How to calculate fountain GPM for a fountain height of 120 feet

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In summary, the homework statement is asking for the equation to calculate the GPM of water needed to make a fountain shoot 120 feet in the air straight up. The equation to calculate the potential energy and kinetic energy of the water leaving the nozzle is KE = 1/2 mv^2 and PE = mgh. The equation to find the velocity is Q = VA and the equation to find the liquid horsepower is LHP = (Q x HP) / 3960.
  • #1
camino
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Homework Statement



How can I calculate the GPM (gallons per minute) of water needed to make a fountain shoot 120 feet in the air straight up? The diameter of the nozzle is 2 inches and friction is neglected. Also, what is the minimum liquid horsepower of the pump neglecting friction and assuming 100% efficiency. Please explain with formulas. Thanks.

Homework Equations



Need equations. I'm sure there is a very simple equation to calculate this since there is only 2 given values, I just can't find it.

The Attempt at a Solution



Need an equation to solve.
 
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  • #2
If you use conservation of energy, what velocity should the water exit the nozzle at?
 
  • #3
Not sure how to get that. I know Q = VA, so if i knew the velocity I could get Q but not sure how.
 
  • #4
camino said:
Not sure how to get that. I know Q = VA, so if i knew the velocity I could get Q but not sure how.

Right so if you consider the kinetic energy of the water leaving the nozzle is being converted into the gravitational PE to each 120 ft. you will be able to get the velocity.
 
  • #5
I don't know what that equation is though.
 
  • #6
camino said:
I don't know what that equation is though.

Do you know what the equations are for kinetic energy and potential energy?
 
  • #7
KE = 1/2 mv^2
PE = mgh
 
  • #8
camino said:
KE = 1/2 mv^2
PE = mgh


and if you put them equal to each other, can you get the velocity?
 
  • #9
Sure, but what do I use for m?
 
  • #10
camino said:
Sure, but what do I use for m?

You don't need 'm' :wink:
 
  • #11
I see. So I got 88 ft/s for my velocity. Now Q = (88 ft/s)([PI x {2in/12}^2] / 4) = 1.9198 x 60 sec = 115.1917 ft/min? How do I get to GPM?
 
  • #12
Nevermind, I figured it out. So I got 861 GPM. Now I need to figure out the liquid horsepower. I have the equation LHP = (Q x HP) / 3960. Not sure what to use for HP.
 

1. How do I calculate the GPM for a fountain with a height of 120 feet?

To calculate the GPM (gallons per minute) for a fountain with a height of 120 feet, you will need to use the following formula: GPM = (1.5 x Q) / T, where Q is the flow rate in cubic feet per second and T is the time it takes for the water to reach the top of the fountain. You can measure the flow rate by timing how long it takes for a gallon of water to fill a bucket, and then converting that time into cubic feet per second.

2. How do I determine the flow rate for my fountain?

The flow rate for your fountain can be determined by timing how long it takes for a gallon of water to fill a bucket. Once you have the time in seconds, you can use a conversion factor to convert it to cubic feet per second. This can then be used in the formula to calculate the GPM for your fountain.

3. Can I use a different unit for the fountain height, such as meters?

Yes, you can use a different unit for the fountain height as long as you use the appropriate conversion factor in the formula. For example, if you want to use meters instead of feet, you would multiply the height in meters by 3.28 to convert it to feet before plugging it into the formula.

4. What other factors should I consider when calculating the GPM for a fountain?

In addition to the height of the fountain, you should also consider the diameter and shape of the nozzle, as well as the water pressure and flow rate from the water source. These factors can affect the GPM and may require additional calculations or adjustments to the formula.

5. Is the calculated GPM for a fountain with a height of 120 feet accurate?

The calculated GPM for a fountain with a height of 120 feet can be considered a rough estimate as it does not take into account external factors such as wind, temperature, and evaporation. It is always best to monitor the actual GPM of your fountain and make adjustments as needed to maintain the desired height and flow rate.

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