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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