# If a governing equation represents volume change in an element, then the weight function in its weak form must be like a force that causes the volume change.

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If a governing equation represents volume change in an element, then the weight function in its weak form must be like a force that causes the volume change.

(a) True

(b) False

This question was addressed to me by my college director while I was bunking the class.

I need to ask this question from Velocity in division Flows of Viscous Incompressible Fluids of Finite Element Method

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Correct choice is (a) True

The explanation is: The governing equation $\frac{\partial v_x}{\partial y}+\frac{\partial v_y}{\partial x}$ represents the volume change in an element of dimensions dx and dy. Therefore, the weight function (w) in its weak form must be like a force that causes the volume change. Volume changes occur under the action of hydrostatic pressure, hence w=-P.

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