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 32P
To determine

The total power required and the reduction in the required power input.

Expert Solution & Answer
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Explanation of Solution

Given:

Angular velocity (ω) is 200 rad/s.

Thickness of the oil film (t) is 1.2 mm.

Dynamic viscosity of the SAE 10W oil at 20°C (μ@20°C) is 0.1 Pas.

Dynamic viscosity of the SAE 10W oil at 80°C (μ@80°C) is 0.0078 Pas.

Calculation:

Determine the expression of shear stress.

  τw=μdudr=μVh=μωrh

Determine the expression of shear force.

  dF=τwdA=μωrhdA

Determine the expression for torque.

  dT=rdF=μωr2hdA

Differentiate the above equation.

  T=μωhAr2dA

Determine the expression for power required.

  W˙sh=ωT=μω2hAr2dA

Determine the expression for power required from the top.

  W˙sh, top =μω2hr=0D/2r2(2πr)dr=2πμω2hr=0D/2r3dr=2πμω2hr44|r=0D/2=πμω2D432h

Determine the expression for power required from the bottom.

  W˙sh, bottom =πμω2d432h

Determine the expression for power required from the top.

  W˙sh, top =μω2hr=0D/2r24πLDdrdr=4πμω2Lh(Dd)r=d/2D/2r3dr=4πμω2Lh(Dd)r44|r=d/2D/2=πμω2L(D2d2)16h(Dd)

Determine the total power required.

  W˙sh, total =W˙sh, top +W˙sh, bottom +W˙sh,side =πμω2D432h(1+(dD)4+2L(1(dD)4)Dd)

  W˙sh total ={π(0.1 Ns/m2)(200 rad/s)2(0.12 m)432(0.0012 m)(1+(13)4+2(0.12 m)(1(13)4)](0.12 m0.04 m))(1 W1 Nm/s)}=270 W

Thus, the total power required is 270 W_.

Determine the power required at 80°C.

  W˙sh, total ,80°C=μ80°Cμ20°CW˙sh, total 20°C=0.0078 Ns/m20.1 Ns/m2(270 W)=21.1 W

Determine the reduction in the required power input.

  Reduction=Wsh, total,20°CWsh, total,80°C=270 W21.1 W=248.9 W

Thus, the reduction in the required power input is 248.9 W_.

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Chapter 10 Solutions

Fundamentals of Thermal-Fluid Sciences

Ch. 10 - The analysis of a propeller that operates in water...Ch. 10 - A pump is used to transport water to a higher...Ch. 10 - In a piping system, the water temperature remains...Ch. 10 - The analysis of a propeller that operates in water...Ch. 10 - Prob. 15PCh. 10 - Prob. 16PCh. 10 - Prob. 17PCh. 10 - How does the dynamic viscosity of (a) liquids and...Ch. 10 - Consider two identical small glass balls dropped...Ch. 10 - The viscosity of a fluid is to be measured by a...Ch. 10 - Prob. 21PCh. 10 - Consider the flow of a fluid with viscosity μ...Ch. 10 - A thin 30-cm × 30-cm flat plate is pulled at 3 m/s...Ch. 10 - A rotating viscometer consists of two concentric...Ch. 10 - Prob. 25PCh. 10 - The dynamic viscosities of carbon dioxide at 50°C...Ch. 10 - Prob. 28PCh. 10 - For flow over a plate, the variation of velocity...Ch. 10 - In regions far from the entrance, fluid flow...Ch. 10 - Prob. 31PCh. 10 - Prob. 32PCh. 10 - Prob. 33PCh. 10 - A large plate is pulled at a constant speed of U =...Ch. 10 - Prob. 35PCh. 10 - A small-diameter tube is inserted into a liquid...Ch. 10 - Prob. 37PCh. 10 - Prob. 38PCh. 10 - Is the capillary rise greater in small-or...Ch. 10 - Prob. 40PCh. 10 - Prob. 41PCh. 10 - A 1.2-mm-diameter tube is inserted into an unknown...Ch. 10 - Determine the gage pressure inside a soap bubble...Ch. 10 - A 0.03-in-diameter glass tube is inserted into...Ch. 10 - Prob. 45PCh. 10 - Prob. 46PCh. 10 - A capillary tube is immersed vertically in a water...Ch. 10 - Prob. 48PCh. 10 - Prob. 49PCh. 10 - Prob. 50RQCh. 10 - Consider a 55-cm-long journal bearing that is...Ch. 10 - Prob. 52RQCh. 10 - The pressure on the suction side of pumps is...Ch. 10 - Consider laminar flow of a Newtonian fluid of...Ch. 10 - Prob. 56RQCh. 10 - Prob. 57RQCh. 10 - Some rocks or bricks contain small air pockets in...
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