I have a fluid dynamics homework question I could really use some help solving.(adsbygoogle = window.adsbygoogle || []).push({});

"Consider a straight, circular pipe of inside radius R, through which flow an incompressible fluid. At the pipe entrance, the flow velocityVois uniform and parallel to the pipe centreline. The flow is affected by the action of viscosity and the no-slip condition at the inside wall. The velocity profile far downstream of the entrance,V(r), becomes parabolic with radius from the centreliner. Note thatV(r)are parallel to the centreline for allr. Assume laminar flow.

Find an expression forV(r), the flow speed distribution, in terms ofVoandR.

The Bernoulli Equation would show a large variation in static pressure across the pipe at the downstream station, but this is not the case. Why is the Bernoulli Equation inappropriate here?"

I'm not great at fluid dynamics, and I'm not sure where to start. I initially thought I could use the Hagenâ€“Poiseuille equation to solve it, but I don't think I have enough information to, not unless I make more assumptions for pipe length and viscosity values, but if I do that thenV(r)will have more unknown terms in it than justVoandR.

Also, I read that Bernoulli's equation assumes a non-viscous flow, which is why it is inappropriate for this question. Is that correct?

Thank you in advance for your help, it means a lot.

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# Homework Help: Fluid Dynamics - Flow through a pipe

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