Consider the two-dimensional velocity field given by $\to V = (5 + a_{1} x + + b_{1} y)^i + (4 + a_{2} x + b_{2} y)^j$ where $a_{1}, b_{1}, a_{2} a n d b_{2}$ are constants. Which one of the following conditions needs to be satisfied for the flow to be incompressible?

a_{1} + b_{1} = 0

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a_{1} + b_{2} = 0

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a_{2} + b_{2} = 0

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a_{2} + b_{1} = 0

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Solution

The correct option is B $a_{1} + b_{2} = 0$
Given that the flow is incompressible.
$∴ d i v \to V = 0$
$\frac{\partial}{\partial x} (5 + a_{1} x + b_{1} y) + \frac{\partial}{\partial y} (4 + a_{2} x + b_{2} y) = 0$
$a_{1} + b_{2} = 0$

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Similar questions

\to V = (5 + a_{1} x + b_{1} y)^i + (4 + a_{2} x + b_{2} y)^j

a_{1}, b_{1}, a_{2}

b_{2}

2 x y^i - y^{2}^j

V = (a_{1} x + a_{2} y + a_{3} z) i + (b_{1} x + b_{2} y + b_{3} z) j + (c_{1} x + c_{2} y + c_{3} z) k,

a_{1} = 2

c_{3} = - 4

b_{2}

- \to U = A (x^i - y^j)

\to

\to \infty

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