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

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


\(\begin{array}{l}\eta\end{array} \)
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 = Unit of 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
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.


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