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Viscosity is the degree to which a fluid resists flow when a force is applied. The coefficient of viscosity denotes the measure of the viscosity of the fluid. Denoted by the Greek letter η (eta), it is also called dynamic viscosity.
- It is a result of the internal friction between the fluid molecules.
- Viscosity is calculated as the tangential friction force per unit area divided by the velocity gradient under streamlined flow conditions.
- The more resistant a fluid is, the higher its viscosity.
- Liquids such as water and alcohol have low viscosity and can flow more freely.
- On the other hand, honey and oil have higher viscosity, and are therefore more resistant to flow.
- The unit used to measure the coefficient of viscosity is pascal-second (Pa·s).
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Key Terms: Viscosity, Fluid, Resistance, Coefficient of viscosity, Oil, Water, Molecules, Friction
Coefficient of Viscosity
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The coefficient of viscosity is a measure of a fluid’s resistance to flow i.e. a measure of its viscosity. It is calculated using the Poiseuille’s method. In this method, a liquid flows through a tube at different pressure levels.
- The coefficient of viscosity decreases with an increase in temperature.
- Gas viscosity, on the other hand, increases with higher temperatures.
- Fluid viscosity depends on temperature as it affects molecular bonds.
- Higher temperatures lead to a weakening of bonds in fluids.
- Weakened bonds further result in decreased fluid viscosity.
- In gases, increased temperature strengthens viscosity due to changed molecular interactions.
Viscosity of a Fluid
The coefficient of viscosity is also related to the pressure of the fluid. The coefficient of viscosity increases as the pressure increases. This is why it is more difficult to pump high-viscosity fluids at high pressures.
Read More: Unit of Viscosity
Coefficient of Viscosity Formula
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The formula to calculate the coefficient of viscosity is:
η = F / (A * dv/dx)
where:
- η is the coefficient of viscosity
- F is the tangential friction force
- A is the area in square meters
- dv/dx is the velocity gradient
The velocity gradient refers to the change in velocity per unit distance. The tangential friction force is the force that resists the flow of the fluid.
Solved ExampleA ball is falling through a viscous fluid. The tangential friction force between the ball and the fluid is 0.1 N. The area of the ball in contact with the fluid is 0.01 m2. The velocity gradient of the fluid is 10 s-1. Solution: The coefficient of viscosity of the fluid can be calculated as follows: η = F / (A * dv/dx) Substituting the values in the formula - η = 0.1 N / (0.01 m2 * 10 s-1) = 1 Pa·s Therefore, the coefficient of viscosity of the fluid is 1 Pa·s. |
Unit of Coefficient of Viscosity
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Viscosity is calculated as it helps manufacturers predict how a specific material will react when consumed by the customers.
- The SI unit of the coefficient of viscosity is the pascal-second (Pa·s).
- It is also commonly expressed in centipoise (cP) and poise (P).
- The coefficient of viscosity of water at 20 °C is about 1 cP.
1 Pa·s = 10 Poise = 1000 Centipoise
Read Also: Sphygmomanometer
Things to Remember
- The coefficient of viscosity (η) is a measure of a fluid's resistance to flow.
- It is measured in Pascal-seconds (Pa·s) in the SI system.
- Dynamic viscosity refers to the resistance to flow during linear motion.
- Kinematic viscosity involves the fluid's resistance to flow under the influence of gravity.
- For liquids, viscosity tends to decrease with rising temperature.
- Viscosity is often measured using devices like viscometers, with various types such as capillary and rotational viscometers.
- It is important in petroleum, chemical, and food, influencing processes.
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Sample Questions
Ques. Give the dimensional formula of the coefficient of viscosity. (1 mark)
Ans. The dimensional formula of the coefficient of viscosity is [ML-1T-1]
where:
- M is mass
- L is length
- T is time
The coefficient of viscosity is force per unit area divided by a velocity gradient.
- The force is in Newtons
- Area is in square meters
- Velocity gradient is in inverse seconds.
Therefore, the coefficient of viscosity has the dimensions of [ML-1T-1].
Ques. What is the coefficient of viscosity of glycerine? (1 mark)
Ans. The coefficient of viscosity of glycerine at room temperature is about 1.49 Pa·s. Glycerine is a very viscous fluid. It has a high resistance to flow. Therefore, it is used in lubricants and food additives.
Ques. Derive the coefficient of viscosity formula. (5 marks)
Ans. The coefficient of viscosity formula can be derived from W = Fd
where:
- W is the work done
- F is the force applied
- d is the displacement
If fluid pushed by a force F is flowing through a pipe, it resists the force due to its viscosity. The work done is equal to the potential energy lost by the fluid. This potential energy is converted into kinetic energy.
The coefficient of viscosity is the ratio of the tangential friction force to the velocity gradient. The coefficient of viscosity formula is:
η = F / (A * dv/dx)
The velocity gradient is calculated as follows:
dv/dx = (v2 - v1) / d
The tangential friction force is calculated as follows:
F = η * A * dv/dx
Substituting this equation into the equation for the velocity gradient, we get the coefficient of viscosity formula:
η = F / (A * dv/dx)
= F / (A * (v2 - v1) / d)
= Fd / (A * (v2 - v1))
Ques. How does the coefficient of viscosity affect the flow of fluids? (2 marks)
Ans. A fluid with a high coefficient of viscosity will flow more slowly than a fluid with a low coefficient of viscosity. Fluids with high coefficients of viscosity are also more difficult to pump.
Ques. Give an application of the coefficient of viscosity. (3 marks)
Ans. It is important to consider the coefficient of viscosity of a lubricant when choosing it for a particular application.
- A lubricant with a high coefficient of viscosity will provide more protection against wear and tear.
- However, it will also be more resistant to flow, which can lead to increased friction and heat generation.
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