## Basic Hydrostatics question, RL applications

Any feedback will be appreciated.

I live on a semi-rural property and the owner charged me with a real-world problem involving hydrostatics. On the water pump, we currently get only 11 psi of water pressure. His goal is to get 30psi. His plan is to get a 2500 gallon water tank and let hydrostatic pressure deliver the desired water pressure.

The ultimate goal is to figure out how, given that the tank will be on the ground, long the "outflow" pipe must be to end up with 30 psi of water pressure.

In our situation (on the left), the height marked "LEVEL" in the above picture will be on the ground and the pipe going down will be buried.. Instead of the tank being elevated as it is in the picture. Note that 60' is not the answer; it's just there in this pic I am stealing.

Another constraint/fact is that we are located 3000 feet above sea level.

First of all, I need to know what the right formula is. I think it is this:

P_air + P_water = P_total

where P_air is the pressure supplied by the ambient atmosphere, P_water is how much water pressure is caused by water and P_total is total pressure. P_air depends on my elevation (and other factors I'm sure) and P_water will depend on the length (or depth or height, if you will) h of the vertical pipe at the bottom of the tank.

Specifically, I believe that this formula is the one I have to solve:

13.16 + 0.43h = 30

Where 13.16 psi is the atmospheric pressure at 3000' of elevation above sea level and 0.43 is a number I found elsewhere on the internet. h is measured in feet. Solving this for h yields

h=39.2 feet

rounding...

h must be at least 40 feet to ensure 30psi.

Questions:
(1) Is the formula in bold correct?
(2) Do I need to account for our 3000' elevation? If not, I get the formula P_total = 14.7 + 0.43h which gives h = about 36 feet
(3) If the answer isn't 40 feet, what is the correct answer?
(4) What affect on the situation does the diameter of the outflow pipe have?

Thank you very much for reading this!

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 Quote by phoenixthoth Any feedback will be appreciated. I live on a semi-rural property and the owner charged me with a real-world problem involving hydrostatics. On the water pump, we currently get only 11 psi of water pressure. His goal is to get 30psi. His plan is to get a 2500 gallon water tank and let hydrostatic pressure deliver the desired water pressure. The ultimate goal is to figure out how, given that the tank will be on the ground, long the "outflow" pipe must be to end up with 30 psi of water pressure. In our situation (on the left), the height marked "LEVEL" in the above picture will be on the ground and the pipe going down will be buried.. Instead of the tank being elevated as it is in the picture. Note that 60' is not the answer; it's just there in this pic I am stealing. Another constraint/fact is that we are located 3000 feet above sea level. First of all, I need to know what the right formula is. I think it is this: P_air + P_water = P_total where P_air is the pressure supplied by the ambient atmosphere, P_water is how much water pressure is caused by water and P_total is total pressure. P_air depends on my elevation (and other factors I'm sure) and P_water will depend on the length (or depth or height, if you will) h of the vertical pipe at the bottom of the tank. Specifically, I believe that this formula is the one I have to solve: 13.16 + 0.43h = 30 Where 13.16 psi is the atmospheric pressure at 3000' of elevation above sea level and 0.43 is a number I found elsewhere on the internet. h is measured in feet. Solving this for h yields h=39.2 feet rounding... h must be at least 40 feet to ensure 30psi. Questions: (1) Is the formula in bold correct? (2) Do I need to account for our 3000' elevation? If not, I get the formula P_total = 14.7 + 0.43h which gives h = about 36 feet (3) If the answer isn't 40 feet, what is the correct answer? (4) What affect on the situation does the diameter of the outflow pipe have? Thank you very much for reading this!
Because the atmospheric pressure is present everywhere in your system, including at the exit of the outlet pipe, you should be working with "gage pressures" rather than absolute pressures. What you really want is 30 psi above atmospheric at the outlet pipe (i.e., 30 psig = 43.6 psia). Therefore, on this basis, it doesn't matter whether the pressure of the atmosphere is 14.7 psi or 13.6 psi. The amount of flow through the outlet pipe won't be affected by the atmospheric pressure. So, get rid of the 13.6 in your equation. You're gonna need 70 ft.