# 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.

## The formula for Dynamic Viscosity

$\mu =\tau y/u$

Where,

u = shear velocity (m/s)

y = distance between the layers

$\tau$= shearing stress

μ = dynamic viscosity

The SI unit for Dynamic Viscosity = $Ns/m^{2}$

## Solved Example

Question: 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 $\tau$ = 2 $Ns/m^{2}$

The shearing stress is given by,

$\mu =\tau y/u$

μ= 2 * 0.75/2

μ= 0.75 $Ns/m^{2}$

Therefore, the dynamic viscosity = 0.75 $Ns/m^{2}$