling and cutting.
b) Electric clock: For an electric clock, a synchronous motor would be a suitable choice. Synchronous motors are known for their precise speed control and low power consumption, making them ideal for accurate timekeeping in clocks.
c) Refrigerator: A refrigerator typically requires a compressor motor to circulate refrigerant and maintain the desired temperature. The most common type of motor used in refrigerators is a hermetic induction motor, which provides reliable and efficient operation.
d) Vacuum cleaner: A vacuum cleaner requires a motor with strong suction power and airflow. A suitable choice would be a high-performance brushless DC (BLDC) motor or a powerful AC induction motor, both of which can provide the necessary suction and airflow for effective cleaning.
e) Air conditioner fan: An air conditioner fan requires a motor with good efficiency and airflow. A suitable choice would be a permanent magnet synchronous motor (PMSM) or a high-efficiency AC induction motor, as they can provide the required airflow while minimizing energy consumption.
f) Air conditioner compressor: The compressor in an air conditioner requires a motor with high power and efficiency. A common choice is a scroll compressor driven by a three-phase induction motor, as it can deliver the necessary compression power while maintaining energy efficiency.
g) Electric sewing machine: Electric sewing machines typically use a small and compact motor known as a servo motor. Servo motors offer precise speed control, quiet operation, and high torque, making them well-suited for sewing applications.
h) Electric shaver: Electric shavers often use a small DC motor with high rotational speed and vibration control. A suitable choice would be a small and lightweight DC motor, such as a brushed or brushless DC motor, to provide the necessary shaving performance.
i) Electric toothbrush: Electric toothbrushes commonly utilize small DC motors with oscillating or vibrating motions. A suitable motor choice would be a compact and efficient DC motor, such as a brushed or brushless DC motor, to deliver the required brushing action for oral care.
The selection of the best motor for each application depends on factors such as power requirements, speed control, efficiency, size, and specific performance needs.
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During winter time, the central heating system in my flat isn't really enough to keep me warm so luse two extra oil heaters. My landlord is hasn't got around to installing carbon monoxide alarms in my flat yet and the oil heaters start to produce 1g/hr CO each. My flat floor area is 40 m' with a ceiling height 3m. a. If I leave all my windows shut how long will it take to reach an unsafe concentration?
b. The concentration gets to around 20,000 micrograms/m3 and I start to feel a little dizzy so I decide to turn on my ventilation (which provides 0.5 air changes per hour). What steady state concentration will it eventually get to in my flat? c. I'm still not feeling very good, so I switch off the heaters and leave the ventilation running... how long before safe concentration levels are reached? d. In up to 10 sentences, describe the assumptions and limitations of your modelling in this question and 7/how it could be improved
During winter time, the central heating system in my flat isn't enough to keep me warm, so I use two additional oil heaters. My landlord hasn't installed carbon monoxide alarms in my flat yet, and the oil heaters begin to produce 1g/hr CO each.
My flat floor area is 40 m' with a ceiling height of 3m.(a) How long will it take to reach an unsafe concentration if I leave all my windows shut?
Carbon monoxide has a molecular weight of 28 g/mol, which implies that one mole of CO weighs 28 grams. One mole of CO has a volume of 24.45 L at normal room temperature and pressure (NTP), which implies that 1 gram of CO occupies 0.87 L at NTP. Using the ideal gas law, PV=nRT, we can calculate the volume of the gas produced by 1 g of CO at a given temperature and pressure. We'll make a few assumptions to make things simple. The total volume of the flat is 40*3=120m³.
The ideal gas law applies to each gas molecule individually, regardless of its interactions with other gas molecules. If the concentration of CO is low (below 50-100 ppm), this is a fair approximation. The production of CO from the oil heaters is constant, and we can disregard the depletion of oxygen due to combustion because the amount of CO produced is minimal compared to the amount of oxygen present.
Using the above assumptions, the number of moles of CO produced per hour is 1000/28 = 35.7 mol/hr.
The number of moles per hour is equal to the concentration times the volume flow rate, as we know from basic chemistry. If we assume a well-insulated room, the air does not exchange with the outside. In this situation, the volume flow rate is equal to the volume of the room divided by the air change rate, which in this case is 0.5/hr.
We get the following concentration in this case: concentration = number of moles per hour / volume flow rate = 35.7 mol/hr / (120 m³/0.5/hr) = 0.3 mol/m³ = 300 mol/km³. The safe limit is 50 ppm, which corresponds to 91.25 mol/km³. The maximum concentration that is not dangerous is 91.25 mol/km³. If the concentration of CO in the flat exceeds this limit, you must leave the flat.
If all windows are closed, the room's air change rate is 0.5/hr, and 1g/hr of CO is generated by the oil heaters, the room's concentration will be 300 mol/km³, which is three times the maximum safe limit. Therefore, the flat should be evacuated as soon as possible.
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