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# For the velocity field of Prob. 4-23, calculate the fluid ## Problem 23P Chapter 4

Fluid Mechanics | 2nd Edition

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Problem 23P

For the velocity field of Prob. 4-23, calculate the fluid acceleration along the diffuser centerline as a function of x and the given parameters. For L = 1.56 m, uentrance = 24.3 m/s, and uexit=16.8 m/s, calculate the acceleration at x =0 and x = 1.0 m.

PROBLEM: Consider steady flow of air through the diffuser portion of a wind tunnel (Fig. P11–20). Along the centerline of the diffuser, the air speed decreases from uentrance to uexit as sketched. Measurements reveal that the centerline air speed decreases parabolically through the diffuser. Write an equation for centerline speed u(x), based on the parameters given here, from x = 0 to x = L.

FIGURE: Step-by-Step Solution:

Solution 23P

Step 1</p>

In this problem, a fluid is flowing through a diffuser. So, we have to calculate the acceleration of the fluid through the center line of the diffuser.

So, we have the equation for velocity of the diffuser. It can be written as, Where, - fluid velocity at entrance through the center line - fluid velocity at exit through the center line - Length of the diffuser - Position at center line

Step 2</p>

Finding out the acceleration through center line

Standard expression for the acceleration in three dimensional space is, But, in the problem, they have provided that, the flow is steady. So, the time derivative would be zero.

That is, Similarly, the fluid flow is only towards the center line. Therefore, the terms and will be zero.

Therefore, Therefore, the expression for the acceleration towards the center line is, Step 3 of 3

##### ISBN: 9780071284219

The full step-by-step solution to problem: 23P from chapter: 4 was answered by , our top Engineering and Tech solution expert on 07/03/17, 04:51AM. This full solution covers the following key subjects: Centerline, diffuser, air, speed, acceleration. This expansive textbook survival guide covers 15 chapters, and 1547 solutions. The answer to “For the velocity field of Prob. 4-23, calculate the fluid acceleration along the diffuser centerline as a function of x and the given parameters. For L = 1.56 m, uentrance = 24.3 m/s, and uexit=16.8 m/s, calculate the acceleration at x =0 and x = 1.0 m.PROBLEM: Consider steady flow of air through the diffuser portion of a wind tunnel (Fig. P11–20). Along the centerline of the diffuser, the air speed decreases from uentrance to uexit as sketched. Measurements reveal that the centerline air speed decreases parabolically through the diffuser. Write an equation for centerline speed u(x), based on the parameters given here, from x = 0 to x = L.FIGURE:” is broken down into a number of easy to follow steps, and 111 words. Since the solution to 23P from 4 chapter was answered, more than 716 students have viewed the full step-by-step answer. Fluid Mechanics was written by and is associated to the ISBN: 9780071284219. This textbook survival guide was created for the textbook: Fluid Mechanics, edition: 2nd.

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