Define terminal velocity derive an expression for it
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Derive the expression of terminal velocity.
Answered by admin @
Hi
Here is ur answer
STATEMENT:
# The maximum constant velocity acquired by a body while falling through a viscous medium is called its Terminal Velocity.
# It is attained when force of resistance of a medium is equal and opposite to the force of gravity.
DERIVATION:
Expression for terminal velocity,
V = Vt
Density of a sphere = ρ
Density of a viscous fluid = σ
Density of a sphere rolling on a viscous force = ( ρ - σ )
Volume of the sphere = 4 /3 πr³
Viscous force = mg
6πηrv = mg
6πηrv = ( d × v ) g
6πηrv = ( ρ - σ )4 /3 πr³
Here π and r will get cancelled out,
6ηv = ( ρ - σ )4 /3 r²g
v = ( ρ - σ )4 /3 r²g × 1 /6η
= ( ρ - σ ) 2r²/9η .g
Therefore,
V = 2r² ( ρ - σ ) g / 9η
Hope it helps U
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