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How can I calculate water discharge velocity?

04/23/2008 11:31 PM

I am pumping 10 GPM (say water)through a 1" pipe @ 1000 psi. I then will cap the end of the pipe leaving a 1/8" gap 360 deg. open for discharge. I need to calculate the foot per second velocity the water will escape at. I can do the calculation for variation in flow and pressure if formula is supplied, also diameter of pipe can change along with circumference gap. This is to create an umbrella effect discharge with varing diameter.

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#1

Re: How can I calculate water discharge velocity?

04/23/2008 11:49 PM

Water velocity = volumetric flow rate÷cross-sectional area

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#3
In reply to #1

Re: How can I calculate water discharge velocity?

04/24/2008 10:41 PM

Some body gave you vote for Good Answer. But I disagree because:

It is not so simple. Your formula is basic formula. But the flow rate in your formula is not simple to find unless you use flow measuring device (with no resistance, like Electromagnetic Flowmeter)

With capping, the resistance to flow will increase, thus the losses in the pipe system resistance. This will increase the pressure in pipe and flow may decrease.

Better way is to find the flow rate using electromagnetif flowmeter and then use the basic formula (as you have given)

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Guru
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#4
In reply to #3

Re: How can I calculate water discharge velocity?

04/25/2008 3:04 AM

I agree you gsuhas, the case is not so easy as derived. The frictional losses must be taken into consideration where all parameters shall be affected by friction loss, and the velocity is one from those parameters. Also, I'd like to say that the velocity thorough the pipe cross-sectional is not the same, it is a parabolic, where it is max. at center of pipe and zero adjacent to the pipe wall.

Only we considerer the calculated velocity -as an approximation- as the average velocity through the pipe cross-sectional.

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#6
In reply to #4

Re: How can I calculate water discharge velocity?

04/25/2008 4:03 AM

I do not agree with your Parabola assumption. The parabolic flow profile is in case of laminar flow, which is very very rare, only in case of very viscous fluids at low velocities or in blood vessels. Parabolic flow profile is as shown below:

You will never find this profile in water flow.

In case of water flow the shape of flow profile is different as below:

Besides, the velocity through the capped end as discribed in original thread has nothing to do with flow profile in the pipe. The velocity will ve uniform all over which is Flow rate / Area of flow.

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#8
In reply to #6

Re: How can I calculate water discharge velocity?

04/25/2008 7:47 AM

The only case where there is magnitude to the velocity adjacent to to inner pipe wall is only the case where there is no friction, and zero friction is not actually exists, except in the ideal cases such as assumptions for using a pipe from glass with zero friction. So, for any fluid whatever it is viscous or non viscous, the velocity adjacent the pipe wall is zero. May be the shape of parabolic is differ from fluid to another depending on its viscosity and pipe relative roughness.

Even in case of water flow, the shape is parabolic, since the velocity adjacent to pipe wall is zero. May be there is a portion of velocity curve closest to pipe wall has another parabolic relation or may be nearest to a straight line.

Note. For the same ID of a pipe you can draw a lot of parabolic shapes (ID represents its major axis) depending on the magnitude of its minor axis (max. velocity at center of pipe). So, the parabolic of blood flow is actually differs from the parabolic of water flow at the same pipe.

Please gsuhas, if you have another knowledge for that specific subject, please let me know you sources and/or references .

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#20
In reply to #8

Re: How can I calculate water discharge velocity?

04/27/2008 11:00 PM

There is no doubt that in any pipe velocity in the centre is maximum and velocity at pipe surface is zero, irrespective of whether it is parabolic or otherwise. Zero friction is non existant.

But my point is in practice parabolic curve is very rare.

In practical case, the velocity near pipe is zero but this boundry layer is very small and it reaches to average velocity within another 1/8 R. Remaining rise of velocity takes place in balance 7/8 R.

