The Maximum Surface Temperature Of The 20-mm-diameter Shaft Of A Motor Operating In Ambient Air At 27C (2024)

Engineering College

Answers

Answer 1

The maximum heat rate per unit length and the convection coefficient as a function of rotational speed is 2.83 kW/m

The effects of mixed convection may become significant.

The exchange of radiation can have a significant impact on heat transfer from the shaft to the surroundings.

How to calculate convection coefficient and the maximum heat?

(a) For rotating cylinders, the correlation for estimating the convection coefficient is given by:

Nap = 0.133 Rep^0.6 Pr^0.4

where Rep = OD' and Pr is the Prandtl number. For air at 27°C, Pr = 0.71 and OD = 20 mm.

The rotational speed in the range from 5000 to 15000 rpm corresponds to angular velocities of 524 to 1571 rad/s.

At 5000 rpm, Rep = 0.02 x 1571 x 0.02 = 0.6284

At 15000 rpm, Rep = 0.02 x 524 x 0.02 = 0.2096

Using the correlation, we can calculate the convection coefficient for the given range of rotational speeds:

At 5000 rpm, Nap = 0.133 x (0.6284)^0.6 x (0.71)^0.4 = 10.9 W/(m²K)

At 15000 rpm, Nap = 0.133 x (0.2096)^0.6 x (0.71)^0.4 = 47.2 W/(m²K)

The maximum heat rate per unit length can be calculated using the following formula:

qmax = hmax × (Ts - Tinf)

where Ts is the maximum surface temperature (87°C), Tinf is the ambient air temperature (27°C), and hmax is the maximum convection coefficient obtained at the highest rotational speed (15000 rpm).

At 15000 rpm, qmax = 47.2 x (87 - 27) = 2.83 kW/m

(b) For a stationary shaft, the free convection correlation for a horizontal cylinder is:

Nuf = 0.60 + 0.387 (Gr Pr / (1 + (0.559 / Pr)^(9/16))^ (16/27))

where Gr = g beta (Ts - Tinf) D³ / nu², beta is the thermal expansion coefficient, nu is the kinematic viscosity, and g is the gravitational acceleration.

For air at 27°C, beta = 3.41e-3 K⁻¹, nu = 1.49e-5 m²/s, and D = 20 mm.

The Grashof number can be calculated using the maximum surface temperature:

Gr = 9.81 x 3.41e⁻³ x (87 - 27) x (0.02)³ / (1.49e-5)²= 1.71e+11

The Prandtl number is the same as before (0.71).

Using the correlation, we can calculate the free convection coefficient:

Nuf = 0.60 + 0.387 (1.71e+11 * 0.71 / (1 + (0.559 / 0.71)^(9/16))^ (16/27)) = 16.5 W/(m^2*K)

The maximum heat rate per unit length can be calculated using the same formula as before:

qmax = hmax × (Ts - Tinf)

where hmax is the free convection coefficient obtained above.

At stationary conditions, qmax = 16.5 x (87 - 27) = 1.65 kW/m

Mixed free and forced convection effects may become significant for Rep < 4.7(Gr/Pr). For the given range of rotational speeds, Rep < 4.7(Gr/Pr) holds true. Therefore, mixed convection effects may become significant.

(c) Radiation exchange is important since the emissivity of the shaft is given as 0.8, radiation exchange is important. The net radiation heat transfer rate between the shaft and the surroundings is given by the Stefan-Boltzmann law:

qrad = ε σ (Ts^4 - Tinf^4) A

where ε is the emissivity, σ is the Stefan-Boltzmann constant, Ts is the surface temperature of the shaft, Tinf is the ambient air temperature, and A is the surface area of the shaft.

Assuming a length of 1 m for the shaft, the surface area is:

A = π D L = π (0.02) (1) = 0.0628 m^2

Using the given values, we can calculate the radiation heat transfer rate:

qrad = 0.8 x 5.67e⁻⁸ x (87⁴ - 27⁴) x 0.0628 = 455 W/m

Therefore, radiation exchange can have a significant impact on the heat transfer from the shaft to the surroundings.

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Answer 2

The maximum heat rate per unit length and the convection coefficient as a function of rotational speed is 2.83 kW/m

The effects of mixed convection may become significant.

