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What is the minimum required diameter d (in cm) for a solid circular shaft if it is to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa?
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What is the minimum required diameter d (in cm) for a solid circular s...
Calculating the Required Diameter of the Shaft
- Given data:
- Power (P) = 40 HP = 40 x 746 W (conversion to Watts) = 29840 W
- Speed (N) = 600 RPM
- Allowable shear stress (τ) = 27.57 MPa = 27.57 x 10^6 Pa
- Formula for power transmission in a shaft:
P = 2πNT/60
- Rearranging the formula for T (torque):
T = (60 x P) / (2πN)
- Substituting the values:
T = (60 x 29840) / (2π x 600) = 298400 / 3770.8 = 79.08 Nm
- Formula for shear stress in a solid circular shaft:
τ = 16T / (πd^3)
- Rearranging the formula for d (shaft diameter):
d = (16T / (πτ))^(1/3)
- Substituting the values:
d = (16 x 79.08 / (π x 27.57 x 10^6))^(1/3) = (1265.28 / 86506017.35)^(1/3) = 0.00001463 m
- Converting the diameter to cm:
d = 0.00001463 m x 100 cm/m = 0.001463 cm
Therefore, the minimum required diameter of the solid circular shaft to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa is approximately 1.46 cm.
- Given data:
- Power (P) = 40 HP = 40 x 746 W (conversion to Watts) = 29840 W
- Speed (N) = 600 RPM
- Allowable shear stress (τ) = 27.57 MPa = 27.57 x 10^6 Pa
- Formula for power transmission in a shaft:
P = 2πNT/60
- Rearranging the formula for T (torque):
T = (60 x P) / (2πN)
- Substituting the values:
T = (60 x 29840) / (2π x 600) = 298400 / 3770.8 = 79.08 Nm
- Formula for shear stress in a solid circular shaft:
τ = 16T / (πd^3)
- Rearranging the formula for d (shaft diameter):
d = (16T / (πτ))^(1/3)
- Substituting the values:
d = (16 x 79.08 / (π x 27.57 x 10^6))^(1/3) = (1265.28 / 86506017.35)^(1/3) = 0.00001463 m
- Converting the diameter to cm:
d = 0.00001463 m x 100 cm/m = 0.001463 cm
Therefore, the minimum required diameter of the solid circular shaft to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa is approximately 1.46 cm.
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What is the minimum required diameter d (in cm) for a solid circular shaft if it is to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa?
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What is the minimum required diameter d (in cm) for a solid circular shaft if it is to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about What is the minimum required diameter d (in cm) for a solid circular shaft if it is to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the minimum required diameter d (in cm) for a solid circular shaft if it is to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa?.
What is the minimum required diameter d (in cm) for a solid circular shaft if it is to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about What is the minimum required diameter d (in cm) for a solid circular shaft if it is to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the minimum required diameter d (in cm) for a solid circular shaft if it is to transmit 40 HP at 600 RPM without exceeding an allowable shear stress of 27.57 MPa?.
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