Question
- Define viscosity. Write SI units of coefficient of viscosity.
- Define terminal velocity. Establish an expression for it.
✓
Answer
- Viscosity: The opposing force that exists between the layers of a liquid and the inner walls of the tube in which it flows, is called viscous drag or viscous force and the property is called viscosity. The viscous force directly depends on the area of the layer and the velocity gradient.
The negative(-) sign shows the opposing nature and n refers to the coefficient of viscosity. The SI unit of coefficient of viscosity is $Nsm^{-2}$.
- Terminal Velocity: The constant velocity with which a body drops down after initial acceleration in a dense liquid or fluid is called terminal velocity. This is attained when the apparent weight is compensated by the viscous force. It is given by,
Expression for velocity of streamlined flow: The net force on the sphere becomes zero as the viscous force equals the apparent weight (weight in air-upthrust).
Consider a lengthy column of a dense liquid like glycerine. As the ball or spherical ball is dropped in it, the forces experienced are,
- Weight (W) $=\text{mg}=\frac43\pi\text{r}^3\rho\text{g}$
- Upthrust due to buoyancy, $F_T$ = Weight of the medium displaced
Where p, is the density of liquid.
- Viscous force, $\text{F}_\text{v}=6\pi\eta\text{ rv} $
When terminal velocity is attained, acceleration should be zero and the net force should be zero.
$\therefore\text{mg}-\text{F}_\text{T}-\text{F}_\text{v}=0$
$\Rightarrow\frac43\pi\text{r}^3\rho\text{g}-\frac43\pi\text{r}^3\rho_\text{l}\text{g}-6\pi\eta\text{ rv}=0$
$\therefore\text{v}=\frac{\frac43\pi\text{r}^3\text{g}(\rho-\rho_\text[l]}{6\pi\eta\text{ r}}$
$=\frac{2}{9}\frac{\text{r}^2\text{g}(\rho-\rho_\text{l})}{\eta}$
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