The exchange of radiation can have a significant impact on heat transfer from the shaft to the surroundings.

How to calculate convection coefficient and the maximum heat?

(a) For rotating cylinders, the correlation for estimating the convection coefficient is given by:

Nap = 0.133 Rep^0.6 Pr^0.4

where Rep = OD' and Pr is the Prandtl number. For air at 27°C, Pr = 0.71 and OD = 20 mm.

The rotational speed in the range from 5000 to 15000 rpm corresponds to angular velocities of 524 to 1571 rad/s.

At 5000 rpm, Rep = 0.02 x 1571 x 0.02 = 0.6284

At 15000 rpm, Rep = 0.02 x 524 x 0.02 = 0.2096

Using the correlation, we can calculate the convection coefficient for the given range of rotational speeds:

At 5000 rpm, Nap = 0.133 x (0.6284)^0.6 x (0.71)^0.4 = 10.9 W/(m²K)

At 15000 rpm, Nap = 0.133 x (0.2096)^0.6 x (0.71)^0.4 = 47.2 W/(m²K)

The maximum heat rate per unit length can be calculated using the following formula:

qmax = hmax × (Ts - Tinf)

where Ts is the maximum surface temperature (87°C), Tinf is the ambient air temperature (27°C), and hmax is the maximum convection coefficient obtained at the highest rotational speed (15000 rpm).

At 15000 rpm, qmax = 47.2 x (87 - 27) = 2.83 kW/m

(b) For a stationary shaft, the free convection correlation for a horizontal cylinder is:

Nuf = 0.60 + 0.387 (Gr Pr / (1 + (0.559 / Pr)^(9/16))^ (16/27))

where Gr = g beta (Ts - Tinf) D³ / nu², beta is the thermal expansion coefficient, nu is the kinematic viscosity, and g is the gravitational acceleration.

For air at 27°C, beta = 3.41e-3 K⁻¹, nu = 1.49e-5 m²/s, and D = 20 mm.

The Grashof number can be calculated using the maximum surface temperature:

Gr = 9.81 x 3.41e⁻³ x (87 - 27) x (0.02)³ / (1.49e-5)²= 1.71e+11

The Prandtl number is the same as before (0.71).

Using the correlation, we can calculate the free convection coefficient:

Nuf = 0.60 + 0.387 (1.71e+11 * 0.71 / (1 + (0.559 / 0.71)^(9/16))^ (16/27)) = 16.5 W/(m^2*K)

The maximum heat rate per unit length can be calculated using the same formula as before:

qmax = hmax × (Ts - Tinf)

where hmax is the free convection coefficient obtained above.

At stationary conditions, qmax = 16.5 x (87 - 27) = 1.65 kW/m

Mixed free and forced convection effects may become significant for Rep < 4.7(Gr/Pr). For the given range of rotational speeds, Rep < 4.7(Gr/Pr) holds true. Therefore, mixed convection effects may become significant.

(c) Radiation exchange is important since the emissivity of the shaft is given as 0.8, radiation exchange is important. The net radiation heat transfer rate between the shaft and the surroundings is given by the Stefan-Boltzmann law:

qrad = ε σ (Ts^4 - Tinf^4) A

where ε is the emissivity, σ is the Stefan-Boltzmann constant, Ts is the surface temperature of the shaft, Tinf is the ambient air temperature, and A is the surface area of the shaft.

Assuming a length of 1 m for the shaft, the surface area is:

A = π D L = π (0.02) (1) = 0.0628 m^2

Using the given values, we can calculate the radiation heat transfer rate:

qrad = 0.8 x 5.67e⁻⁸ x (87⁴ - 27⁴) x 0.0628 = 455 W/m

Therefore, radiation exchange can have a significant impact on the heat transfer from the shaft to the surroundings.

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To design a noninverting summer for five inputs with equal gains of 10, we can use an operational amplifier (op-amp) circuit. The noninverting summer circuit is a type of op-amp circuit that allows us to add multiple input signals together without affecting their original amplitude.

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The magnitude of the resultant force the elbow exerts on the pipe is 188 N when water is discharged through the 40-mm-diameter elbow at 0.012 m3/s.

