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A two-dimensional fluid element of dimensions dx and dy
Chapter 4, Problem 70P(choose chapter or problem)
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
Questions & Answers
QUESTION:
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
ANSWER:
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