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basic fluid flow problem - is there a way to switch pressure to a flow rate in analyt

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Old   December 4, 2010, 12:02
Default basic fluid flow problem - is there a way to switch pressure to a flow rate in analyt
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vladimir nikolic
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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
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Old   September 15, 2016, 08:58
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Jonas T. Holdeman, Jr.
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For fully-developed flows, the flow ∆ψ and pressure gradient ∇P are known to be related by a geometry-dependent Poiseulle constant cP, nĚ∇P = cP ∆ψ . See: G P Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations, Vol. I – Linearized Steady Problems. Springer-Verlag, New York, 1994, p309.
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Old   September 15, 2016, 11:59
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Filippo Maria Denaro
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Quote:
Originally Posted by vlnikolic View Post
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
are you talking about laminar or turbulent flow in a duct
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Old   September 16, 2016, 04:07
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Filippo Maria Denaro
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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 stream-wise (z-direction) velocity, normal to the (x,y) plane of the rectangular section.
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