When a solid sphere moves through a liquid the liquid opposes is the motion with a force the magnitude of the force depends upon the coefficient of viscosity of the liquid the radius of the sphere find the expression of force using dimension formula:
Consider the movement of a ball inside a viscous fluid:
1) Radius -$$ r$$
2) Coefficient of Viscosity -$$ η$$
3) Density of the ball -$$ d$$
4) Density of the liquid - $$ρ$$
5) Acceleration due to Gravity - $$g$$
The ball is subjected to the influence of three forces: they are the weight, upthrust and the viscous force - drag or liquid friction.
Weight of the ball = mg = $$\dfrac{4}{3} πr³dg$$
Upthrust on the ball by the liquid =$$ v×ρ×g = \dfrac{4}{3}×πr³×ρg$$.
According to Stokes Law,
Viscous force = $$6πηV$$, (where V is the velocity at a given a time).
At the outset, the downward force, weight, is greater than the combination of the upward forces.
So, initially, the ball accelerates. The viscous force, which depends of the velocity, however, keeps increasing.
As a result, at some point, the net force on the ball becomes zero and the velocity of the ball becomes constant.
It is the Terminal Velocity -$$ Vt$$
When the balls moves at the terminal velocity,
$$=> \dfrac{4}{3πr3d}= \dfrac{4}{3πr3ρg} + {6πηVt}$$
$$=> Vt = \dfrac{2(d - ρ)gr^2 }{ 9η}.$$
A horizontal plate ($$10 cm\times 10 cm$$) moves on a layer of oil of thickness $$4$$ mm with constant speed of $$10$$ cm/s. The coefficient of viscosity of oil is $$4$$ poise. The tangential force applied on the plate to maintain the constant speed of the plate is?
The coefficient of viscosity for hot air is
The tangential forces per unit area of the liquid layer required to maintain unit velocity gradient is known as:
If $$ \eta $$ represents the coefficient of viscosity and $$T$$ the surface tension, then the dimension of $$ \dfrac{T}{\eta} $$ is same as that of :
The dimensional formula for viscosity is $$[ML^{-1}T^{-1}]$$. One poise, i.e, C.G.S. unit of viscosity is:
A sliding fit cylindrical body of mass of 1 kg drops vertically down at a constant velocity of 5 cm $$s^{-1}.$$ Find the viscosity of the oil.