Flow through pipe at 40 psi 1

[rrewis]

I need to determine the flow of water in gpm through a 12" section of 4" diameter schedule 40 steel pipe under 40 psi of constant pressure. Temperature and elevation out of the equation. Is an answer possible with such limited information or is this question so "kindergarten" that I should be ashamed to even ask?

Russell

 

[zdas04]

Fluids always flow from a higher potential (either elevation or pressure) to a lower potential. That is all that fluids can do. A system "at constant pressure" everywhere will not flow because there is no potential difference.

David

 

[rrewis]

Here's an example of my vision of what's happening.
Take a fire hydrant flowing all it can through one of it's 2-1/2" butts at the water supplies somewhat constant residual pressure. Insert a pitot gauge into the water stream and I will get a somewhat constant pressure for a period. Wrong?

 

[zdas04]

Very much wrong. The pressure at any one point may be more or less constant, but if the pressure everywhere was constant then there would be no flow. Consequently, the pressure at the start of the hose is actually (infantessimally) less than the pressure at the butt.

I know this sounds pedantic, but it really is crucial to doing an Engineering analysis. On your original post, if you had said you "had a 12-inch long piece of 4-inch pipe with 40 psig on the upstream end and atmospheric pressure on the downstream end, how much water is flowing", I could give you an answer that would match very closely with measured values. If you had said "I have a pipe with a 1 inWC dP down a 12" long 4" diameter line" I could tell you how much is flowing. Also, with a constant 40 psig on the pipe I can tell you the flow rate--zero.

David

 

[TenPenny]

So what you're saying is the pressure is constant over time, not over the length of pipe.

As an estimate, 40 psi through a 4" nozzle will give you something around 3000 gpm, if I recall.

 

[zdas04]

With 40 psig discharging into atmophperic pressure down a 12-inch long 4-inch ID nozzle, I get (using Hazen Williams) 17,000 gpm in new steel pipe.

David

 

[rrewis]

David, that's the senerio I was attempting to discribe but apparently failed to do so, sorry. The answer you gave in your last reply is what I was looking for.
Thanks for the help.
Russell

 

[zdas04]

If instead of

I need to determine the flow of water in gpm through a 12" section of 4" diameter schedule 40 steel pipe under 40 psi of constant pressure. Temperature and elevation out of the equation. Is an answer possible with such limited information or is this question so "kindergarten" that I should be ashamed to even ask?

you had said

I need to determine the flow of water in gpm through a 12" section of 4" diameter schedule 40 steel pipe under 40 psi of constant upstream pressure discharging to atmonsphere. Temperature and elevation out of the equation. Is an answer possible with such limited information.

it would have been fine.

David

 

[rrewis]

Hey "TenPenny" according to the Factory Mutual Hydraulics Tables Manual P6920 you are the winner. You said around 3,000 gpm well the manual states 3021. Thanks

 

[cvg]

next step is to make sure you can supply 40 psi to the upstream end of the nozzle at 3,000 gpm. Unless you have a pump there with a constant discharge pressure of 40 psi at any flow rate up to 3,000 psi or alternatively, a much larger water main which can provide a "somewhat constant" 40 psi, then you need to continue your analysis up to the source to calculate the pressure drop.

 

[rrewis]

Thanks for the heads up. The situation I am dealing with is a pressurized on grade water tank supplying a fire protection sprinkler system. The tank size is 15,000 gallons containing 10,000 gallons of water. Full, it is under 120 psi air pressure. As it is about to empty the air pressure is 40 psi.

 

[ione]

Well I am a bit puzzled: I used Hazen Williams formula and got approx the value reported by zds04


Q = 0.442*C*D^2.63* (?P/L)^0.54 ? 17,381 gpm

Where

Q = flow rate [gpm]
C = 140 [friction loss coefficient for new steel pipe]
D = pipe diameter 4”
?P = pressure drop 40 psi
L = pipe length 1 ft

Where is the bug?

