Solved Examples on Viscosity
Example 1: There is a 3 mm thick layer of glycerin between a flat plate and a large plate. If the viscosity coefficient of glycerin is 2 N s/m2 and the area of the plane plate is 48 cm. How much force is required to move the plate at a speed of 6 cm/s?
Solution:
Given,
- Thickness of the layer, dx = 3 mm = 3 × 10-3 m.
- Coefficient of viscosity, η = 2 N s/m2
- Change in speed, dv = 6 cm/s = 6 × 10-2 m/s.
- Area of the plate, A = 48 cm2 = 48 × 10-4 m2
Formula to calculate the force required to move the plate is,
F = ηA × (dv/dx)
Substitute the given values in the above expression as:
F = 2 N s/m2 × 48 × 10-4 m2 × (6 × 10-2 m/s / 3 × 10-3 m)
= 192 × 10-3 N
= 0.192 N
Example 2: The diameter of a pipe is 2 cm. what will be the maximum average trick of water for level flow? The viscosity coefficient for water is 0.001 N-s/m2.
Solution:
Given,
- Diameter of the pipe, D = 2 cm = 0.02 m
- Viscosity coefficient, η = 0.001 N-s/m2
- Density of water, ρ = 1000 kg/m3
Since, the maximum value of K for level flow is 2000
Therefore, the formula to calculate the maximum speed of water is,
v = Kη / ρD
Substitute the given values in the above expression to calculate v as,
v = 2000 × 0.001 N-s/m2 / 1000 kg/m3 × 0.02 m
= 0.1 m/s
Example 3: The shear stress at a point in a liquid is found to be 0.03 N/m2. The velocity gradient at the point is 0.21 s-1. What will be its viscosity?
Solution:
Given,
- Shear stress, F/A is 0.03 N/m2
- Velocity gradient, dv/dx is 0.21 s-1
Formula to calculate the viscous force is,
F = -ηA (dv/dx)
η = -(F/A) / (dv/dx)
Substitute the given values in the above expression to calculate η
η = – 0.03 N/m2 / 0.21 s-1
= – 0.14 N s/m2
Example 4: Water is flowing slowly on a horizontal plane, the viscosity coefficient of water is 0.01 poise, and its surface area is 100 cm2. What is the external force required to maintain the velocity gradient of the flow 1 s-1?
Solution:
Given,
- Viscosity coefficient of water, η = 0.01 poise = 0.001 kg/ms
- Surface area, A = 100 cm2 = 10-2 m2
- Velocity gradient of the flow, dv/dx = 1 s-1
Formula to calculate the viscous force,
F = -ηA (dv/dx)
Substitute the given values in the above expression to calculate F
F = 0.001 kg/ms × 10-2 m2 × 1 s-1
= 10-5 N
Read, More,
What is Viscosity?
Viscosity is the measurement of the resistance of the flowing liquid. Let us learn more about viscosity with an example suppose we take two bowls, one bowl contains water and the other has honey in it, we drop the content of both bowls then we see that water flows much faster than honey which concludes that honey is more viscous than water.
Viscosity is the property of the liquids that prevents liquids from spreading. The force generated due to viscosity is called Viscous Force. Since this force is between the layers of liquids, it is also called internal friction. In this article, we will learn about viscosity its formula, measurement, and much more in detail.
Table of Content
- What is the Meaning of Viscosity?
- Viscosity Formula
- Types of Viscosity
- Measurement of Viscosity
- Applications of Viscosity
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