Partial Diversion of a Stream through a Slot
Partial Diversion of a Stream through a Slot
Consider an inviscid uniform fluid flowing with velocity (expressed in ) 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 The volumetric flow rate of withdrawn fluid is (expressed in /s).
U
m/s
Q
3
m
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 or large values of , 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.
Q
U