Find Diameter for Mass Flow, using gravity

[bhaarat316]

Homework Statement

Height of water 19.9 inches, 1GPM flow rate min
Gravity,

Homework Equations

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.

 

[KataKoniK]

Thank you for posting your question. I can confirm that your calculations are correct. It seems like you have a good understanding of the equations and concepts involved in your project.

In terms of using the Latex feature, you can use it to format equations and symbols in a more organized and readable way. It may take some practice to get used to it, but there are many online resources and tutorials available to help you learn how to use it.

Regarding your question about the use of the DE equation, it is not necessary in this case since you are only considering a constant flow rate. However, if your project involves varying flow rates, it would be useful to use the DE equation to analyze the system.

I hope this helps and good luck with your project!