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The rate of flow (V) of a liquid flowing...

The rate of flow (V) of a liquid flowing through a pipe of radius r and pressure gradient (P/I) is given by Poiseuille's equation` V = (pi)/(8)(Pr^4)/(etaI)` Chack the dimensional correctness of this relation.

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Here, V= Rate of flow of liquid `=("Volume")/("Time")`
`[V]=([L^(3)])/([T])=[L^(3)T^(-1)]`
`(P)/(l)="Pressure gradient"= ("Pressure")/("Length")`
`[(P)/(l)]=([ML^(-1)T^(-2)])/([L])=[ML^(-2)T^(-2)]`
`r= "radius" [r]= [L]`
Now, `[eta]=[(pi Pr^(4))/(8lV)]`
`=([ML^(-2)T^(-2)][L^(4)])/([L^(3)T^(-1)])`
`=ML^(-1)T^(-1)]`.
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