How to Convert Feet to PSI When Calculating Water Pressure

As we work with water pumps, we find that pressure is presented to us in two common units: PSI (pounds per square inch) or feet of head. As we size a pumping system, we'll want to accomplish building pressure (PSI). The relationship between PSI and feet of head is that 2.31 feet of head = 1 PSI. 

Translated, that means that a column of water that's 1-inch square and 2.31 feet tall will weigh 1 pound. 

Or, one-foot column of water that's 1-inch square weighs .433 pounds. 

These two numbers, .433 and 2.31, are the conversion numbers used to convert from one unit to the other. 

 

How to convert dynamic head to PSI:

As we learned in school, to solve a problem we need to be in common units. As we work through a problem, we need to convert to the unit that is most common – feet of head. 

When working with pumps and plumbing, you'll work between feet of head and PSI routinely. Becoming familiar with the units and where they come from will make your work easier and faster. 

So, let's do a short conversion exercise: 

We are looking to purchase a pump, that we will call Model number: XYZ123.  XYZ123 pump is capable of pumping a maximum of 100 feet of total dynamic head. So what is the maximum pounds per square inch?

100 feet of head ÷ 2.31 = 43.29 PSI

However, this would be at what is called “dead head”.  The dead head of a water pump simply means that there is zero (0) flow of water at the maximum total distance of head.  

In the example above, we could say that XZY123 pump is capable of a maximum of 100 feet of total dynamic head (total head feet) and a maximum pounds per square inch of 43.29 PSI.

Now, let’s say that we only need to pump water a total of 40’ high. Using XYZ123 pump, how much pressure will we have at 40’?

40 feet of head ÷ 2.31 = 17.32 PSI

Still not sure what is happening? Picture for a moment a water hose that you hold in your hands. You are watering your garden, but you can’t quite reach the tomatoes that are at the back of the garden. It’s been a long week and you are tired and don’t want to walk all the way across the garden.  You decide the simplest solution is to place your thumb over the end of the hose as opposed to walking the distance to the tomatoes. What happens?

The water goes farther but not as much water comes out of the hose and it takes a bit longer to give the tomatoes the amount of water that they need. While you are able to reach the tomatoes with the water, because the flow has been decreased it takes you a bit longer.

What you have done, even though we don’t tend to think of it this way, is that you have increased the pressure (back pressure) because you have actually made the outlet a smaller diameter by placing your thumb over the end of the hose.

So, while less water is now flowing out of the end of the hose (discharge), you have increased the pressure and now you are able to spray water a further distance (total head).

An easy rule of thumb (pun intended) is to remember:

  • Higher head = Higher pressure (PSI) but lower flow (GPM)
  • Lower head = Lower pressure (PSI) but higher flow (GPM)

 

How to covert weight of a cubic foot of water:

If you have 1 cubic foot of water holding 7.48 gallons, and the weight of one gallon of water being 8.33 pounds, you'll get 62.37 pounds per cubic foot of water. 

But don't become confused with mass and pressure. 

If you lift our 1 cubic foot of water to 23.1 feet of elevation, we will only generate 10 PSI of pressure at the bottom where we started, as opposed to the 62.37 pounds mass we lifted up in the air. 

So, let's apply this knowledge to practical use: 

Let's say we have a lake cottage on the top of the bank, and we want to know how much pressure our pump needs to push the water to the top of the hill. We don't have time for a surveyor, or the money, but we still need to know the elevation change from lake level to cottage. 

If we take a garden hose or tub and run it up the hill, put a pressure gauge at the bottom, then fill the hose or tube with water, we can tell what the elevation is on the hill. If the gauge reads 40 PSI when the hose is filled with water, we know that the elevation is 92.4 feet. We simply take 40 PSI x 2.31 which equals 92.4. This is not distance, but feet of head. We may have run 1000 feet to rise 92.4 feet, but either way, we will have 40 PSI to overcome to pump water to the top of the hill. 

To illustrate the effects in relationship of head vs. PSI under static conditions, we must note several items. 

The amount of water with the same height will give the same pressure at the bottom no matter how many gallons are in the tank or the size of the pipe. Remember we said not to confuse mass with pressure. The common element is the head which is 115.5 feet, and if we divide that by 2.31, we will come up with 50 PSI. These conditions are true for static conditions. If the water starts to flow, we'll incur friction loss, and for the same height of water, we will have less pressure at the bottom. 

We'll discuss friction loss in our next blog. 

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