Question

the rate of flow of a liquid flowing through a pipe of radius R and a pressure gradient is given by Poisuille's equation: V =(π÷8)×Pr4÷nl

Answer 1

Given :

Radius of the pipe = R

To Check :

The dimensional consistency of Poiseuille equation

Solution :

• The rate of flow of the liquid is given by Poiseuille equation

                 $\frac{v}{t} =\frac{\pi pr^{4} }{8\eta l}$

• The dimensional formula of  L.H.S is

                $[\frac{v}{t}]=[L^{3}T^{-1}]$

• The dimensional formula of R.H.S is

                $[\frac{\pi pr^{4} }{8\eta l}]=[\frac{[ML^{-1}T^{-2}][L^{4}]}{[ML^{-1}T^{-1}][L]} ]=[T^{-1}L^{3}]$

• Both the sides of the equation gives same values, so it is clear that the equation is correct

 The given formula is dimensionally correct

             

Answer 2

Explanation:

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