Question:
State Stokes law.Using Stokes law , prove that a body would attain a terminal speed when falling through a viscous liquid,under gravity.Derive an expression for this terminal velocity.
Answer:
Stokes law is based on the forces acting upon a spherical particle suspended in liquid, to calculate the viscosity of the liquid using the terminal velocity of the particle.
Let us understand the use of Stokes law to derive the terminal velocity of a body falling through a viscous liquid,under gravity
Weight of the body = mg
= Vρg
W = 4/3 πr3ρg
where r is the radius of the body, r is density, g is the gravity due to upward viscous drag Fv = 6phvr (Stokes law).
where h is coefficient of viscosity, v is the velocity of body, r is radius of the body.
Upthrust or Buoyant force FT = weight of displaced liquid
= Volume of body
x density of liquid x acceleration due to gravity
FT = Vρg
= 4/3 πr3σg
When the body moves with terminal velocity,
that is, V = VT, total upward force = downward force
6πη VT r + 4/3 πr3σg = 4/3 πr3ρg
6πη VT r = = 4/3 πr3 (ρ - σ)g
VT = [2r2(ρ - σ)g]/9η
Not what you are looking for? Go ahead and submit the question, we will get back to you.
