Continuity Equation for an Incompressible flow

For an incompressible flow density is a constant. Accordingly we have

$${\partial u\over {\partial x}} + {\partial v\over {\partial y}}  + {\partial w \over {\partial z}} = 0$$ (4.16)

and in polar coordinates we have,

$${1 \over r} {\partial \over \partial r} (r v_r) + {1 \over r} {\partial \over \partial \theta}( v_\theta) + {\partial \over \partial z}( v_z)=0$$ (4.17)

As noticed for the control volume analysis the continuity equation for an incompressible flow is the same whether the flow is steady or unsteady.

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