# How do I find a stream function given a volumetric flow rate?

How do I find a stream function given a volumetric flow rate?

The flow only occurs in one direction, between 2 plates, and I have no knowledge of velocity.

I know that volumetric flow rate = change in stream function between two points but I have no idea how to apply this.

• It isn't possible to determine the stream function, given only the volumetric flow rate. Were you given any other information, such as what the total area perpendicular to the flow is? Or did you perhaps misread the problem, and it's actually the volumetric flux that's given, instead of the volumetric flow rate? – Red Act Feb 26 '16 at 18:36
• Is the fluid flow pressure-driven laminar flow, or is it generated by moving one of the plates? – Chet Miller Feb 26 '16 at 19:20
• it's a pressure driven flow ie like a river flowing wiith the plates as its banks and I know the distaance between the two plates. what's the difference between flux and flow rate? i am given a quantity in units of vol/time – E.Smith Feb 27 '16 at 22:10

If it is pure shear flow, with the top plate moving with velocity V and the lower plate stationary, the stream function is given by $$\psi=Q\left(\frac{y}{h}\right)^2$$where Q is the total volumetric flow rate, equal to Vh/2, h is the distance between the plates, and y is the distance measured upward from the bottom plate.