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# Converging duct flow is modeled by the steady, two ISBN: 9780071284219 39

## Solution for problem 52P Chapter 4

Fluid Mechanics | 2nd Edition

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Problem 52P

Converging duct flow is modeled by the steady, two dimensional velocity field of  Prob. 4‒17. A fluid particle (A) is located on the x-axis at x = xA  at time t = 0 (Fig. P4-54). At some later time t, the fluid particle has moved downstream FIGURE P4‒54

with the flow to some new location. x = xA, as shown in the figure. Since the flow is symmetric about the x-axis, the fluid particle remains on the.x-axis at all times. Generate an analytical expression for the.x-location of the fluid particle at some arbitrary time t in terms of its initial location xA  and constants U0 and b. In other words, develop an expression for xA (Hint: We know that u = dxparticle/dt following a fluid particle. Plug in u. separate variables, and integrate.) Step-by-Step Solution:

Step 1:-

The velocity field is given as, Where, And .

Step 2:-

The acceleration field in this case can be written as, Where, and .

Step 3 of 4

Step 4 of 4

##### ISBN: 9780071284219

This full solution covers the following key subjects: particle, fluid, axis, location, some. This expansive textbook survival guide covers 15 chapters, and 1547 solutions. Fluid Mechanics was written by and is associated to the ISBN: 9780071284219. Since the solution to 52P from 4 chapter was answered, more than 888 students have viewed the full step-by-step answer. The answer to “Converging duct flow is modeled by the steady, two dimensional velocity field of Prob. 4?17. A fluid particle (A) is located on the x-axis at x = xA at time t = 0 (Fig. P4-54). At some later time t, the fluid particle has moved downstream FIGURE P4?54with the flow to some new location. x = xA, as shown in the figure. Since the flow is symmetric about the x-axis, the fluid particle remains on the.x-axis at all times. Generate an analytical expression for the.x-location of the fluid particle at some arbitrary time t in terms of its initial location xA and constants U0 and b. In other words, develop an expression for xA (Hint: We know that u = dxparticle/dt following a fluid particle. Plug in u. separate variables, and integrate.)” is broken down into a number of easy to follow steps, and 132 words. The full step-by-step solution to problem: 52P from chapter: 4 was answered by , our top Engineering and Tech solution expert on 07/03/17, 04:51AM. This textbook survival guide was created for the textbook: Fluid Mechanics, edition: 2.

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