If the pressure difference across a pipe of r | vedclass

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Question

(A) According to Poiseuille's equation for the steady flow of an incompressible,viscous fluid through a cylindrical pipe,the volume flow rate $V$ is g

Vedclass · Accepted Answer

$V = \frac{\pi p r^4}{8 \eta l}$

Vedclass · Answer

(A) According to Poiseuille's equation for the steady flow of an incompressible,viscous fluid through a cylindrical pipe,the volume flow rate $V$ is given by:$V = \frac{\pi p r^4}{8 \eta l}$Where:$p$ is the pressure difference,$r$ is the radius of the pipe,$\eta$ is the coefficient of viscosity,$l$ is the length of the pipe.Dimensional analysis confirms this:$V = [L^3 T^{-1}]$$p = [M L^{-1} T^{-2}]$$r = [L]$$\eta = [M L^{-1} T^{-1}]$$l = [L]$Substituting these into the formula:$V = \frac{[M L^{-1} T^{-2}] [L^4]}{[M L^{-1} T^{-1}] [L]} = [L^3 T^{-1}]$Since the dimensions of both sides match,the expression is correct.

If the pressure difference across a pipe of radius $r$ and length $l$ is $p$,then the volume of liquid flowing out per second is $V$. Find the correct expression for $V$.

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