MCQ
What is $\ce{SI}$ unit of viscosity coefficient $(\eta )\ ?$
- Apascal.
- ✓$Nsm^{-2}$.
- C$km^{-2}s.$
- DNone of these
✓
Answer
Correct option: B.
$Nsm^{-2}$.
The $\text{SI}$ unit of velocity coefficient $(\eta)$ is $N m^{-2} s$ or $ N m^{-2}$
As we know that, $\text{f}=\eta\text{A}\frac{\text{dv}}{\text{dx}}$
Where, $f =$ force
$(\eta) =$ viscosity coefficient.
$\frac{\text{dv}}{\text{dx}}=$ velocity gradient.
Substitute $\text{SI}$ units of $f = N, dx = m, A = m^2$ and $v = m s^{-1}$ in above equation,
We get,
$\eta=\frac{\text{N}\times\text{m}}{\text{m}^2\times\text{m s}^{-1}}=\text{N m}^{-2}\text{s}$
Hence, the $\text{SI}$ unit of $\eta =$ is $N s m^{-2}$.
As we know that, $\text{f}=\eta\text{A}\frac{\text{dv}}{\text{dx}}$
Where, $f =$ force
$(\eta) =$ viscosity coefficient.
$\frac{\text{dv}}{\text{dx}}=$ velocity gradient.
Substitute $\text{SI}$ units of $f = N, dx = m, A = m^2$ and $v = m s^{-1}$ in above equation,
We get,
$\eta=\frac{\text{N}\times\text{m}}{\text{m}^2\times\text{m s}^{-1}}=\text{N m}^{-2}\text{s}$
Hence, the $\text{SI}$ unit of $\eta =$ is $N s m^{-2}$.
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