Pressure of water exiting a hole in PVC

[Cmotaval]

TL;DR Summary

Trying to calculate the pressure of water exiting a 1/32" hole in a closed 1" pvc pipe

I have a 1" PVC pipe that is 36" long, closed on one end and hooked up to a pump on the other. The pipe has 10 holes each measuring 1/32" in diameter and I have been trying to use Bernoullis equation to find the pressure of the water exiting those holes. I believe the volume of water that will exit the holes will be 0.16g/min/hole so I wanted to use a pump that has a flow rate of 5 gallons/ min at 60 psi. If I am wrong and the volume exceeds what is pump can provide I can change the pump to one with a higher flow so assuming that no matter what, the pressure at the start of the pvc is 60psi and the flow will 5 g/m or equivalent to the volume of water lost, what is the pressure of the water exiting the holes. I am trying to make a powered sprayer for cleaning a pool filter and was hoping to estimate the pressure so I can choose an appropriate pump and also ensure I do not blow a hole through the cartridge but I am stuck on plugging my numbers into the equation. Any help is appreciated.

 

[russ_watters]

Welcome to PF.

Exit pressure is zero/atmospheric, so I think that's not the real question you want answered. And it seems like you are approaching this backwards. The first thing you need to know to get started is what you want. I'll guess you want a certain exit velocity and/or volumetric flow rate, but I don't know. So...?

 

[Baluncore]

Welcome to PF.
Since the tube is much bigger than the holes, there will be little pressure lost before the water reaches the holes. The critical thing not mentioned is the length of the hole, which is the tube wall thickness. The available pressure will be lost as the water accelerates and moves along that short hole. The profile of the hole may also be important.

 

[Cmotaval]

The device is going to be used to clean a pool filter so high volume and high pressure would be perfect but also never easily achievable. For the pressure, the cartridge can take 150psi max and would like to get as close as possible to that pressure. I was hoping to see final formula and then adjust it depending on what pumps I can find to get as close but not exceeding 150psi with the highest amount of volume.

 

[Cmotaval]

Because the water is in a confined space with a pump going behind it wouldn't the pressure of the water greatly increase as it goes through the hole?

 

[Baluncore]

Because the water is in a confined space with a pump going behind it wouldn't the pressure of the water greatly increase as it goes through the hole?

The pressure is provided by the pump. The pressure falls as the velocity of the fluid increases. The pressure at the exit of the hole is atmospheric pressure, but the fluid then has kinetic energy. If the water jet then hits something, so the water slows down, it will apply a force to the thing it hits.

 

[AZFIREBALL]

Is this the situation?

 

[russ_watters]

Let's not go crazy with the math at this stage please. We don't want to scare the OP away. At this point he has some basic conceptual confusions regarding fluid flow; what pressure and velocity are and how they are related. It's why he's not able to tell us what his requirements are. We need to get that cleared up first.

 

[erobz]

Let's not go crazy with the math at this stage please. We don't want to scare the OP away. At this point he has some basic conceptual confusions regarding fluid flow; what pressure and velocity are and how they are related. It's why he's not able to tell us what his requirements are. We need to get that cleared up first.

I hear you. Loud and clear... I figured I'd just delete the posts for you.

 

[Cmotaval]

Is this the situation?View attachment 302230

Yes that is pretty much it but with 10 holes but even calculating with 1 hole would be very helpful

 

[Cmotaval]

I hear you. Loud and clear... I figured I'd just delete the posts for you.

So the reason I can't provide the requirements is that I want to provide the maximum pressure and volume possible. I am trying to make a device to clean a pool cartridge filter and there is not much data as to how much pressure would poke a hole in the membrane and what volume would be most effective for cleaning. The pump will be the main player in the equation and I was hoping to see the final formula so I can play with the equation to evaluate what pump would get me to the volume and pressure numbers I want and what the cost of that pump would be. What I am hoping for as a starting point is to have 5gal/min at 150 psi exit the hole. V2 would ideally be a more powerful pump and I can work my way up to the point of destroying the cartridge and ten scale back but wanted to try to use math to get me to a better starting point. I do realize that some of my terms are incorrect. It has been many years since my college physics days and surprisingly I don't use a lot of this in the OR, or atleast not in this fashion. I am saying pressure but believe In should be saying force or force at the point of impact

 

[russ_watters]

So the reason I can't provide the requirements is that I want to provide the maximum pressure and volume possible. I am trying to make a device to clean a pool cartridge filter and there is not much data as to how much pressure would poke a hole in the membrane and what volume would be most effective for cleaning. The pump will be the main player in the equation and I was hoping to see the final formula so I can play with the equation to evaluate what pump would get me to the volume and pressure numbers I want and what the cost of that pump would be. What I am hoping for as a starting point is to have 5gal/min at 150 psi exit the hole. V2 would ideally be a more powerful pump and I can work my way up to the point of destroying the cartridge and ten scale back but wanted to try to use math to get me to a better starting point. I do realize that some of my terms are incorrect. It has been many years since my college physics days and surprisingly I don't use a lot of this in the OR, or atleast not in this fashion. I am saying pressure but believe In should be saying force or force at the point of impact

As we have said, the pressure is zero at the exit. It just is. So, this idea that you can get "150 psi exit the hole" just isn't a thing. But as @Baluncore implied, when this atmospheric pressure jet hits the filter it will apply a force, over a small area, which is like applying a pressure. And you can solve for the flow rate/velocity and force/pressure at the impact if we specify the conditions. So let's use the 50 psi in the manifold and 1/32" hole per the diagram from @AZFIREBALL -- and yes, there's no real difference in calculating for one hole than for 10 (just multiply by 10 after). We can ignore the head loss in the rest of the piping system because we'll assume the velocity will be kept low (generously sized piping) - it'll get us close as a starting point. Yes, you can use Bernoulli's equation to calculate the exit velocity...

 

[erobz]

So the reason I can't provide the requirements is that I want to provide the maximum pressure and volume possible. I am trying to make a device to clean a pool cartridge filter and there is not much data as to how much pressure would poke a hole in the membrane and what volume would be most effective for cleaning. The pump will be the main player in the equation and I was hoping to see the final formula so I can play with the equation to evaluate what pump would get me to the volume and pressure numbers I want and what the cost of that pump would be. What I am hoping for as a starting point is to have 5gal/min at 150 psi exit the hole. V2 would ideally be a more powerful pump and I can work my way up to the point of destroying the cartridge and ten scale back but wanted to try to use math to get me to a better starting point. I do realize that some of my terms are incorrect. It has been many years since my college physics days and surprisingly I don't use a lot of this in the OR, or atleast not in this fashion. I am saying pressure but believe In should be saying force or force at the point of impact

I too like to play around with the mathematical model to try and understand the system. I've made a lengthy post that outlines that approach, but I got the feeling it was about to be deleted by the moderator because it was going to "scare you away". So instead of losing all my hard work, I decided to remove it myself.