In other words, local density my change with time ,as the fluid enters and leaves a ‘CV’ at different rates resulting in the accumulation or depletion of mass of the matter per unit volume of the CV. This is referred as the unsteady-state. However, if the fluid is incompressible, its density will be constant and the material rate of change of density will be zero.
(incompressible fluid) can be written for 2D geometries as :
: Cartesian
: Cylindrical
Pay special attention to the last term of the above-equation. For 1D radial flow,
.
(Fig. 13b)
const under steady-state.
To sum-up, total mass flow rate is constant at all locations in the r-direction. However, mass flux changes because the differential area changes in the r-direction
,as the fluid enters and leaves a ‘CV’ at different rates resulting in the accumulation or depletion of mass of the matter per unit volume of the CV. This is referred as the unsteady-state. However, if the fluid is incompressible, its density will be constant and the material rate of change of density will be zero. 
(incompressible fluid) can be written for 2D geometries as : 
: Cartesian
: Cylindrical 
. 
const under steady-state. 
is constant at all locations in the r-direction. However, mass flux 
changes because the differential area changes in the r-direction