To determine the magnitude of the resultant force the elbow exerts on the pipe, we will use the following information:
1. Water is discharged through the 40-mm-diameter elbow at a rate of 0.012 m³/s.
2. The pressure at point A is 120 kPa.
First, we'll calculate the velocity of the water. The cross-sectional area of the pipe can be determined using the formula for the area of a circle:
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Now, we can calculate the velocity (v) using the flow rate (Q) and area (A):
Next, we'll calculate the force due to pressure ([tex]F_p[/tex]):
[tex]F_p = P * A = 120,000 Pa * 0.0012566 m^2 = 150.79 N[/tex]
Finally, we can calculate the force due to water discharge ([tex]F_d[/tex]):
[tex]F_d[/tex] = ρ * Q * v
where ρ is the density of water (approximately 1000 kg/m³). Plugging in the values, we get:
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The concept you are referring to is called abstraction.

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Answer 5: I cannot directly observe the results of your ping test, but if you received a reply, then the ping was successful.

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The answer is option d. 6 views. The Glass Box Theory suggests that there are 6 views of an object.

The Glass Box Theory is a software testing technique that involves testing a system by examining its internal workings. It states that there are six different possible views of an object that can be tested, including the input, output, internal workings, error handling, performance, and security. The Glass Box Theory demonstrates that there are 6 possible views for any given object, providing a comprehensive understanding of its shape and dimensions.

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The alternator producing 25 amps at 14 volts and with an efficiency of 74% will take away approximately 0.35 horsepower from the propeller.

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350 watts x 0.74 = 259 watts

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Consider the following class definitions.
public class Thing1
{
public void calc(int n)
{
n *= 3;
System.out.print(n);
}
}
public class Thing2 extends Thing1
{
public void calc(int n)
{
n += 2;
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System.out.print(n);
}
}
The following code segment appears in a class other than Thing1 or Thing2.
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MongoDB is a document-oriented NoSQL database that stores data in a flexible, JSON-like format called BSON. A database in MongoDB is a container for collections, which are groups of documents. In this case, the "business1000" is a database that contains a "businesses" collection.
The find() method is used to retrieve all the documents from a collection that match a given query. The sort() method is used to sort the result set in ascending or descending order based on a specified field. In this case, the sort() method is sorting the documents in the "businesses" collection in descending order based on the "review_count" field.
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The answer to the apply damage function triggers any damaging event is True.

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Answers

The result will give you the electric field everywhere, both inside and outside the spherical void, considering the presence of the hom*ogeneous material with dielectric constant ε.

To solve for the electric field everywhere due to a point dipole p at the center of a spherical void of radius R in a hom*ogeneous material with dielectric constant ε, you can follow these steps:
1. First, calculate the electric field E due to the point dipole p in free space using the formula:
E = (1/(4πε₀)) x (3(p⋅r)r - p) / |r|³
where ε₀ is the vacuum permittivity, r is the position vector from the dipole, and |r| is the magnitude of r.
2. Next, use the method of image charges to account for the presence of the spherical void in the hom*ogeneous material. This involves finding an equivalent set of dipoles, called image dipoles, outside the spherical void that produce the same electric field on the boundary of the void as the original dipole.
3. To find the image dipoles, consider that the dielectric constant of the material affects the boundary conditions for the electric field on the surface of the spherical void. These boundary conditions help determine the locations and magnitudes of the image dipoles.
4. Once the image dipoles are found, calculate the total electric field by summing up the contributions from the original dipole and the image dipoles.

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Hi! To find the input-output relationship for the given RC op-amp circuit, please follow these steps:

1. Identify the input and output points: In an RC op-amp circuit, the input is typically a voltage signal applied to the non-inverting (+) or inverting (-) terminal of the operational amplifier (op-amp). The output is the voltage signal across the output terminal of the op-amp.

2. Analyze the circuit components: Identify the resistors (R) and capacitors (C) connected to the op-amp, and take note of their values.

3. Determine the type of op-amp circuit: Based on the configuration of the resistors and capacitors, identify whether the circuit is an inverting or non-inverting amplifier, integrator, differentiator, or another type of op-amp circuit.

