Unit of Coefficient of Viscosity

What is the Coefficient of Viscosity?

The coefficient of viscosity is defined for two parallel layers of liquid as the tangential force required to maintain unit velocity gradient between these layers.

The other way of defining the coefficient of viscosity is as the ratio of shear stress to the velocity gradient of the fluid. Mathematical representation is:

Where,

𝛈: coefficient of viscosity

F: tangential force

A: area

v: velocity

r: the distance between the layers

Dimensional Formula of Coefficient of Viscosity

Mathematical representation is:

\(\begin{array}{l}\eta =\frac{Fr}{Av}\end{array} \)

Dimensional formula of force F: M¹L¹T^-2

Dimensional formula of area A: M⁰L²T⁰

Dimensional formula of distance r: M¹L¹T⁰

Dimensional formula of velocity v: M⁰L¹T^-1

\(\begin{array}{l}[\eta] =\frac{\left [ M^{1}L^{1}T^{-2} \right ]\left [ M^{0}L^{1}T^{0} \right ]}{\left [ M^{0}L^{2}T^{0} \right ]\left [ M^{0}L^{1}T^{-1} \right ]}=\left [ M^{1}L^{-1}T^{-1} \right ]\end{array} \)

Dimensional formula of coefficient of viscosity η: M¹L^-1T^-1

Unit of Coefficient of Viscosity

Following is the unit of coefficient of viscosity in different systems:

• SI unit: Ns.m^-2
• CGS unit: poise

Coefficient of Viscosity of Liquid

The coefficient of viscosity of a liquid is defined as the viscous force acting per unit area between two adjacent layers of a liquid such that the velocity gradient is normal to the direction of flow of the liquid. Mathematically it is given as:

\(\begin{array}{l}\eta =\frac{F}{A(\frac{dv}{dx})}\end{array} \)

Where,

F: viscous force

A: unit area

\(\begin{array}{l}\frac{dv}{dx}: \,\, \textup{velocity gradient}\end{array} \)

SI unit of coefficient of viscosity of the liquid is kg m^-1 s^-1 which is similar to the unit of viscosity.

Coefficient of Viscosity of Water

Using Poiseuille’s law, liquid flow through a capillary tube of a uniform cross-section, and the coefficient of viscosity of water can be measured.

\(\begin{array}{l}V=\frac{\pi Pr^{4}}{8\eta L}\end{array} \)

\(\begin{array}{l}\eta = \frac{\pi Pr^{4}}{8VL}\end{array} \)

Where,

P: pressure difference between the two ends

L: length of the capillary tube

r: inner radius of the capillary

V: volume of the liquid

𝛈: coefficient of viscosity

Related Physics Articles:

Viscosity

Surface Tension

Fluid Flow

 

Frequently Asked Questions – FAQs

Q1

What is viscosity?

In the case of fluids, viscosity is the measurement of the fluid’s resistance to deformation at a given speed. In liquid, it is generally referred to as thickness.

Q2

What is the unit of viscosity?

The SI unit of viscosity is the pascal second (Pa·s).

Q3

What is Newton’s law of viscosity?

Newton’s law of viscosity describes that shear stress between the consecutive layers of a particular fluid is proportional to the velocity gradients between the liquid’s two layers.

Q4

What is meant by the coefficient of viscosity?

The coefficient of viscosity is defined for two parallel layers of liquid as the tangential force required to maintain a unit velocity gradient between these layers. In other words, the coefficient of viscosity is the ratio of shear stress to the velocity gradient of the fluid.

Q5

What is meant by the coefficient of viscosity of a liquid?

The coefficient of viscosity of a liquid is defined as the viscous force acting per unit area between two adjacent layers of a liquid such that the velocity gradient is normal to the direction of flow of the liquid.

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