Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 8, Problem 8.105P
To determine

(a)

The hydrodynamic mass of the sphere.

Expert Solution
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Answer to Problem 8.105P

The required value of the mass is 2.78kg.

Explanation of Solution

Given Information:

D=22cmSG=2.7a=12m/s2T=20oC

Formula used:

mh=23ρwaterπa3

Calculation:

To solve this problem for water at 20oC we are taking the value of density as ρ=998kg/m3.

The radius of the sphere is a=11cm.

We are using Eq. (8.103) which gives the hydrodynamic mass and proportional to the water density;

mh=23ρwaterπa3 ;

Put the values in the above equation;

mh=23ρwaterπa3=23(998kg/m3)π(0.11m)32.78kg.

To determine

(b)

The value of the force being applied to the sphere.

Expert Solution
Check Mark

Answer to Problem 8.105P

The required value of the force is 214N.

Explanation of Solution

Given information:

D=22cmSG=2.7a=12m/s2T=20oC

Formula used:

(π/6)ρsphere(D3)

F=(msphere+mh)dVdt

Calculation:

Firstly we will calculate the mass of the sphere;

(π/6)ρsphere(D3)=(π/6)(2.7×998)(0.22)315.02kg

Now we will use Eq. (8.101) to find the applied force;

F=(msphere+mh)dVdt ;

Put the values in the above equation;

F=(msphere+mh)dVdt=(15.02+2.78kg)(12m/s2)214N.

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Chapter 8 Solutions

Fluid Mechanics

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