4. Write down the input-output relationship equation: Depending on the identified type of op-amp circuit, write the input-output relationship equation. This equation will show the relationship between the input voltage (Vin) and the output voltage (Vout).

For example, if the circuit is an inverting amplifier, the input-output relationship is:

Vout = - (R2 / R1) * Vin

Where R1 is the input resistor and R2 is the feedback resistor.

For an integrator, the input-output relationship is:

Vout = - (1 / R1 * C1) * ∫Vin dt

Where R1 is the input resistor, C1 is the feedback capacitor, and ∫Vin dt represents the integral of the input voltage with respect to time.

Once you have identified the type of op-amp circuit and written the input-output relationship equation, you will have found the input-output relationship for the given RC op-amp circuit.

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A steel wire of 2mm diameter is fixed between two points located 2 m apart. The tensile force in the wire is 250N. Determine (a) the fundamental frequency of vibration and (b) the velocity of wave propagation in the wire.

Answers

With μ, we can now calculate the fundamental frequency (f1) using the above formula. By calculating the linear mass density (μ) and using it in the above formula, we can determine the velocity of wave propagation in the steel wire.

To determine the fundamental frequency and wave propagation velocity in the steel wire, we will use the following information:

- Diameter of the wire (d) = 2mm = 0.002m
- Length of the wire (L) = 2m
- Tensile force (T) = 250N

(a) The fundamental frequency (f1) can be calculated using the formula:
f1 = (1/2L) * √(T/μ)
Where μ is the linear mass density of the wire.

To find μ, we need to determine the volume and mass of the wire. The volume (V) can be calculated using the formula:
V = π * (d/2)^2 * L

Assuming the wire is made of steel, its density (ρ) is approximately 7850 kg/m^3. The mass (m) of the wire can be calculated using the formula:
m = V * ρ

Now we can calculate the linear mass density (μ):
μ = m / L

With μ, we can now calculate the fundamental frequency (f1) using the above formula.

(b) The velocity of wave propagation (v) can be calculated using the formula:
v = √(T/μ)

By calculating the linear mass density (μ) and using it in the above formula, we can determine the velocity of wave propagation in the steel wire.

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task indructions
in cell g5 create a data validation rule to allow only whole numbers from 1 to 5 inclusive to be input in the cell.

Answers

Below is how you can create a data validation rule in cell G5 to allow only whole numbers from 1 to 5 (inclusive) to be input in the cell in Microsoft Excel:

What is the data validation rule?

The steps are:

Select cell G5 where you want to apply the data validation rule.Go to the "Data" tab in the Excel ribbon.Click on the "Data Validation" button in the "Data Tools" group to open the "Data Validation" dialog box.In the "Data Validation" dialog box, under the "Settings" tab, select "Whole Number" from the "Allow" drop-down list.Choose "between" from the "Data" drop-down list.In the "Minimum" field, enter "1".In the "Maximum" field, enter "5".Check the "Ignore blank" option if you want to allow blank cells.Optionally, you can add an input message and/or an error message in the "Input Message" and "Error Alert" tabs respectively, to provide guidance or feedback to users.Click on the "OK" button to apply the data validation rule.

Now, cell G5 will only allow whole numbers from 1 to 5 (inclusive) to be entered. If a user tries to input a value outside of this range or a non-integer value, Excel will display an error message (if configured) and prevent the input until a valid value is entered.

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Use the terms primary key field, foreign key field, one-to-many relationship, parent table and child table to describe the following WHERE clause: WHERE Clients.ClientID = Projects.ClientID

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Hi! I'd be happy to help you with your question. The WHERE clause you provided, "WHERE Clients.ClientID = Projects.ClientID", can be described using the terms primary key field, foreign key field, one-to-many relationship, parent table, and child table as follows:

In this scenario, the Clients table is the parent table, and the Projects table is the child table. The primary key field in the parent table (Clients) is ClientID, which uniquely identifies each client. The foreign key field in the child table (Projects) is also ClientID, which establishes a link between the two tables by referencing the primary key in the parent table.

The relationship between the Clients and Projects tables is a one-to-many relationship, as one client (from the Clients table) can be associated with multiple projects (in the Projects table), but each project is linked to only one client.

