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# A two-dimensional fluid element of dimensions dx and dy

ISBN: 9780071284219 39

## Solution for problem 70P Chapter 4

Fluid Mechanics | 2nd Edition

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Problem 70P

A two-dimensional fluid element of dimensions dx and dy translates and distorts as shown in Fig. P4‒74 during the infinitesimal time period dt = t 2‒t 1· The velocity components at point P at the initial time are u and v in the x- and y-directions, respectively. Show that the magnitude of the rate of rotation (angular velocity) about point P in the xy-plane is

FIGURE P4‒74

Step-by-Step Solution:

Problem 70P

Solution 70P

Step 1 of 6 :

In this question,we have two dimensional fluid, we need to show the magnitude of rate of rotation at point  P as

Considering the given figure

Step 2  of 6:

From the definition of angular velocity we have, the rate of rotation at a point is the average rotation rate of two initially perpendicular lines intersect at a point P

Here Line a rotates along an angle  and Line b rotates along an angle

Thus we have average angle of rotation as

Step 3 of 6 :

During time increment

The point P moves distance along right and  upwards

The point A moves distance  along right and  upwards

The point B moves distance   along right and  upwards

Step 4 of 6

Step 5 of 6

##### ISBN: 9780071284219

Since the solution to 70P from 4 chapter was answered, more than 270 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Fluid Mechanics, edition: 2. This full solution covers the following key subjects: velocity, point, initial, dimensions, Directions. This expansive textbook survival guide covers 15 chapters, and 1547 solutions. Fluid Mechanics was written by and is associated to the ISBN: 9780071284219. The answer to “A two-dimensional fluid element of dimensions dx and dy translates and distorts as shown in Fig. P4?74 during the infinitesimal time period dt = t 2?t 1· The velocity components at point P at the initial time are u and v in the x- and y-directions, respectively. Show that the magnitude of the rate of rotation (angular velocity) about point P in the xy-plane is FIGURE P4?74” is broken down into a number of easy to follow steps, and 67 words. The full step-by-step solution to problem: 70P from chapter: 4 was answered by , our top Engineering and Tech solution expert on 07/03/17, 04:51AM.

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