Fluid Mechanics
Fluid Mechanics
8th Edition
ISBN: 9780073398273
Author: Frank M. White
Publisher: McGraw-Hill Education
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Chapter 8, Problem 8.29P
To determine

(a) Is this point outside the body?

Expert Solution
Check Mark

Answer to Problem 8.29P

(a) Yes this point is outside the body.

Explanation of Solution

Given information:

U=20m/s,ρ=998kgm3 , uniform water stream combines with a source at the origin to form a half-body.

at (x,y)=(0,1.2),p=12.5kpap

Calculation:

We know that,

The point on the half body surface just above the m is at y=πa2 where a=mU,U=ma

Apply Bernoulli equation,

p+ρ2U2=(p12500)+ρ2(U2+ ( m 1.2 )2)m=12500×2×(1.2)2/998m=6m2s

As we know, a=mU=620=0.33m

And y=πa2 put the value of a and we get,

y=π(0.33)2=0.47m

Given point is located at

y=1.2m which above then y=0.47m

So this point is outside the body,

m=6m2s.

To determine

(b) The appropriate strength m?

Expert Solution
Check Mark

Answer to Problem 8.29P

(b) m=6m2s

Explanation of Solution

Given information:

U=20m/s,ρ=998kgm3 , uniform water stream combines with a source at the origin to form a half-body.

at (x,y)=(0,1.2),p=12.5kpap

Calculation:

We know that,

The point on the half body surface just above the m is at y=πa2 where a=mU,U=ma

Apply Bernoulli equation,

p+ρ2U2=(p12500)+ρ2(U2+ ( m 1.2 )2)m=12500×2×(1.2)2/998m=6m2s

As we know, a=mU=620=0.33m

And y=πa2 put the value of a and we get,

y=π(0.33)2=0.47m

Given point is located at

y=1.2m which above then y=0.47m

So this point is outside the body,

m=6m2s.

To determine

(c) The pressure at the nose of the body?

Expert Solution
Check Mark

Answer to Problem 8.29P

(c) p=(p+199.6)kpa

Explanation of Solution

Given information:

U=20m/s,ρ=998kgm3 , uniform water stream combines with a source at the origin to form a half-body.

Calculation:

Let pressure at nose is p

And we know that velocity at nose is zero,

Apply Bernoulli equation,

p+ρ2U2=(p)+ρ2(0)2p=p+ρ2202p=(p+199.6)kpa.

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Chapter 8 Solutions

Fluid Mechanics

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