The WHERE clause "WHERE Clients.ClientID = Projects.ClientID" is used to retrieve records where there is a match between the primary key field in the parent table (Clients.ClientID) and the foreign key field in the child table (Projects.ClientID), effectively displaying the combined data for clients and their corresponding projects.

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A helical torsion spring has a spring index of 5. It takes 10 in-lbf of torque to twist the spring 3/4 turns. Determine the torsional spring constant of the spring. (A) 1.02 in-lbf/rad (B) 2.12 in-lbf/rad (C) 5.16 in-lbf/rad (D) 10.2 in-lbf/rad

Answers

To determine the torsional spring constant of the helical torsion spring, we can use the following formula:

Torsional Spring Constant = (torque applied / angle of twist) * (spring index / (2π))

We are given that the spring index is 5 and the torque required to twist the spring 3/4 turns is 10 in-lbf. We can convert 3/4 turns to radians by multiplying it by 2π, which gives us 4.71 radians. Plugging in the values, we get:

Torsional Spring Constant = (10 in-lbf / 4.71 rad) * (5 / (2π))
Torsional Spring Constant ≈ 2.12 in-lbf/rad

Therefore, the answer is (B) 2.12 in-lbf/rad.

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Consider the following sequence of instructions:
or r1, r2, r3
or r2, r1, r4
or r1, r1, r2
Also, assume that the pipelined processor has the following cycle time for the two options.
Cycle time without forwarding: 250 ps, andCycle time with full forwarding: 300 ps.
(a) Identify the dependency that create data hazards for the given sequence of instructions.
(b) Assume there is no forwarding in this pieplined processor. Add NOP instructions (bubbles) to eliminate data hazards.
(c) Assume there is full forwarding. Identify if there are still data hazards and if there are add NOP instructions to eliminate them.
(d) What is the total execution time of this instruction sequence without forwarding and with full forwarding? What is the speedup achieved by adding full forwarding to a pipeline that had no forwarding?

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The third instruction (or r1, r1, r2) depends on both the first and second instructions, as it needs the updated values of r1 and r2. Without forwarding, we need to add NOP instructions to eliminate data hazards: or r1, r2, r3, NOP. With full forwarding, there are no data hazards as the processor can directly forward the required values from one instruction to another. Adding full forwarding to a pipeline that had no forwarding results in a speedup of 1.67.

(a) The dependency that creates data hazards for the given sequence of instructions is:
- The second instruction (or r2, r1, r4) depends on the first instruction (or r1, r2, r3), since it needs the result from r1.
- The third instruction (or r1, r1, r2) depends on both the first and second instructions, as it needs the updated values of r1 and r2.

(b) Without forwarding, we need to add NOP instructions to eliminate data hazards:
1. or r1, r2, r3
2. NOP
3. NOP
4. or r2, r1, r4
5. NOP
6. or r1, r1, r2

(c) With full forwarding, there are no data hazards as the processor can directly forward the required values from one instruction to another.

(d) Execution time without forwarding:
- 6 instructions * 250 ps = 1500 ps

Execution time with full forwarding:
- 3 instructions * 300 ps = 900 ps

Speedup achieved by adding full forwarding:
- Execution time without forwarding / Execution time with full forwarding = 1500 ps / 900 ps = 1.67

Adding full forwarding to a pipeline that had no forwarding results in a speedup of 1.67.

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What is the complexity of maximum subarray sum?

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The complexity of finding the maximum subarray sum is O(n), where n is the size of the input array.

The maximum subarray problem is the task of finding the contiguous subarray within a one-dimensional array of numbers that has the largest sum. One efficient algorithm to solve this problem is the Kadane's algorithm which has a time complexity of O(n), where n is the size of the input array. The algorithm scans the input array and maintains two variables, one to keep track of the maximum subarray sum seen so far, and another to keep track of the current subarray sum. It updates these variables as it scans the array and returns the maximum subarray sum. The algorithm is efficient because it only needs to scan the array once.

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method setlayout is used to specify the layout to specify the layout manager for a container.___________________

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The method setLayout is a built-in method in Java Swing that allows you to set the layout manager for a container.

