 # 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

$$\begin{array}{l}\eta =\frac{\tau }{\gamma }\end{array}$$

Where,

$$\begin{array}{l}\eta\end{array}$$
is the dynamic viscosity
$$\begin{array}{l}\tau\end{array}$$
is the Shearing stress
$$\begin{array}{l}\gamma\end{array}$$
is the Shear rate

The SI unit for Dynamic Viscosity =

## Solved Example

Question:Consider a fluid with shear rate of 0.5 s-1and a shearing stress of 0.76 N/m2. According to its dynamic viscosity, to which one of these fluids corresponds?
a. water: 1 Pa*s
b. air: 0.018 Pa*s
c. mercury: 1.526 Pa*s
Solution:
Substituting the given value in the equation above, we get

$$\begin{array}{l}\eta =\frac{\tau }{\gamma }\end{array}$$

$$\begin{array}{l}\eta =\frac{0.76 }{0.5}=1.52\,Pa*s\end{array}$$

The fluid corresponds to mercury.