Question

The dimension of coefficient of viscosity is :

Answer 1

Hola!

Here is the answer for your question!

≫ ──── ≪•◦ ❈ ◦•≫ ──── ≪

Q)The dimension of coefficient of viscosity is :

≫ ──── ≪•◦ ❈ ◦•≫ ──── ≪

Answer:-

► Coefficient of viscosity is defined as the amount of resistance a fluid exerts against flow caused by external force

► Coefficient of viscosity is expressed by the formula :

$η = \frac{tangential force \: \times distance \: between \: layers}{area \: of \: layer \: \times velocity}$

or

$η = \frac{f \times r}{a \times v}$

now, dimensional formula of each term in the formula :

Force =

${M}^{1} {L}^{1} {T}^{ - 2}$

Distance =

${M}^{0} {L}^{1} {T}^{0}$

Area =

${M}^{0} {L}^{2} {T}^{0}$

Velocity =

${M}^{0} {L}^{1} {T}^{ - 1}$

Putting these values into the formula for coefficient of viscosity :

$η = \frac{( {M}^{1} {L}^{1} {T}^{ - 2})( {M}^{0} {L}^{1} {T}^{0}) }{ ({M}^{0} {L}^{2} {T}^{0})( {M}^{0} {L}^{1} {T}^{ - 1}) }$

Hence,

Dimensional formula of Coefficient of viscosity =

$({M}^{1} {L}^{ - 1} {T}^{ - 1} )$

≫ ──── ≪•◦ ❈ ◦•≫ ──── ≪

Hope this helped with your doubt :)

Answer 2

Explanation:

Dimensional Formula of Coefficient of Viscosity

The dimensional formula of Coefficient of Viscosity is given by,

M1 L-1 T-1

Where,

M = Mass

L = Length

T = Time

Derivation

Coefficient of viscosity (η) = F × r × [A × v]-1 . . . . . (1)

Where F = tangential force, r = distance between layers, A = Area, and v = velocity

Since, Tangential Force (F) = Mass × Acceleration = M × [L T-2]

∴ The dimensional formula of force = M1 L1 T-2 . . . . (2)

And, the dimensional formula of area and velocity = L2 and L1 T-1 respectively . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Coefficient of viscosity = F × r × [A × v]-1

Or, η = [M L T-2] × [L] × [L2]-1 × [L1 T-1]-1 = [M1 L-1 T-1].

Therefore, the Coefficient of Viscosity is dimensionally represented as [M1 L-1 T-1].

Coefficient of viscosity is defined as tangential force required to maintain a unit velocity gradient between two parallel layers of liquid of unit area.

Mathematically,

Coefficient of viscosity (η)= Fr/Av where F = tangential force, r = distance between the layers , v = velocity.

Dimensional Formula of Force = M1L1T-2

Dimensional Formula of Area= M0L2T0

Dimensional Formula of distance= M0L1T0

Dimensional Formula of velocity= M0L1T-1

Putting these values in above equation we get,

[η]= [M1L1T-2][M0L1T0] / [M0L2T0] [M0L1T-1] = [M1L-1T-1]

Dimensional Formula of Coefficient of viscosity (η)=[M1L-1T-1]

SI unit of Coefficient of viscosity (η) is Pascal-second

Please mark me as Brainliest,Thank you and follow me.