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Consider a U–tube filled with mercury as shown in Fig.

Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala ISBN: 9780071284219 39

Solution for problem 134P Chapter 3

Fluid Mechanics | 2nd Edition

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Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala

Fluid Mechanics | 2nd Edition

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Problem 134P

Problem 134P

Consider a U–tube filled with mercury as shown in Fig. P3–142. The diameter of the right arm of the U–tube is D = 2 cm. and the diameter of the left arm is twice that. Oil with a specific gravity of 2.72 is poured into the left arm, forcing some mercury from the left arm into the right one. Determine the maximum amount of oil that can be added into the left arm.

Step-by-Step Solution:
Step 1 of 3

Solution

Introduction

Consider a U tube filled with mercury, the volume of the mercury in the tube is constant and while pouring an oil in to the left arm will reduce  the level of mercury in the left arm and will increase the mercury volume in the right arm.

If the volume of mercury drop an amount x in the left arm and let h is the corresponding rise in the right arm.

STEP 1

Diameter of the right arm, D=2cm

Diameter of the left arm = 2D=4cm

Volume of the left arm, Vleft =x =x=h

Vleft =Vright

The pressure at A and B are equal

Patmoilg(hoil +1 ) =PatmHgg(hHg )

It will result

SGoilρwg(hoil+x)=SGHgρwg(5x)

1=

1=

X =

STEP 2

Specific gravity of the liquid SGoil =2.72

Specific gravity of mercury, SGHg =13.6

Level of oil in the left arm, hoil =12 cm

X = =0.5 cm

STEP 3

So the maximum amount of oil that can added to the left arm

Vmax =(2)2(hoil +x)

Vmax =(2)2(hoil +x)

Vmax =(3.14)(2)2(12 +0.5)

Vmax =157.08 cm3

Vmax =0.157 L

Step 2 of 3

Chapter 3, Problem 134P is Solved
Step 3 of 3

Textbook: Fluid Mechanics
Edition: 2
Author: Yunus A. Cengel, John M. Cimbala
ISBN: 9780071284219

The full step-by-step solution to problem: 134P from chapter: 3 was answered by , our top Engineering and Tech solution expert on 07/03/17, 04:51AM. This full solution covers the following key subjects: arm, left, Right, tube, oil. This expansive textbook survival guide covers 15 chapters, and 1547 solutions. This textbook survival guide was created for the textbook: Fluid Mechanics, edition: 2. The answer to “Consider a U–tube filled with mercury as shown in Fig. P3–142. The diameter of the right arm of the U–tube is D = 2 cm. and the diameter of the left arm is twice that. Oil with a specific gravity of 2.72 is poured into the left arm, forcing some mercury from the left arm into the right one. Determine the maximum amount of oil that can be added into the left arm.” is broken down into a number of easy to follow steps, and 73 words. Since the solution to 134P from 3 chapter was answered, more than 1481 students have viewed the full step-by-step answer. Fluid Mechanics was written by and is associated to the ISBN: 9780071284219.

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Consider a U–tube filled with mercury as shown in Fig.