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The volume of a liquied following out pe...

The volume of a liquied following 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

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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)`
`"Dimension of "V="Dimension of volume"/"Dimension of time"=([L^(3)])/([T])=[L^(3)T^(-1)]`
`(therefore V" is the volume of liquid flowing out per second")`
`"Dimension of "p=[ML^(-1)T^(-2)]`
`"Dimension of "eta=[ML^(-1)T^(-1)]`
`"Dimension of "l=[L]`
`"Dimension of "r=[L]`
`"Dimensions of "LHS,[V]=([L^(3)])/([T])=[L^(3)T^(-1)]`
`"Dimensions of "RHS, ([ML^(-1)T^(-2)]xx[L^(4)])/([ML^(-1)T^(-1)]xx[L])=[L^(3)T^(-1)]`
As dimensions of LHS is equal to the dimensions of RHS.
Therefore, equation is correct dimensionally.
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