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A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is not to exceed 60 MN/m? and internal diameter is 0.6 of the external diameter, find the external and internal diameters of the shaft.?
Verified Answer
A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is...
The power transmitted by a shaft can be expressed as:
P = 2 * pi * T * n / (9.55 * d)
where P is the power transmitted in kW, T is the shear stress in MN/m^2, n is the speed in rpm, and d is the diameter of the shaft in mm.
Since the shear stress is not to exceed 60 MN/m^2, we can set T = 60 MN/m^2. The speed is 80 rpm, and the power transmitted is 300 kW. We can use the above equation to solve for the diameter d:
300 kW = 2 * pi * 60 MN/m^2 * 80 rpm / (9.55 * d)
d = 300 kW * 9.55 / (2 * pi * 60 MN/m^2 * 80 rpm)
= 300 kW * 9.55 / (2 * 3.14 * 60 MN/m^2 * 80 rpm)
= 0.1591 m
= 159.1 mm
The external diameter of the shaft is 159.1 mm.
Since the internal diameter is 0.6 of the external diameter, the internal diameter of the shaft is 0.6 * 159.1 mm = 95.46 mm.
This question is part of UPSC exam. View all SSC courses
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A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is...
Problem Overview
To determine the external and internal diameters of a hollow shaft that transmits 300 kW at 80 rpm, we need to consider the shear stress limitation and the relationship between internal and external diameters.
Given Data
- Power (P) = 300 kW = 300 × 10^3 W
- Speed (N) = 80 rpm
- Maximum Shear Stress (τ) = 60 MN/m² = 60 × 10^6 N/m²
- Internal Diameter (d) = 0.6 × External Diameter (D)
Calculating Torque
Torque (T) can be calculated using the formula:
T = (P × 60) / (2 × π × N)
Substituting values:
T = (300 × 10^3 × 60) / (2 × π × 80)
Calculate T to find torque in N·m.
Shear Stress Formula
The shear stress in a hollow shaft is given by:
τ = (T × r) / J
Where:
- J = (π/32) × (D^4 - d^4)
- r = D/2 (external radius)
Substituting d = 0.6D into the equation for J, we can express everything in terms of D.
Solving the Equations
1. Calculate Torque (T) from the power and speed.
2. Substitute T into the shear stress equation.
3. Rearrange to solve for D.
4. Once D is found, calculate d using the relationship d = 0.6D.
Final Dimensions
1. Compute the value of D and subsequently d.
2. Verify the calculations to ensure the shear stress does not exceed the limit.
This approach provides a systematic way to find the external and internal diameters of the hollow shaft while adhering to the given constraints.
To determine the external and internal diameters of a hollow shaft that transmits 300 kW at 80 rpm, we need to consider the shear stress limitation and the relationship between internal and external diameters.
Given Data
- Power (P) = 300 kW = 300 × 10^3 W
- Speed (N) = 80 rpm
- Maximum Shear Stress (τ) = 60 MN/m² = 60 × 10^6 N/m²
- Internal Diameter (d) = 0.6 × External Diameter (D)
Calculating Torque
Torque (T) can be calculated using the formula:
T = (P × 60) / (2 × π × N)
Substituting values:
T = (300 × 10^3 × 60) / (2 × π × 80)
Calculate T to find torque in N·m.
Shear Stress Formula
The shear stress in a hollow shaft is given by:
τ = (T × r) / J
Where:
- J = (π/32) × (D^4 - d^4)
- r = D/2 (external radius)
Substituting d = 0.6D into the equation for J, we can express everything in terms of D.
Solving the Equations
1. Calculate Torque (T) from the power and speed.
2. Substitute T into the shear stress equation.
3. Rearrange to solve for D.
4. Once D is found, calculate d using the relationship d = 0.6D.
Final Dimensions
1. Compute the value of D and subsequently d.
2. Verify the calculations to ensure the shear stress does not exceed the limit.
This approach provides a systematic way to find the external and internal diameters of the hollow shaft while adhering to the given constraints.
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A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is not to exceed 60 MN/m? and internal diameter is 0.6 of the external diameter, find the external and internal diameters of the shaft.?
Question Description
A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is not to exceed 60 MN/m? and internal diameter is 0.6 of the external diameter, find the external and internal diameters of the shaft.? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is not to exceed 60 MN/m? and internal diameter is 0.6 of the external diameter, find the external and internal diameters of the shaft.? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is not to exceed 60 MN/m? and internal diameter is 0.6 of the external diameter, find the external and internal diameters of the shaft.?.
A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is not to exceed 60 MN/m? and internal diameter is 0.6 of the external diameter, find the external and internal diameters of the shaft.? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is not to exceed 60 MN/m? and internal diameter is 0.6 of the external diameter, find the external and internal diameters of the shaft.? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow shaft is to transmit 300 kW at 80 rpm. If the shear stress is not to exceed 60 MN/m? and internal diameter is 0.6 of the external diameter, find the external and internal diameters of the shaft.?.
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