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Kinematic viscosity is determined by dividing the fluid mass density by the dynamic fluid, viscosity, or absolute fluid viscosity. It is also known as momentum diffusivity on occasion. In terms of both time and space, kinematic viscosity is calculated. The dynamic viscosity-to-density ratio is a measure that is not reliant on any particular force.
Read more: Force and Acceleration
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KeyTerms: Viscosity, kinematics, fluid, dynamic, absolute, dimensional, density.
What is Viscosity?
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A fluid's struggle to flow while being deformed by extensional or shear pressures is described by the concept of viscosity. Kinematic viscosity is determined by dividing the fluid mass density by the dynamic fluid, viscosity, or absolute fluid viscosity.
Viscosity
- It is occasionally referred to as momentum diffusivity.
- Kinematic viscosity is measured in terms of time and space.
- It is a force-independent quantity that is the dynamic viscosity to density ratio.
- It is referred to as m/s or ft22/s since it is the ratio of the area of time.
The video below explains this:
Viscosity Detailed Video Explanation:
Property of Viscosity
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The property of Viscosity are as follows:
- It resists movement.
- It behaves tangentially by moving anticlockwise to the direction of motion.
- It becomes relevant when a liquid's two layers are moving relative to one another.
Formula for Kinematics Viscosity
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The following is the formula for kinematic viscosity:
v = μ / ρ
μ = absolute or dynamic viscosity
ρ = Density
Dimensional Formula for Kinematics Viscosity
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Kinematic Viscosity's dimensional formula is represented by the M0 L2 T-1.
where,
M = stands for mass
L = for length
T = for time
Kinematic viscosity (ν) = Dynamic viscosity × [Density]-1. . . . (1)
Density = Mass × [Volume]-1
⇒ ρ = [M1 L0 T0] × [M0 L3 T0]-1
The density dimensional formula = [M1 L-3 T0] . . . . (2)
Dynamic viscosity (η) = Tangential Force × distance between layers × [Area × velocity]-1 . . . . (3)
Tangential Force = M × a = M × [L T-2]
The dimensions of force = M1 L1 T-2 . . . . (4)
The area and velocity dimensional formula = L2 and L1 T-1 . . . . (5)
When we substitute equations (4) and (5) into equation (3), we get
Dynamic viscosity (η) = [M L T-2] × [L] × [L2]-1 × [L1 T-1]-1 = [M1 L-1 T-1].
The dynamic viscosity dimensions = [M1 L-1 T-1] . . . .(6)
When we substitute equations (2) and (6) into equation (1), we get
Kinematic viscosity (ν) = Dynamic viscosity × [Density]-1
Or, ν = [M1 L-1 T-1] × [M1 L-3 T0]-1 = [M0 L1 T-1].
Kinematic viscosity is represented dimensionally as [M0 L2 T-1].
Read more:
| Relevant Concepts | ||
|---|---|---|
| Unit of pressure | Mechanical properties of fluid | Newton’s law of motion |
| Unit of specific resistance | Ohm’s law | Continuity Equation |
Things to remember
- Viscosity is a term used to indicate a fluid's difficulty in flowing while being bent by extensional or shear pressures.
- The formula for kinematic viscosity is:
- v = μ / ρ
- Dimensionally kinematic viscosity is represented as ρ = [M1 L0 T0] × [M0 L3 T0]-1
- Kinematic viscosity moves anticlockwise to the direction of motion and exhibits tangential behavior.
- In terms of both time and space, kinematic viscosity is calculated.
Sample Questions
Ques. What does kinematic viscosity mean? (2 marks)
Ans. The internal resistance of a fluid to flowing under the influence of gravity is known as kinematic viscosity. It is calculated by timing in seconds how long it takes for a fixed volume of fluid to travel a specific distance by gravity via a capillary inside of a calibrated viscometer at a precise temperature.
Ques. What are the properties that depend on viscosity? (5 marks)
Ans. The properties that influence viscosity are as follows:
- Regarding fluid temperature: Cohesive force diminishes as temperature rises. As a result, liquid viscosity falls as temperature increases.
- Gas molecules diffuse from one moving layer to another moving layer, which causes the viscosity of gasses.
- The rate of diffusion now increases as the temperature rises.
- As a result, the viscosity of gasses increases as temperature rises.
- In relation to fluid pressure: When pressure is increased, liquids become more viscous. Practically regardless of pressure, gas viscosity increases.
Ques. What are Dimensional Formula Limitations? (4 marks)
Ans. Only dependencies of the multiplication type are eligible for usage with this method. This approach cannot be used to create a formula including exponential, trigonometric, and logarithmic functions. It is also impossible to construct formulas with several terms that are added or subtracted, such as s = ut + 1/2 at2. This method's relation does not reveal anything about the dimensionless constants.
Ques. Explain about the Viscosity Characteristics? (3 marks)
Ans. The following section discusses a few viscosity properties:
- It resists motion, for one.
- It behaves tangentially in the opposite direction of motion.
- It is activated when the two liquid layers are moving relative to one another.
Ques. A fluid having kinematic viscosity of 3 m2 /s and absolute viscosity of 0.98 Ns / m2. calculate the fluid's density? (4 marks)
Ans. Given in the question,
Absolute viscosity is equal to 0.98 N/m2.
Kinematic viscosity is equal to 3 m2/s.
ν = μ / ρ
Density is provided by,
ρ = ν / μ
ρ = 3 / (0.98) (0.98)
ρ = 3.0612 kg / m3
So a liquid has a density of 3.0612 kg / m3.
Ques. Why is kinematic viscosity necessary? (2 marks)
Ans. An essential characteristic of fuel is kinematic viscosity, which has a direct bearing on the effectiveness of fuel atomization and the size of the fuel droplet in the spray. In general, the ASTM Standard D445 and EN 3104 test procedures are used to determine kinematic viscosity.
Ques. Define Kinematic viscosity? (1 mark)
Ans. When a liquid is at the same temperature, its kinematic viscosity is calculated by dividing its absolute viscosity by its density.
Ques. Define pure kinematics? (1 mark)
Ans. The area of mechanics that studies pure motion without taking into account the masses or forces at play.
Ques. What is the kinematic viscosity of a liter of 2 kg of mercury? (4 marks)
Ans. The answer is that mercury has a dynamic viscosity of 1.526 Pa*s. Using the equation mass ρ = mass/volume, first determine the density mass of mercury.
ρ = 2 kg per one liter, or 2000 kg per cubic meter.
then utilize its formula to determine the kinematic viscosity,
v = η / ρ
(1.526 N*s/m2) / (2000 Kg/m3) = 1.526 Pa*s / 2000 Kg/m3
ν = 0.000763 m2/s
Ques. What is the density of a fluid whose dynamic viscosity is 0.018 Pa*s and whose kinematic viscosity is 1 m2/s? (2 marks)
Ans. We can determine the density using the kinematic viscosity formula,
After inserting the values for ρ = η / v,
The formula is: ρ = (0.018 N*s/m2) / (1 m2/s) = 0.018 Kg/m3.
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