It is assumed that the water velocity is uniform over the inlet- and outlet ports. Also, note that the velocity vector of incoming water to the inlet of the tank is opposite to the area- vector.
Simplifying,
Example 2: Consider the steady-state flow of water in a circular tube of variable area:
(Fig. 12c)
The velocity at the inlet to the tube is uniform at . The velocity profile in both sections of the tube is parabolic.
Apply the conservation of mass equation to calculate maximum velocity in the tube (both sections) in terms of known quantities.
Consider :
(1st term is zero for steady-state condition)
Therefore, :, where
. The velocity profile in both sections of the tube is parabolic.
: 
, where 
