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Fluid Mechanics | 2nd Edition | ISBN: 9780071284219 | Authors: Yunus A. Cengel, John M. Cimbala
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Consider steady flow of water through an axisymmetric

Chapter 4, Problem 2P

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QUESTION:

Problem 2P

Consider steady flow of water through an axisymmetric garden hose nozzle (Fig. P11–2). Along the centerline of the nozzle, the water speed increases from uentrance toexit as sketched. Measurements reveal that the centerline water speed increases parabolically through the nozzle. Write an equation for centerline speed u(x), based on the parameters given here, from x = 0 to x = L.

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QUESTION:

Problem 2P

Consider steady flow of water through an axisymmetric garden hose nozzle (Fig. P11–2). Along the centerline of the nozzle, the water speed increases from uentrance toexit as sketched. Measurements reveal that the centerline water speed increases parabolically through the nozzle. Write an equation for centerline speed u(x), based on the parameters given here, from x = 0 to x = L.

ANSWER:

Solution 2P

We need to write an equation for centerline speed for the given flow.

Step 1

The general equation of a parabola is …..(1)

Here, (h,k) is the coordinate of the vertex of the parabola.

From the figure give, when , the speed is equal to .

Let

So,

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