Name: Angle of Contact
Uploaded: 2019-07-19
Duration: 6 min 57 s
Description: What is the contact angle? Which factor does the contact angle depend on? Why does the contact angle for the same liquid on different surfaces differ? Let's...

Question

(i) State Stoke's law. Derive an expression for terminal velocity using it.
(ii) What are the limitations of Bernoulli's principle?

Accepted Answer

(i) Stoke's law states that the viscous drag $F$ on a sphere of radius $' a'$ moving with velocity $v$ through a fluid of viscosity $η$ is given as
$F = - 6 π η a v$ .
Thus, the force is directly proportional to the velocity of the sphere but acts in the direction opposite to that of velocity.
Derivation of Terminal velocity :
When the sphere falls freely in a fluid, its speed increases due to acceleration of gravity. As a result viscous drag of the fluid increases in the opposite direction. At some stage the viscous drag and the upward buoyant force become sufficient enough to balance the weight of the sphere in the fluid. The sphere then comes down with a constant velocity called terminal velocity $v_{T} \cdot$
Thus at $v_{T}$
Viscous drag $+$ upward buoyant force $=$ Weight of the sphere
$6 π η a v_{T} + V σ g = V ρ g$
[ $ρ$ $=$ density of sphere, $σ =$ density of fluid, $V =$ volume of sphere]

$\Rightarrow 6 π η a v_{T} = V (ρ - σ) g$
But $V = \frac{4}{3} π a^{3}$

$\Rightarrow 6 π η a v_{T} = \frac{4}{3} π a^{3} (ρ - σ) g$

$\Rightarrow v_{T} = \frac{2 a^{2}}{9 η} (ρ - σ) g$

(ii) Limitations of Bernoulli's Principle Bernoulli's equation is based on the principle of conservation of energy it is valid for
(a) Non-viscous fluids so that no energy is dissipated due to viscous drag
(b) Streamline flow
(c) Incompressible fluids
(d) Irrotational flow

(i) State Stoke's law. Derive an expression for terminal velocity using it.
(ii) What are the limitations of Bernoulli's principle?

Important Questions on Mechanical Properties of Fluids

Learn and Prepare for any exam you want !

(i) State Stoke's law. Derive an expression for terminal velocity using it. (ii) What are the limitations of Bernoulli's principle?

Important Questions on Mechanical Properties of Fluids

Learn and Prepare for any exam you want !

(i) State Stoke's law. Derive an expression for terminal velocity using it.
(ii) What are the limitations of Bernoulli's principle?