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Question 4.6: The velocity components in 2-D flow are u = ax and v = by. S......

The velocity components in 2-D flow are u = ax and v = by. Show that a = -b if the components satisfy the continuity equation.

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Given: u = ax and v = by

Hence,                                                 \frac{\pmb{\delta}u}{\pmb{\delta} x}=a                                                    (i)

and                                                      \frac{\pmb{\delta}v}{\pmb{\delta} y}=a                                                    (ii)

In order to satisfy continuity equation in 2-D, we have

\frac{\pmb{\delta}u}{\pmb{\delta} x} + \frac{\pmb{\delta}v}{\pmb{\delta} y}=0

Substituting the values from Eqs. (i) and (ii), we get

a + b= 0

Hence,                                                   a= -b

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