 

[zdas04]

ione,
I got the same number as you, I just rounded it off. I have to think that the 3,000 gpm number is not 40 psid over 12", but down a length of hose into a fire nozzle.

One would hope that Engineers would not blindly accept a number published in a book (or the results of an equation) without understanding the assumptions and boundary conditions of that table or equation. It makes me sad how often educated people do in fact blindly accept some published "authority".

David

 

[rrewis]

17,000 gpm through a 4" hole under 40 psi?!

"a number published in a book"

Obviously you don't know who FM Global is. They have been in the business since the late 1800's and I can assure you that they have plenty of quailifed engineers on staff. So it's not just a number from some book. Also since my first post I have found other sources that match.

Besides, didn't you get your degree from numbers in some book?

 

[TenPenny]

As I said fairly clearly, with an inlet pressure of 40 psig, the flow through a 4" nozzle is about 3000 gpm.

I did not state this was the flow through a 12" piece of 4" sched 40 pipe, or anything of the sort.

I think that before engineers criticise posts, they could take the time to read them and understand what they say.

If you don't think flow through a 4" nozzle approximates the problem at hand, then don't use that number.

 

[ione]

rrewis,

The length of the pipe is a fundamental parameter, so are you sure the reference you’ve quoted indicates a 4” pipe 1 ft (12") long?

 

[TenPenny]

Using the formula for flow through an orifice or nozzle (see Cameron Hydraulics, 2-8 in my version ):

Q = 19.636 * C * d1 * d1 * h^0.5

C = 0.82 for a longer nozzle; 1.0 for a hole
d1= diameter in inches, call it 4
h = 40 psig x 2.31 = 92.4

Q = 19.636 * 0.82 *1 * 92.3^0.5
aprox 2475 usgpm
If you use 1.0 for the C factor, ie, a sharp edged hold, it's about 3020 usgpm

So I'll stick with my approximation.

 

[zdas04]

rrewis,
I do know who FM Global is, and last time I looked their books were published on paper, not stone. I also know that any published table was developed by people, and has a large number of givens, assumptions, and boundary conditions. I often see people who ignore these boundary conditions.

I just ran the Hazen Willams equation with 25 ft of 4-inch pipe with a 40 psid differential and got a flow rate of around 3,000 gpm. Aren't fire hoses around 25 ft long?

TenPenny,
I don't see anything above that is critical of your post. Maybe you're being a bit sensitive?

David

 

[mauricestoker]

TenPenny,

Hate to say it, but you have a math error in your book: the cofactor is 19.649, derived from the Darcy equation. Outside of that I came up with close to the same number using C = 1. From the Crane manual, for d1/d2 = .33 and Re =2.1^6 (terminal side), the listed C value for nozzles is betwen 0.99 and 1.0.

 

[katmar]

ione asked "where is the bug?". The bug is in the exit (acceleration) losses.

If you measured the pressure drop across a 12" section of a very long 4" pipe and found a pressure drop of 40 psi over that short section then you could conclude that the flow was about 17,000 USgpm. But when the 40 psi is across a nozzle discharging to atmosphere about 95% of the pressure drop is in the kinetic energy of the issuing stream of water.

If we assume the nozzle is on the end of a 25' pipe it is very important where and how you measure the pressure. If you measure the pressure where the hose joins the nozzle you will get very different readings if you use a normal pressure gauge or a pitot tube. If it is a 4" hose the water has already been accelerated and the static pressure (i.e. as per normal gauge stuck in the side) at 3000 USgpm will only be about 2 psi. But a pitot tube would see 40 psi.

Similarly, if the nozzle is directly onto a large tank (velocity = 0) and there is 40 psi static pressure in the tank, then about 2500 USgpm will flow using 2 psi to overcome the friction in the nozzle and the rest to overcome the entrance losses and to accelerate the water to 60 feet per second.

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