Question

the critical velocity of the flow of a liquid through a pipe of radius r is given by vc=kn/ rp where p is the densityand n is the coefficient of viscosity of the liquid. check if this relation is dimensionally correct



​

Answer 1

Answer ⇒ The given relation is dimensionally correct.

Explanation ⇒ For the equation to be dimensionally correct, dimension of L.H.S. must be equal to dimension on R.H.S.

For L.H.S.,

Dimension of L.H.S. = Velocity dimension = LT⁻¹.

For R.H.S.,

Dimension of R.H.S. = [η]/[r][p]

Since, k is Reynold's number which is dimensionless.

[η] = ML⁻¹T⁻¹

[r] = L and [p] = ML⁻³

∴ [η]/[r][p]  = [ML⁻¹T⁻¹][L⁻¹][M⁻¹L³]

= LT⁻¹

Since, the dimension of L.H.S. = R.H.S.

Hence, the given relation is dimensionally correct.

Hope it helps.

Answer 2

Answer:

L.H.S= R.H.S

Explanation:

correct answers