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:
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
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