Pipe Flow and Pressure

[Job314]

This may be an elementary question, but I am having the hardest time finding the answer.

I have a 2" pipe that is running water at 50 psi (city pressure) with a valve on the end. Total length from the city main to the valve is about 100 ft. If I open this pipe up, fully open, to fill up a tank, what will the flow rate (gpm) be?

Thanks in advance for any help.

 

[vpl]

Since you're fairly new to the site, and this is your first question:

This isn't homework is it?

Additionally, is it work related?


Patricia Lougheed

******

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[Job314]

This is not homework and is work related. It is for a fire station where they are filling up the their trucks with this water. I want to know how long it will take to fill up the truck. If I get the flow rate... I can get the fill time.

 

[Job314]

Okay I found my own answer.

Flow is area*Cd*Sqrt(2gh)

Convert pressure to ft and plug in for 'h' = 50 psi = 115 ft H20

Cd is about 0.98 for a smooth opening

g is 32.2 ft/sec/sec

Comes out to about 55 GPM.

 

[Job314]

I meant to say velocity is area*Cd*Sqrt(2*g*h).

Velocity was calculated to be 5.6 ft/sec. Once I have the velocity the flow is calculated pretty easily through a 2" pipe.

Thus the answer is 55 GPM.

 

[katmar]

This question comes up so often here I think we need a FAQ for it.

The big unknown is always whether the mains pressure will remain at the indicated value when the branch is flowing. But assuming that it remains at 50 psi you can use the online calculator at

http://www.freecalc.com/fric.htm

to determine the flow. Actually you have to do a bit of trial and error because the calculator requires you to enter the flow rate and it calculates the pressure drop.

Apart from the length and diameter, the details of the fittings are important. You can model the actual branch from the mains to the 2" pipe as one entrance effect plus one short radius 2" elbow. Also include one exit and your valve.

It looks like you should get about 240 USgpm.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[ione]

The formula you’ve used gives approx 565 usgpm, but what is more important to me is that you’ve approached your scenario as it were a tank emptying problem. So you have completely neglected pressure drop in your pipe length and any minor loss due to fittings present in your branch line.

 

[waterpipe]

Just a suggestion here.
I recommend downloading EPANET software (from EPA) and having it to model every pressurized net from a simple pipe to a full city network. So easy to use and still capable. You can even use it as a learning tool by playing the parameters and observing the results.
I have to say that I acknowledge the concept of "understanding" and then doing the model by few "clicks".

 

[Latexman]

Usually fire trucks are connected to water mains/lines using hoses. What length hose do they use? It appears you are neglecting this resistance to flow also.

Good luck,
Latexman

 

[Ziggypump]

Correct me if I'm wrong but I believe you guys are trying to get to this equation:

HD2/HD1=(GPM2/GPM1)^2

HD1 is known: 50 psi
HD2 can be calculated by the pipe loss from the valve to the truck
GPM1 is calculated from HD1
and GPM2 is the fill rate of the tank

Job, you calculated the leaving flow rate from the valve. Now you need to figure the rest of the way.

It's been awhile since I've had to figure a flow rate this way. Usually I size the pump for full flow, and have to calculate the head to determine the pump size needed.

 

[Job314]

Thanks for your responses. I have spent over an hour with a fellow co-worker and 2 textbooks trying to figure this "simple" problem.

Ione- You are on the right track. I also made some unit mistakes in my initial calculation.

Using the formula
Flow = Area * Cd * Sqrt (2 * g * h) is correct, but it is like a tank emptying problem with no head loss. However, this is a representative equation if I know the pressure at the end of my line.

I calculated my head loss through my line with all the valves, fittings and turns and end up with about 30 PSI at the end of the line coming out to fill the truck.

If I recalculate with this number using the above equation and use Cd = 0.64 for a sharp edged nozzle I come up with...

0.93 ft^3/sec = 417 GPM.

Still seems like way too much. So after all that I'm still a little confused. I am expecting something less then 100 GPM out of a 2" line.

 

[jte]

I realize we're all engineers and all... But a simple experiment would be just as easy, and more accurate. Go to the fire station, get a 55 gallon drum, get the pipe/hose, fill 'er up. Don't forget to time the process. This avoids all of our debates over boundary conditions, and is arguably more accurate.

jt

 

[ione]

Job314,

I calculated my head loss through my line with all the valves, fittings and turns and end up with about 30 PSI at the end of the line coming out to fill the truck.

To calculate the pressure drop you must have assumed a trial flow rate (which is the unknown of your problem).

