Question

The momentum equation is $\rho\frac{Du}{Dt}=-\frac{\partial p}{\partial x}+\frac{\partial \tau_{xx}}{\partial x}+\frac{\partial \tau_{yx}}{\partial y}+\frac{\partial \tau_{zx}}{\partial z}+\rho f_x$. Which of these statements about sign convention can be inferred from this equation?

(a) Pressure force is taken as negative

(b) Tensile force is taken as negative

(c) Pressure force is taken as positive

(d) Pressure force is unsigned

The question was asked in a job interview.

The question is from Momentum Equation topic in chapter Governing Equations of Fluid Dynamics of Computational Fluid Dynamics

Answer 1

Correct choice is (a) Pressure force is taken as negative

Easiest explanation: When all the other forces and accelerations are positive, gradient of pressure force is negative(-$\frac{\partial p}{\partial x}$). This is possible only when pressure force is signed posititve.