Fundamentals of Thermal-Fluid Sciences
Fundamentals of Thermal-Fluid Sciences
5th Edition
ISBN: 9780078027680
Author: Yunus A. Cengel Dr., Robert H. Turner, John M. Cimbala
Publisher: McGraw-Hill Education
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Chapter 10, Problem 25P
To determine

The transmitted torque.

Expert Solution & Answer
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Explanation of Solution

Given:

Thickness of the oil film (h) is 2 mm.

Dynamic viscosity (μ) is 0.38 Ns/m2.

Diameter of the clutch (D) is 30 cm.

Driving speed of the shaft (n1) is 1450 rpm.

Driven speed of the shaft (n2) is 1398 rpm.

Calculation:

When one of the plate is stationary, the linear velocity of the other plate is V=(ω1ω2)r.

Consider a small area dA on the surface of the disc.

Write the expression of the shear force on the disc on the area dA.

  dF=μ(dA)(Vh)dF=μ(2πrdr)(Vh)dF=μ(2πr)((ω1ω2)rh)dr

Write the expression of torque on the small area dA.

  dT=(μ(2πr)((ω1ω2)rh)dr)rdT=2πμr3(ω1ω2)drh

Integrate the above equation.

  0TdT=r=0D/22πμr3(ω1ω2)drh0TdT=2πμ(ω1ω2)hr=0D/2r3dr(T)0T=2πμ(ω1ω2)h(r44)r=0D/2T0=2πμ(ω1ω2)h((D/2)440)

  T=πμ(ω1ω2)D432hT=πμ[2π(n1n2)]D432hT=π(0.38 Ns/m2)[2π(1450 rpm1398 rpm)(1 min60 s)](30 cm(1 m102cm))432(2 mm(1 m103mm))T=0.823 Nm

Thus, the transmitted torque is 0.823 Nm_.

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Chapter 10 Solutions

Fundamentals of Thermal-Fluid Sciences

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