- Home/
- SSC & Railways/
- Article
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 BYJU'S Exam Prep
Updated on: September 25th, 2023
(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
Related Questions:-
- What is the Shape of the Earth
- An Electron Moving With a Velocity of 5 10 4ms 1 Enters Into a Uniform Electric Field and Acquires…
- A Train 150m Long is Running at 72 Kmhr It Crosses a Bridge in 13 Sec Find the Length of the Bridge
- A Vapour Pressure of Chloroform Chcl3 and Dichloromethane Ch2cl2 at 298 K Are 200 Mm Hg and 415 Mm Hg..
- An Athlete Completes One Round of a Circular Track of Radius R in 40 Sec What Will Be the Magnitude…
- Describe the Process of Photosynthesis