5 replies to this topic

Dear sir I have a fundamental doubt in the concept of terminal velocity
While deriving the equation for terminal velocity of a freely falling droplet or particle
Force balance is
Drag force + Buoyancy force = Gravity force
Lets take the case of freely falling droplet in a gas liquid separator, gas is flowing upwards and droplet is falling down now my, fundamental doubt is
1.When all the force acting on the droplet get balanced (cancel out together), how the droplet can still fall?
2.Terminal velocity by definition is relative velocity of gas and droplet?
Please clear my fundamentals
you can also suggest some references
Thank you

Ravi

[latexman]

1.When all the force acting on the droplet get balanced (cancel out together), how the droplet can still fall?

Because the drag force that balances the equation occurs at a certain terminal velocity, not zero velocity.

2.Terminal velocity by definition is relative velocity of gas and droplet?

Correct.

hi
latexman
thank you very much for reply
i am not clear , can you please elaborate it more

thank you

[latexman]

Sure. Let's assume you just solved a gravity settling problem and found the terminal velocity was 20 m/s.

At 20 m/s, the sum of the forces = 0.
As you can see the velocity is NOT = 0.

At 0 m/s the forces are NOT balanced, therefore 0 m/s is not a valid solution indicating the particle will not be at rest and will, in fact, fall thru the fluid.

[JoeWong]

Latexman has given all you needs to know...
This is an interesting topic and i just would like to elaborate a little more...

Let say...You are holding a metal ball and release it in the air...

FORCE BALANCE
Drag force + Buoyancy force + External force + Gravity force = 0
Upward direction, Fd + Fb + Fe +(-Fg) = 0
==> Fd + Fb + Fe = Fg

Event at 0- second...
When the ball is at static condition (you are holding the ball),
==> Fd is function of velocity and . As velocity is zero ==> Fd = 0
==> Fb is function of relative density between ambient and ball. Ball density (say metal ball is approx. 3000 kg/m3) relative to air (~1.3 kg/m3), it is almost negligible. ==> Fb=0

Read more in http://en.wikipedia.org/wiki/Buoyancy

==> Thus, Fe= Fg, V=0 m/s


Event at 0+ second...
When the ball is just released (o+ second),
==> Fe = 0
==> Fb negligible. ==> Fb=0
==> Fg maintain with no change
==> Fd is function begin to increasing...

Net Force (Fg > Fd) will drive the ball downward. Ball velocity begin to increase.


Event at t second...
When the ball velocity increase upto terminal velocity (relative velocity between ball and gas),
==> Fe = 0
==> Fb negligible. ==> Fb=0
==> Fg maintain with no change
==> Fd increase upto terminal velocity

Ball velocity increased upto a velocity where Fg = Fd, this velocity is called terminal velocity.
Net force =0 as Fd = Fg ==> No further increase in velocity. Constant velocity.

Read more in http://en.wikipedia....wiki/Drag_force.

& http://en.wikipedia....rminal_velocity

Ball as compare to droplet, same principle applied. The only different is the droplet shape may change from time to time, the drag coefficient will change from time to time. From engineering perspective, the change (too small) is negligible.

Other fundamental aspect in gas-liquid separation you may have to aware (as engineer) but not necessary master :
- Droplet distribution (and/or function deriving it )
- Droplet coalescence and break-up mechanism
- how physical properties i.e. surface tension, density, etc affecting above mechanism
- Droplet shape change lead to different drag coefficient
- Entrainment mechanism...
- Inception of entrainment
- Droplet trapping mechanism
.
.
.

Hope above helps.

NOW I GOT IT CLEAR


thank you very much both Latexman & JoeWong
and
JoeWong Hats off to you for such a beautiful explanation