The volume of a liquid flowing out per second of a pipe of length I and radius r is written by a student as V=(pi)/(8)(pr^(4))/(etal) where p is thepressure difference between the two ends of the pipe and eta is coefficent of viscosity of the liquid having dimensional formula (ML^(-1)T^(-1)). Check whether the equation is dimensionally correct.

The volume of a liquid flowing out per second of a pipe of length I an

1.	The volume of a liquid flowing out per second of a pipe of length I and radius r is written by a student as V=(pi)/(8)(pr^(4))/(etal) where p is thepressure difference between the two ends of the pipe and eta is coefficent of viscosity of the liquid having dimensional formula (ML^(-1)T^(-1)). Check whether the equation is dimensionally correct.
Answer» <P> Solution :The VOLUME of a liquid flowing out per second of a pipe is GIVEN by `V=(pi)/(8)(pr^(4))/(etal)` `[V]=(["Volume"])/(["Time"])=([L^(3)])/([T])=L^(3)T^(-1)` `[p]=[ML^(-1)T^(-2)]` `[eta]=[ML^(-1)T^(-1)]` `[l]=[L]` `[r]=[L]` `[LHS]=[V]=([L^(3)])/([T])=L^(3)T^(-1)` `[RHS]=([ML^(-1)T^(-2)]xx[L^(4)])/([ML^(-1)T^(-1)]xx[L])=[L^(-3)T^(-1)]` `[LHS]=[RHS]` Thus, equation is dimensionally correct.