I can reassure you that 417 usgpm in a 2” commercial steel pipe 100 ft long (neglecting fittings and entrance/exit effect) lead to a pressure drop of approx 120 psi. How could the main line be at 50 psig? You can’t force your scenario to be something different from what it is.

 

[cvg]

come on guys, this is undergrad level fluid mechanics, we should have all had this class.

pressure at the main is 50, pressure once the fluid leaves the nozzle is atmospheric. You have 50 psi or about 115 feet of head to work with. That head will be lost due to friction and turbulance losses 1)through the valve 2)through the pipe 3)through any bends or fittings 4)through the nozzle at the end. Ignoring all the minor losses and assuming all loss is due to pipe friction alone, your velocity will be 22 feet/sec and flow rate 220 gpm - more or less. Including the minor losses, I would expect much less flow.

Try Hazen-Williams method

http://www.engineeringtoolbox.com/hazen-williams-water-d_797.html

http://en.wikipedia.org/wiki/Hazen–Williams_equation

 

[waterpipe]

I've reviewed all the post but getting confused of some weired talks. Anyhow, by just looking to the question in the first post, I have to say a parameter is missed in the question and that's the level (elevation) of the end of your 2 inch pipe.

The simple solution to your question is Bernoulli's equation (yes the simple equation for this simple question).
First, neglect the losses. considering Bernoulli, 50 psi (3.4 bar) corresponds to 34 meter height. if you have the end of your pipe in an elevation higher than 34 meter, then you will have no flow in the pipe (quite obvious, water doesn't run uphill!).But your pipe is 100 ft long(30.5 meter), so it never reaches to 34 meter above the city main (lucky you!).

Now, imagine your pipe end (filling tank)is in the same level as the city main (like taking water from the city main by a 2inch pipe to extinguish a fire at the ground level). Using Bernoulli, then you have V=25.8 meter/s that means 50 lit/sec (790 gpm)flow. Ummm, quite high. Did I misses something? YES, the losses. so again put the hf term (losses)in Bernoulli and solve the equation. Doing so you'll be able to calculate the flow.

Guys, I'm sorry but I'm a bit ahead in time of you that are sitting in US. I have to rush to get to a Friday party. But please you go ahead and follow some fundamentals here:

And

And

And after this review, I'd suggest to use EPANET or any other software to get out of the hand calculations.

Have a nice weekend.

 

[waterpipe]

@ cvg: you are right. you've got the point. but it's even more undergrad level fluid mechanics since dealing with Bernoulli!
Just to acknowledge, the exercises posted are from "2500 solved problems in fluid mechanics & hydraulics" by Evett and Cheng Liu.

 

[cvg]

thankyou waterpipe, you illustrated the one form of head loss that I forgot, elevation difference. I assume that unless you are on a very steep hill, the difference is negligble, however if you are filling the tank from the top and the water main is below ground, you will lose 3 or 4 psi due to elevation difference, further reducing the flow.

 

[katmar]

cvg calculated 220 USgpm and I got to 240 USgpm. That is as close as you will get with the level of information provided. Until we know

1. Will the mains pressure drop when flow starts
2. What is the elevation difference to the truck
3. What schedule is the 2" pipe
4. What material (i.e. how rough) is the 2" pipe
5. What number and type of valves are in the line
6. What is the exact length of the line
7. What other fittings are in the line

we can really only give a ballpark figure.

Katmar Software
Engineering & Risk Analysis Software

http://katmarsoftware.com

 

[vpl]

In his second post, Job314 explains that he wants to know the flow rate in order to calculate how long it is going to take some firemen to fill up their truck tanks.

However, I wonder why he didn't just ask the firemen? They've presumably been doing this all along and probably know reasonably closely how long it takes them to do it.




Patricia Lougheed

******

Please see FAQ731-376: Eng-Tips.com Forum Policies for tips on how to make the best use of the Eng-Tips Forums.

 

[Job314]

@ vpl. This pipe is not installed yet. Initial design had a 3" line. The question they are asking is if they switch from a 3" to a 2" fill line what effect will it have on the time required to fill the tank. Thus my question.

The calculator Katmar posted and the Hazen-Williams method posted by cvg seem to be the most helpful.

Also most likely the residual pressure will be less then 50 psi when that 2" valve is wide open. Often we can get residual pressure tests on those main lines. That is something I will need to track down.

So with the reduced residual pressure the number will be less then 220 gpm and along with the fittings/valve losses I plugged into the on-line calculator I am ballparking the flow rate to be around 125 gpm. Once I get the residual pressure I will get a more definative answer.

Thanks for your help!