Dimensions of Viscosity

When the fluid exerts resistance against its motion or flow, its measurement is called viscosity. Viscosity can be symbolised by formula . Fluids that exhibit viscous resistance, like, honey, oil, cream, ink, and so on, are utilised daily. The dimensions of viscosity are used to derive the formula or equation slang with the measurements of viscous fluids.

Non-viscous vs Viscous Fluid

Image: Non-viscous vs Viscous Fluid

Table of Contents:

The Formula of Viscosity
Units of Viscosity
Dimensional Formula of Viscosity
Derivation of Viscosity
Uses of Dimensional Formula of Viscosity
Restrictions of Dimensional Formula of Viscosity
Practice Problems
Frequently Asked Questions

The Formula of Viscosity

Viscosity is the calculation of the ratio between shearing stress with the fluid’s velocity gradient. Mathematically, if a sphere is dipped in any viscous fluid, the formula can be expressed as follows:

formula

Where formula represents the density difference between the fluid and sphere tested

formula illustrates the radius of the sphere

formula denotes the velocity of the sphere, and

g is the acceleration due to gravity.

Units of Viscosity

Viscosity can be measured in Poiseuille, denoted by PI (SI Unit). Also, Newton-second per square metre (Nsm^-2) or Pascal-second (Pa - s) can be used to measure the viscosity value.

Dimensional Formula of Viscosity

The formula for the dimensions of viscosity can be expressed as follows:

formula

M expresses the Mass,

L determines the Length, and

T is the Time.

Derivation of Viscosity

The formula for the dimensions of viscosity can be derived via the following steps.

Viscosity = Tangential Force Distance between Layers [Area Velocity]^-1 ------ (Equation 1)

We know formula

Therefore, the dimensional formula of Tangential Force formula —---- (Equation 2)

The dimensional formula of Area formula

The dimensional formula of Velocity formula —------- (Equation 3)

Now, we substitute equations 2 and 3 in equation 1. We get

Viscosity = Tangential Force Distance between Layers [Area Velocity]-1

formula .

Therefore, the formula for the dimensions of viscosity can be illustrated as formula .

Uses of Dimensional Formula of Viscosity

There are various uses of the dimensional formula of viscosity. They include the following:

It assists in checking the correctness and consistency of the formulas and equations.
Aids in deriving new formulas and equations.
Helps in performing the approximate measurements and estimates of physical quantities.
It helps in the conversion of units of one system to another.
The dimensional formula aids in determining the relationship between two or more variables.

Restrictions of Dimensional Formula of Viscosity

Despite various benefits, dimensional formulas also hold certain limitations. They include the following:

They avoid dimensionless contents and ratios.
It does not determine whether the physical quantity is vector or scalar.
They cannot work for non-linear relationships between the variables.
Strictly restricted to homogeneous formulas or equations.
It does not provide any accurate numeric values.
Provide an incomplete illustration of the intricacies of physical phenomenons.

Practice Problems

Q1. Choose the correct formula of viscosity

formula

Q2. The symbol that denoted the viscosity

formula

Q2. Choose the correct formula for the dimensions of viscosity.

a. formula

formula

Q4. The SI unit of viscosity is

a. Poiseuille
b. Ampere
c. Coulomb
d. Pascal

Ans. a. Poiseuille

Q5. A U-tube viscometer is also called

a. Glass capillary viscometer
b. Ostwald viscometer
c. Bulb capillary
d. Both a and b

Ans : d. Both a and b

Glass capillary viscometers and Ostwald viscometers are the other names of U-tube viscometers.

formula

Image: U-Tube Viscometers

Frequently Asked Questions

Q1. What are the different types of viscosity?
Answer: The measurement of fluid causing friction to its flow is called viscosity, and the measurement can be performed in two ways, i.e., dynamic viscosity and kinematic viscosity.

Q2. State one difference between Newtonian and non-newtonian fluids.
Answer: Newtonian fluid follows Newton’s law of constant viscosity and remains constant when the applied stress or deformation rate is intense. At the same time, non-newtonian fluid does not possess constant viscosity and varies based on the magnitude of applied stress.

Q3. What is stress?
Answer: The force exerted within a substance per unit is due to the external force applied is called stress. The impact of that stress is called strain. The symbol denotes stress is formula . The stress formula can be expressed as formula .