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The volume of a liquid flowing out per s...

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 the pressure 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.

Text Solution

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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.
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