# Calculating water pressure from flow rate + hose radius

We have a few things at work whose instructions say to run water through them at a specific pressure (in pounds per square inch). We have a hose that attaches to our faucet and has the proper connection to the objects in question.

With the cold water faucet turned on full blast and connected to the hose, our sink will fill to the 1 gallon mark in 55 seconds. The inside radius of the business end of the hose is 1 mm. It seems like knowing those (and maybe the density of water) should be enough to calculate the water pressure, but I can’t figure out how to do so. Can anyone help me out?

You need a little more information than that, but it can be done. I’m not sure what you mean by the business end of the hose though, 1 mm seems pretty small. The friction would be calculated using the diameter and length of the hose, a roughness factor for the hose wall friction, the Reynolds number and viscosity of the fluid. Here’s awebsitethat will do it for you.

If you just have to ensure the pressure is a tiny minimum, you can do it with an extension hose up into the air… using gravity to measure pressure., perhaps just a 3 metre long house is enough ?

If you put the hose up 4 metres and still get flow you know its got 4 meters of head - which means that much pressure…

1 metre of head is 1.4 psi or 10 kPa
Its also a way to empirically measure flow rate from that much pressure… put a bucket up on the roof, drain the bucket with the hose … measure the flow rate down that distance…

Normal residential water supply pressure is around 60 psi, but can be closer to 100 psi if the regulator is maladjusted. If this is really critical, you can buy a water pressure gauge that screws into a hose spigot (that link is Amazon, but I’d bet you can get them at Lowe’s/Home Depot as well). If your device needs a lower pressure, you can buy a regulator to dial it down to what you need.

And, only because you mentioned it, it’s my understanding, once it starts getting up above 100psi, it can start blowing connections off the fittings. That’s when people call the plumber reporting that they keep ruining garden and washing machine hoses as the burst or they pop right off the spigots and they have no idea what’s going on.

You are going to a lot of work to figure out the pressure.
Go to the hardware store. In stock should be a pressure gauge that has a hose adaptor to connect it to a hose bib. cost less than \$15.

if you are really averse to spending money, stores that specialise in garden irrigation (reticulation?) generally have a few pressure gauges they loan out to people. when you want to design a new retic system for home, you need to know pressure to select sprinklers and work out pipe sizes etc, hence they have the gauges as loaners.

Out of curiosity I checked my UK water supplier. They say “Mains are usually 2 -4 bars (30psi-60psi ).”

Did you use/“guess” the word “reticulation” because it makes sense (a network, here of water tubes/pipes) because it would make sense, or because it actually is a word used in irrigation?

It’s a nice word, and thanks for prompting me to look it up.

Thanks for the replies – I tried Bill Door’s website at first, but I got locked out of it after clicking on a few links to check definitions and values. The end of the hose that attaches to the instruments at work really does have an inner diameter of roughly 2 millimeters – it’s a Luer fitting (the same type of connector that a hypodermic syringe uses to connect to needles, although without the locking threads).

The minimum pressure for the instruments is 30 psi and, now that I think about it, I know that the water pressure we get is like 60-80 psi. Does that mean the water I run through the hose will be approximately 60-80 psi, or in any case significantly higher than 30 psi? The hose is made of a smooth plastic material with a smooth metal tip that I assume is stainless steel. The flow is laminar. From what I remember of Bill Door’s website’s links, the pressure out will be similar to the pressure in given those stats.

Leo, retic (as an abbreviated form of reticulation) is the word commonly used where I’m from to describe residential irrigation. Calling your garden bed pipes an irrigation system would be a bit of a misnomer. Irrigation is for the larger stuff like farms and commercial arrangements.

I am under the impression north americans use the word irrigation in the residential context though hence i used it first

The pressure is always going to be dependent on the flow. If the flow is zero the pressure will be the same throughout the system minus whatever the static head is. If you have an open end to your hose the flow will be whatever flow gives a friction loss equivalent to the inlet pressure minus the static head.

Does your instrument require a certain flow at that pressure, or does it just require that pressure?

Just the pressure.

I should note that this is now really just an academic question for me now – I got confirmation earlier today from my boss (who had looked into all of these issues in his earlier position here) that the pressure’s fine. I mostly originally asked because I thought there was an easy answer that I was overlooking.