1.

The rate flow (V) of a liquid through a pipe of radius (r ) under a pressure gradient (P//I) is given by `V = (pi)/(8)(P R^4)/(I eta),` Where `eta` is coefficient of visocity of the liquied. Check whether the formula is correct or not.

Answer» `V = volume//sec =[L^3 T^(-1)]`
`(P)/(I) = "pressure gradient" = (ML^(-1) T^(-2))/(L)`
` = [ML^(-2)T^(-2)]`
Now `L.H.S. = V = [L^3 T^(-1)]`
`R.H.S = (pi)/(8)xx(P)/(I)xx(r^4)/(eta) = ((ML^(-2)T^(-2))L^4)/((ML^(-1)T^(-1))) = [L^3 T^(-1)]`
As L.H.S. = R.H.S., dimensionly, therefore
the formula is correct.


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