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The volume of a liquied flowing out per ...

The volume of a liquied flowing out per second of a pipe of length I and radius r is written by a student as `upsilon =(pi)/(8)(Pr^4)/(etaI)` where P is the pressure difference between the two ends of the pipe and `eta` is coefficient of viscosity of the liquid having dimensioal formula `ML^(-1)T^(-1).` Check whether the equation is dimensionally correct.

Text Solution

Verified by Experts

The given relation is `upsilon = (pi)/(8) (Pr^4)/(eta I)`
`LHS = upsilon = (L^3)/(T) = L^3 T^(-1) = [M^0 L^3 T^(-1)]`
`RHS = (pi)/(8) (P r^4)/(eta I) = (ML^(-1)T^(-2)(L^4))/(ML^(-1)T^(-1)(L)) = [M^0 L^3 T^(-1)]`
As LHS = RHS, dimensionally. :. Formula is dimensionally correct.
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Knowledge Check

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