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# Converging duct flow is modeled by the steady, ## Problem 17P Chapter 4

Fluid Mechanics | 2nd Edition

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Problem 17P Problem 17P

Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 11–15. The pressure field is given by where P0  is the pressure at x =0. Generate an expression for the rate of change of pressure following a fluid particle.

PROBLEM: Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P11–15). A simple approximate velocity field for this flow is where U0 is the horizontal speed at x= 0. Note that this equation ignores viscous effects along the walls but is a reasonable approximation throughout the majority of the flow field. Calculate the material acceleration for fluid particles passing through this duct. Give your answer in two ways: (1) as acceleration components ax and ay and (2) as acceleration vector . Step-by-Step Solution:

Step 1:

Consider a duct flow which is steady, converging and incompressible. The flow happens at two dimensional space.

The pressure field is given by

P = -  ----(1)

Where P0 is the pressure at x = 0

Step 2:

To generate an expression for the rate of change of pressure following a fluid particle

The material derivative of pressure function as given in the velocity field = + + + -------(2)

Step 3:

In the case of steady flow = 0

And two dimensional flow = 0

The (2) becomes = + -----------------------(3)

Step 4:

Differentiating (1) with respect to x =  =  = ---------------(4)

Step 5 of 7

Step 6 of 7

##### ISBN: 9780071284219

Since the solution to 17P from 4 chapter was answered, more than 754 students have viewed the full step-by-step answer. Fluid Mechanics was written by Sieva Kozinsky and is associated to the ISBN: 9780071284219. The answer to “Converging duct flow is modeled by the steady, two-dimensional velocity field of Prob. 11–15. The pressure field is given by where P0 is the pressure at x =0. Generate an expression for the rate of change of pressure following a fluid particle.PROBLEM: Consider steady, incompressible, two-dimensional flow through a converging duct (Fig. P11–15). A simple approximate velocity field for this flow is where U0 is the horizontal speed at x= 0. Note that this equation ignores viscous effects along the walls but is a reasonable approximation throughout the majority of the flow field. Calculate the material acceleration for fluid particles passing through this duct. Give your answer in two ways: (1) as acceleration components ax and ay and (2) as acceleration vector .” is broken down into a number of easy to follow steps, and 123 words. The full step-by-step solution to problem: 17P from chapter: 4 was answered by Sieva Kozinsky, 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: 2nd. This full solution covers the following key subjects: flow, Field, duct, pressure, acceleration. This expansive textbook survival guide covers 15 chapters, and 1547 solutions.

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