Continuity Equation for steady flow

For a steady flow the time derivative vanishes. As a result 4.7 becomes,

$${\partial \over {\partial x}}(\rho u) + {\partial \over {\partial y}}(\rho v)  + {\partial \over {\partial z}}(\rho w) = 0$$ (4.14)

The equation in polar coordinates also undergoes the same simplification.

$${1 \over r} {\partial \over \partial r} (r \rho v_r) + {1 \over ... ...over \partial \theta}(\rho v_\theta) + {\partial \over \partial z}(\rho v_z)=0$$ (4.15)

These equations are the ones that are to be used for a compressible flow as we have kept density, $\rho$ still variable.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney