basic fluid flow problem  is there a way to switch pressure to a flow rate in analyt
hello to all
i would like to know is there a analytical equation for pressure drop for problem of fluid flow through rectangular channel eg. i would like to prescribe Q (flow rate) instead of P (pressure) so is there a way to switch deltaP with some Q dependent formula thank you very much 
For fullydeveloped ﬂows, the ﬂow ∆ψ and pressure gradient ∇P are known to be related by a geometrydependent Poiseulle constant cP, n·∇P = cP ∆ψ . See: G P Galdi, An Introduction to the Mathematical Theory of the NavierStokes Equations, Vol. I – Linearized Steady Problems. SpringerVerlag, New York, 1994, p309.

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just to add that for laminar incompressible steady flow, you can solve exactly the velocity field from the problem
d2w/dx^2 + d2w/dy^2 = Re*dp/dz w=0 on the boundaries of the rectangular section where w=w(x,y) is the streamwise (zdirection) velocity, normal to the (x,y) plane of the rectangular section. 
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