# Dynamic Viscosity Formula

Dynamic Viscosity Formula for a fluid defines its internal resistance to flow due to some shearing force. A tangential force which acts when one horizontal plane moves with another one. The viscosity acts an important fluid property while analyzing the liquid behaviour and fluid motion near solid boundaries.

Formula for Dynamic Viscosity

T = μμ uyuy.

Where,

u= shear velocity (m/s),

y= distance between the layers,

T =shearing stress,

μμ = dynamic viscosity (Ns/m22).

The SI unit for Dynamic Viscosity = Ns/m22, Pa s or kg/ms.

Question 1: A fluid is flowing between two layers. Find the shearing force if the shear velocity is 0.25 m/s and has length 2 m and dynamic viscosity is 2Ns/m22.

Solution:

Given:

Shear velocity u = 0.25 m/s,

shear stress y = 0.125/s

dynamic viscosity μμ = 2 Ns/m^2

The shearing stress is given by,

F = μμ A uyuy

F = 2 Ns/m22 ×× 0.125 /s

F = 0.5 N/m22

Therefore, the shearing stress is 0.5 N/m22.

Question 2: A fluid moves along length 0.75 m with velocity 2m/s and has shearing stress of 2 N/m22. Find its dynamic viscosity.

Solution:

Given: Shear velocity u = 2m/s, length y = 0.75 m, shearing stress T = 2 N/m22

The shearing stress is given by,

T = μμ uyuy.

μμ = T yuyu

μμ = 2 N/m22 ×× 0.375 m/s

μμ = 0.75 Ns/m22.

Therefore, the dynamic viscosity = 0.75 Ns/m22.