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A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60
𝑁/𝑚𝑚2
and the internal diameter is 0.6 of the external diameter, find the external
and internal diameters, assuming the maximum torque is 1.4 times the mean torque.?
𝑁/𝑚𝑚2
and the internal diameter is 0.6 of the external diameter, find the external
and internal diameters, assuming the maximum torque is 1.4 times the mean torque.?
Most Upvoted Answer
A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is ...
Given Data:
- Power transmitted, P = 30 kW
- Speed, N = 80 rpm
- Maximum shear stress, τ_max = 60 N/mm^2
- Internal diameter, Di = 0.6 * Do
- Maximum torque, Tmax = 1.4 * mean torque
Solution:
Step 1: Calculate Torque (T)
Given power, P = 30 kW
Speed, N = 80 rpm
We know, P = 2πNT/60
30,000 = (2 * 3.14 * 80 * T) / 60
T = 178.86 Nm
Mean torque, Tmean = T / 2 = 89.43 Nm
Maximum torque, Tmax = 1.4 * 89.43 = 125.21 Nm
Step 2: Calculate External Diameter (Do)
Tmax = (π/16) * τ_max * (Do^4 - Di^4)
125.21 = (π/16) * 60 * (Do^4 - (0.6 * Do)^4)
Solving this equation gives Do ≈ 56.6 mm
Step 3: Calculate Internal Diameter (Di)
Given Di = 0.6 * Do
Di = 0.6 * 56.6 = 33.96 mm
Therefore, the external diameter is approximately 56.6 mm and the internal diameter is approximately 33.96 mm.
- Power transmitted, P = 30 kW
- Speed, N = 80 rpm
- Maximum shear stress, τ_max = 60 N/mm^2
- Internal diameter, Di = 0.6 * Do
- Maximum torque, Tmax = 1.4 * mean torque
Solution:
Step 1: Calculate Torque (T)
Given power, P = 30 kW
Speed, N = 80 rpm
We know, P = 2πNT/60
30,000 = (2 * 3.14 * 80 * T) / 60
T = 178.86 Nm
Mean torque, Tmean = T / 2 = 89.43 Nm
Maximum torque, Tmax = 1.4 * 89.43 = 125.21 Nm
Step 2: Calculate External Diameter (Do)
Tmax = (π/16) * τ_max * (Do^4 - Di^4)
125.21 = (π/16) * 60 * (Do^4 - (0.6 * Do)^4)
Solving this equation gives Do ≈ 56.6 mm
Step 3: Calculate Internal Diameter (Di)
Given Di = 0.6 * Do
Di = 0.6 * 56.6 = 33.96 mm
Therefore, the external diameter is approximately 56.6 mm and the internal diameter is approximately 33.96 mm.
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A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.?
Question Description
A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.?.
A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.?.
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A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.?, a detailed solution for A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.? has been provided alongside types of A hollow shaft is to transmit 30 kW at 80 rpm. If the shear stress is not to exceed 60 𝑁/𝑚𝑚2 and the internal diameter is 0.6 of the external diameter, find the external and internal diameters, assuming the maximum torque is 1.4 times the mean torque.? theory, EduRev gives you an
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