# 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 The volumetric flow rate of withdrawn fluid is (expressed in /s).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