Question

Check the correctness of the relation : `upsilon = (pi P(a^2 - x^2))/(2etaI),`
Where`upsilon` is velocity, p is pressure difference, a is radius of tube, x is distance from the axis of tube, `eta` is coeff. Of viscosity and I is length of the tube.

Answer 1

`LHS = upsilon = [M^0 L^1 T^(-1)]`
`RHS = (pi p(a^2 - x^2))/(2 eta I) = ([ML^(-1) T^(-2)]L^2)/([ML^(-1) T^(-1)][L])`
` = [M^0 L^1 T^(-1)]`
As dimensions on both sides are same, the
formula is correct.