# Find Diameter for Mass Flow, using gravity

1. Apr 8, 2012

### bhaarat316

1. The problem statement, all variables and given/known data
Height of water 19.9 inches, 1GPM flow rate min
Gravity,

2. Relevant equations

3. The attempt at a solution

Here is the run down first, I'm trying to find a min mass flow rate for my project which needs to be 1 GPM, and max 4 GPM. Now water is going out of a 5 gallon jug, that has the top cut off, and the water is flowing into a PVC pipe. I need to find the velocity of water at atm pressure, and then the diameter of the circle which the water will funnel through. I did some work I just need help making sure I did it right, basically a check over. think of it as a Deer Park 5 gallon bottle, like the ones for water dispenser, but the top cut off, and it flowing out the nozzle.

Man how do I use the Latex thing?

So, I know V=Sqrt(2∗19.5inches∗387.6inches/s^2)
V=122.95 inches/sec, 10.245 ft/s = 614.7 ft/min

Now the simple equation of Q=VA

1 GPM->.13ft^3/min = 614.7ft/min * A
.03024 in^2 = A(min)
sqrt(.03024/∏)= r(min) = .09811 inches

We would have to reduce our inner diameter to .19622 inches.
Now is this right? I can't believe that? I was initial thinking it would be a DE since our mass flow would be varying, depending the height of the water, gravity would be pushing it through the main system.