“Coefficient of Viscosity and Stoke’s Law” MHT-CET Class 12 Physics Crash Course | Chapter Mechanical Properties of Fluids
In this session G.S. Khairnar discussed the theory and MCQ’s of “Coefficient of Viscosity and Stoke’s Law”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Coefficient of Viscosity and Stoke’s Law:-
Hello dear students, in previous articles we had learnt about the viscosity and the velocity gradient. The property by virtue of which there is opposition to relative motion between the layers of liquid is called as viscosity.
The liquid with more viscosity flows slowly than that of liquid with low value of viscosity. Eg. honey and water
Also ratio of change in velocity per unit change in distance of the layer is constant for the given liquid known as velocity gradient.
Velocity gradient is helpful to understand the viscous force acting on the area of fluid.
Let’s discuss the concept of for coefficient of viscosity……………!
According to Sir Isaac Newton,
Viscous force acting between the layers of liquid in streamline flow depends upon two factors viz. area of layer and velocity gradient. Newton said that, the viscous force is
- Directly proportional to area (A) of layer
- Directly proportional to velocity gradient of liquid
Then from the above conditions we can write that,
Where ‘η’ is constant of proportionality known as coefficient of viscosity. From above equation we have,
Hence coefficient of viscosity is defined as ‘the viscous force acting per unit area per unit velocity gradient of liquid.’
Some important points to note…!
- The formula for coefficient of viscosity is valid for streamline flow only.
- Coefficient of viscosity for liquid decreases with increase in temperature.
- Coefficient of viscosity for gases increase with increase in temperature.
- SI unit of coefficient of viscosity is N. s/m2 and CGS unit is dyne.s/cm2 or poise
Where, 1 N.s/m2= 10 poise
- Dimensions of coefficient of viscosity are, [M1L-1T-1]
Now we are going to learn about the Stoke’s law…………..!
Consider the spherical body of radius ‘r’ is falling freely in viscous fluid as shown in fig. below,
Let, η=coefficient of viscosity of fluid
r=radius of spherical body
v=velocity of spherical body
When the spherical body is falling in viscous fluid, the velocity of body is decreases due to opposition by fluid. This means that the fluid has exerted the force on spherical body.
Sir G. Stoke’s has given as law to find the magnitude of viscous force acting on the spherical body. The Stoke’s law stated as,
“Viscous force acting on the spherical body falling freely in viscous fluid is directly proportional to,
- Velocity of body (v).
- Radius of spherical body(r).
- Coefficient of viscosity of fluid (η).
∴ F α r∙v∙η
∴ F=k∙ r ∙v ∙η
Where ‘k’ is constant of proportionality.
The magnitude of k was obtained through some experiments and it is given by,
k=6π
Then the formula for viscous force acting on the spherical body falling freely in viscous fluid is,
∴ F=6π∙ r∙ v ∙η
This formula can be verified dimensionally for checking its correctness.
Coefficient of Viscosity and Stoke’s Law:-
Let’s solve following MCQ’s…….!
Q.1) Which among the following is correct formula to find coefficient of viscosity of fluid?
Q.2) Relation between SI and CGS unit of coefficient of viscosity is…
a) 1 N.s/m2= 10 poise
b) 10 N.s/m2= 1 poise
c) 1 N.s/m2= 100 poise
d) 100 N.s/m2= 1 poise
Answer
a) 1 N.s/m2= 10 poise
Q.3) Fluid layers of surface area 32 cm2 and velocity gradient of 1.6 cm/s exerts the viscous force of magnitude 64×10-6 N. Coefficient of viscosity of fluid is….
a) 25 poise
b) 12. 5 poise
c) 125 poise
d) None of these
Answer
b) 12. 5 poise
Q.4) Coefficient of viscosity of layers of fluid is 0.8 poise area of layers 12 cm2 and velocity gradient is 2.4 cm/s. The viscous force acting between layers is….
a) 2.3 N
b) 2.3 mN
c) 2.3 kN
d) 2.3 μN
Answer
b)
Q.5) According to Stoke’s viscous force acting on spherical body falling freely in viscous fluid is ….
a) Directly proportional to velocity of body
b) Directly proportional to radius of body
c) Directly proportional to coefficient of viscosity of fluid
d) all of these
Answer
d) all of these
Q.6) A spherical metal ball of radius 4 mm falling at the rate of 2.5 cm/s in humid air having coefficient of viscosity of 1.2 poise. Viscous force acting on the ball is
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