converting rate of volume to speed?

Question

I work on infusion pumps all day, and a coworker and I were discussing how fast a infusion pump would have to pump to match the speed of gravity (Terminal Velocity). I believe most of my math is correct, but can't figure out a way to convert ml/h to m/s or mph. I know a falling water droplet would make a tear shaped mass but i used a sphere for my calculations.
rate of decent from gravity = 9.81286538m/s^2
A sphere has a drag coefficient of 0.47
So a sphere with a:
diameter = 5 mm
Area = 78.54 mm^2
Volume = 65.45 mm^3
Mass = 70 mg
Should have a terminal velocity of 23.83 m/s or 53.31 mph

So how can i convert that to a rate of ml/h?

PS: Some random information i jotted down:
1 ml = 1 g
70 mg = 0.07 g
It'll take ~14.29 drops (of the above droplet) to = 1 g

kirchwey · Accepted Answer

You're asking for the volume rate corresponding to a given drop volume and speed. The units don't match. For a given volume rate Q with a given drop volume V you'd need to specify the number of drops per second N. Q = NV. 
And the terminal speed is not controllable by the pump volume rate since that's just a property of the drop. However, you can control the pump exit speed, and make it equal to the terminal speed if you wish. If you want a specified exit speed v from a nozzle for a given volume rate Q you'd need to adjust the nozzle area A. Q = vA. Thus NV = vA ==> A = NV/v. 
So that gives you a stream with speed = terminal speed, with flow rate Q supplying enough water to make N drops of volume V per second. But getting that flow to form drops of the size you want is something else.

converting rate of volume to speed?

Related Questions

Trending Questions