WOLFRAM|DEMONSTRATIONS PROJECT

Partial Diversion of a Stream through a Slot

​
uniform fluid velocity parallel to wall
volumetric flow rate of withdrawn fluid
Consider an inviscid uniform fluid flowing with velocity
U
(expressed in
m/s
) parallel to a wall. A narrow slot in the wall allows some of the fluid to be diverted. The volumetric flow rate of withdrawn fluid is
Q
(expressed in
3
m
/s
).
The Demonstration plots the stream function for this partial diversion problem, which is given by:
ψ=Ux-
Q
π
-1
tan
y
x
.
For small values of
Q
or large values of
U
, the velocity profiles approach that of a uniform flow. Far from the slot, the velocity field is again almost that of uniform flow parallel to the wall.