Stokes Law

Card # 26-Stoke’s law According to Stoke’s law, if a sphere of radius r moving with velocity V through a fluid whose coefficient of viscosity isη , the viscous force F on the sphere Viscosity force Fαη Fα a a= radius of sphere FαV V= velocity of body in the fluid

Fαη aV F = Kη aV

K is a constant of proportionality for spherical bodies its value is 6π thus

F = 6πη aV

Equation of continuity

We consider a fluid flowing in a tube of varying areas of cross section. Let a1 , v1 and ρ1 respectively be the area of the cross section of the tube, velocity of flow the fluids particle and density of the fluid at point A. Similarly a2 , v2 and ρ2 be the area of cross section, velocity of the fluid particles and density of the fluid at point B. Since there is no source of fluid between point A and B Mass flux at fluid at A = Mass flux of fluid at B

a1v1ρ1 = a2v2 ρ2

Since liquid is incompressible ρ1 = ρ2 = ρ (constant)

a1v1 = a2v2

Thus av = constant

This is the equation of continuity. It states that when area of cross section decreases velocity of fluid flow increases

aα

1 v

Area of cross section

α

1 velocityoffluid

Bernoulli’s Equation Bernoulli’s equation states that for the steady flow of an incompressible and non-viscous fluid, the total energy (pressure energy, potential energy and kinetic energy) the fluid remains constant throughout the flow. Mathematically

1 P + ρ gh + ρ v 2 = cons tan t 2 P = Pressure energy per unit ρ gh = Potential energy per unit volume. 1 2 ρ v = Kinetic energy per unit volume. 2