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[Mainak Sarkar]

Dear all I required a equation that can be used for finding time required to reach terminal velocity for a bubble starting with initial velocity vi through a fluid medium.


FBY= Buoyancy force
FG= Gravitational force
FD= Drag force
FN= Net force
MB = Mass of the bubble
ρ= Density of the fluid medium
A= Projected area of the bubble
CD= Drag coefficient
µ = Viscosity
dB=Diameter of the bubble
Re= Reynolds’s number (Re = (ρ*v*dB)/µ)
a= Acceleration/deceleration


FN = FBY - FG - FD

FBY - FG = K (constant for a particular Case)

FD = ½ *ρ*A*v2*CD

CD = f (Re) (CD varies in the range of 0.47 to 1.0 within the Re ranging from 104 to 102.)

Assumption: CD is considered to be constant and the average of 0.47 to 1.0 within the flow range

FN = K-½ *ρ*A*CD* v2

MB*a= K – K’* v2 (K’=½ *ρ*A*CD)

MB*a= K – K’* v2
or
M_B×dv/dt=K-K'×v^2

Solving for time (t) to reach Terminal velocity

Please comment and suggest a better solution if possible.

[latexman]

You may want to review Stoke's law.

 

http://en.wikipedia....iki/Stokes'_law