Q37 of 44 Page 9

The volume of a liquid flowing out per second of a pipe of length l and radius r is written by a student as


where P is the pressure difference between the two ends of the pipe and η is coefficient of viscosity of the liquid having dimensional formula ML-1 T-1. Check whether the equation is dimensionally correct.


Given:


The equation for volume flow per second V=


The for the equation to be dimensionally correct the the dimensional formula of the equation must be equal to the dimensional formula of the volume flow per second.


Thus dimensional formula of


Dimensional formula of pressure


Dimensional formula of coefficient of viscosity


Dimensional formula of length


Dimensional formula of radius


Thus dimensional formula of RHS of the equation




And dimensional formula of LHS



Therefore, LHS = RHS


Thus, the given equation is dimensionally correct.


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