This method takes a LayoutManager object as an argument, which specifies how the components within the container should be arranged. The layout manager can be set to a variety of different options, such as BorderLayout, GridLayout, or FlowLayout, depending on the desired layout for the container.

Built-in methods are typically part of the core functionality of a programming language or library and are always available for use without the need for additional code or libraries to be installed. These methods are often optimized for performance and reliability, and are designed to work seamlessly with other built-in methods and language features.

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Aluminum Filter is used to remove what items from the beam?

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Grease and other contaminants are eliminated from the air in commercial kitchen ventilation systems using aluminium filters.

Commercial kitchen ventilation systems frequently employ aluminium filters to filter out grease and other airborne contaminants. The aluminium filters, which are used to stop grease and other particles from entering the ductwork or being circulated back into the kitchen, are used to filter the air as it is drawn through the system. This lowers the risk of a fire occurring in the kitchen, keeps it clean, and makes sure the ventilation system is working properly. To guarantee optimum performance, the filters can be readily taken out and cleaned or changed as necessary.

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briefly explain why, upon solidification, an alloy of eutectic composition forms a microstructure consisting of alternating layers of the two solid phases.

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Hi! Upon solidification, an alloy of eutectic composition forms a microstructure consisting of alternating layers of the two solid phases because:

1. The eutectic composition represents a specific proportion of the two elements in the alloy, at which the lowest melting point is achieved.
2. As the alloy cools down to the eutectic temperature, both elements begin to solidify simultaneously, leading to the formation of two distinct solid phases.
3. These solid phases grow together in a cooperative manner, creating a layered structure with alternating layers.
4. The layered microstructure occurs as a result of minimizing the energy and maximizing the stability of the two solid phases, allowing for efficient heat and mass transport during the solidification process.

In summary, the eutectic composition of an alloy results in the formation of alternating layers of two solid phases upon solidification, due to the cooperative growth of both elements and the need for minimized energy and enhanced stability.

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you need not replace bearings on high-speed equipment unless wear has increased the shaft clearance to _________ times the original clearance.

Answers

You need not replace bearings on high-speed equipment unless wear has increased the shaft clearance to three times the original clearance.

Bearings are mechanical components that support and reduce friction between moving parts in a machine. In high-speed equipment, bearings are subjected to a lot of stress and wear, and they may need to be replaced periodically to ensure optimal performance and prevent mechanical failures.

Shaft clearance refers to the space between the rotating shaft and the stationary bearing. As bearings wear down over time, this clearance increases, which can cause the machine to vibrate, operate less efficiently, and even fail if left unchecked.

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Which of the following statements about operator overloading in C++ classes are incorrect? a. You cannot change the outcome/result of a parameter when overloaded. b. If'<<' is overloaded, then'>>'must also be overloaded at the saem time. c. Methods for overloading binary operators like 't'or-'must always specify two parameters. d. All existing parameters can be overloaded in C++ classes. e. New parameters like or '%' can be defined.

Answers

I'll address each statement about operator overloading in C++ classes and identify which are incorrect:

a. You cannot change the outcome/result of a parameter when overloaded. - Incorrect. Operator overloading allows you to redefine the behavior of an operator for custom types, which means you can change the outcome/result of the operation.

b. If '<<' is overloaded, then '>>' must also be overloaded at the same time. - Incorrect. While it's common to overload both '<<' and '>>' for consistency, it's not mandatory to overload them at the same time.

c. Methods for overloading binary operators like '+' or '-' must always specify two parameters. - Correct. Binary operators require two operands, so the overloading function must specify two parameters, one for the left-hand side operand and one for the right-hand side operand.

d. All existing operators can be overloaded in C++ classes. - Incorrect. Some operators, like scope resolution (::), member selection (.), and member selection through a pointer to function (.*), cannot be overloaded.

e. New operators like '|' or '%' can be defined. - Incorrect. While you can overload existing operators for custom behavior, you cannot create entirely new operators in C++.

So, the incorrect statements are: a, b, d, and e.

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The Maximum Surface Temperature Of The 20-mm-diameter Shaft Of A Motor Operating In Ambient Air At 27C (2024)
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