If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [ηx ρy rz] , where η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then values of x, y and z are given by

By K Balaji|Updated : November 12th, 2022

(a) 1, 1, 1

(b) 1, -1, -1

(c) -1, -1, 1

(d) -1, -1, -1

We know that

[V] = [LT-1]

η = F/ A dv/dx

[η] = [MLT-2]/[L2] [T-1] = [M1L-1T-1]

[ρ] = [ML-3]

[LT-1] = [M1L-1T-1]x [ML-3]y [L]z

Equating the exponents of M, L and T on both LHS and RHS

M0 = M (x + y)

y = -x

For T,

-1 = -x

x = 1

y = -x = -1

For L

1 = -x - 3y + z

1 = 2 + z

z = -1

Viscosity

We call this impedance to motion that most fluids offer by virtue of their "viscosity." Viscosity forms when there is relative mobility between the fluid's layers. It measures flow resistance that is primarily caused by internal friction between fluid layers as they pass one another during fluid flow. A fluid's thickness or resistance to being pierced by outside objects are both referred to as "viscosity."

In a fluid with a high viscosity, strong intermolecular forces cause a lot of internal friction, which makes it challenging for layers to pass one another. On the other hand, a fluid with low viscosity flows easily because its molecular structure produces less friction when it is in motion. Gases also have viscosity, however it is less noticeable in normal circumstances.

Summary:-

If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [ηx ρy rz] , where η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then values of x, y and z are given by (a) 1, 1, 1 (b) 1, -1, -1 (c) -1, -1, 1 (d) -1, -1, -1

If dimensions of critical velocity vc of a liquid flowing through a tube are expressed as [ηx ρy rz] , where η, ρ and r are the coefficient of viscosity of liquid, density of liquid and radius of the tube respectively, then values of x, y and z are given by 1, -1, -1

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