Poiseuille law vs. Flow Rate Equation Intuition

[Overmjnd]

Hi guys. So according to the flow rate equation, Q=A1V1=A2V2 , the flow rate is not proportional to the length of the pipe; there is no "L" term for length.

However, according to Poiseuille's law, Flow = delP(*pi*R^4/8*coef.viscosity*L) .

In other words, according to Poiseuille's law, the flow rate is inversely proportional to the pipe's length. May I be the first to kindly ask, wtf?

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[metal432]

Think of flow rate as a derivative, with the movement of fluid per cross section A spanning an infinitesimally small length L. While A gets bigger, V gets smaller in that really tiny section length L. In other words, L is being held constant in that equation, and flow rate is measuring how much volume of fluid is being passed through length L per second.

When comparing two pipes with a different L that is significantly large, v1a1=v2a2 doesn't apply, and the length of the pipes need to be accounted for in a different equation, with L varying inversely with flow rate.

 

[ModernAlchemist]

Think of the continuity equation as applying to ideal fluids and Poiseuille's law applying to non-ideal fluids (have significant value for viscosity) so the acknowledgement of friction explains the flow rate to change with length of the pipe.