I was selling a engineering educational equipment, to measure the flow profile across the pipe croass section, using pitot tube. The statements I am making are based on what is observed. Also, no specific reference is needed. Any fluid mechanics theory says same thing. You refer any fluid mechanics professor in engineering collages.

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#7
In reply to #3

Re: How can I calculate water discharge velocity?

04/25/2008 7:40 AM

"Water velocity = volumetric flow rate÷cross-sectional area"

In answer to the original question, the answer above that was given and received "Good Answer" replies, is actually correct. The original question had information that was not relevant to the question. The question without the extraneous information would be "What is the vlocity of water flowing through a 1" pipe at 10 GPM." The 1000 psi pressure has no bearing on the question. Someone pointed out that the physics of pumping at 1000 psi through a 1" pipe is nearly impossible, but 10 GPM is easily attainable. So the validity of the above answer is confirmed.

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Guru

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#9
In reply to #1

Re: How can I calculate water discharge velocity?

04/25/2008 8:25 AM

It's been a while since I've looked at the Bernoulli equation and its application but it seems that if we're going to obey the law of conservation of mass the above equation would have to be correct. If 10 GPM is going into the system then 10 GPM has to come out. If we take friction into consideration then wouldn't that affect the volumetric flow rate?

Like I said, it's been a while since I've worked with this so please correct me if I'm wrong.

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#2

Re: How can I calculate water discharge velocity?

04/24/2008 12:56 PM

Maybe you were just using it as an example, but you will never achieve anywhere near 1000 PSI with a flow of 10 GPM through the 1/8" circumferential gap. Is the velocity so important here or is it the flow rate? Are you trying to calculate the discharge velocity?

From what I gather of what you want to do, it seems that some experimentation is in order to: a. achieve the pattern(s) you want to disperse, b. cover the area you wish to umbrella. There are different types of nozzles for what I think you're trying to achieve.

If you want to maintain the same flow rate, the discharge nozzle will have to be the adjusting factor. If you want to maintain the same internal system pressure, the flow rate can be changed according to the pattern you wish to disperse. In either case, the discharge velocity (I think you're looking for) will change.

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#10
In reply to #2

Re: How can I calculate water discharge velocity?

04/25/2008 8:41 AM

That is one ugly cat...

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Guru
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#5

Re: How can I calculate water discharge velocity?

04/25/2008 3:38 AM

The velocity V in this case is a function of P (pressure in ft of liquid), pump head HP in case of using a pump, Z (net relative elevations), flow rate Q, pipeline equivalent length L , pipe inside diameter D, friction loss f, losses at inlets and exits K, and g is the gravitational constant:

V = [ 2 g (P+Z+HP) / (f L/D + K +1)]0.5

It is easy to proceed a derivation for that equation. Note:if there is no pump, use HP = 0 & and for atmospheric pressure inside the vessel or container, use P =0.

The friction loss f is a function of V, and a lot of steps are to be carried out to calculate f and intern V.

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#11

Re: How can I calculate water discharge velocity?

04/25/2008 9:21 AM

I am pumping 10 GPM (say water)through a 1" pipe @ 1000 psi. I then will cap the end of the pipe leaving a 1/8" gap 360 deg. open for discharge. I need to calculate the foot per second velocity the water will escape at. I can do the calculation for variation in flow and pressure if formula is supplied, also diameter of pipe can change along with circumference gap. This is to create an umbrella effect discharge with varying diameter.

The Parameters are these:

Conduit = 1" I.D.

Flow =10 GPM in 10 GPM out

Resistance = 1/8" GAP 360°

Pressure = 1000 PSI

The pressure is only given as a variable to consider overcoming resistance (1/8" GAP) (Completely adjustable)

Seeing the fact that there are no compressible elements, only water, flow rate in and out fixed. Resistance s/b uniform at discharge point at which velocity is to be measured.

I can change the flow, pressure and conduit to obtain the breadth of the "umbrella".

The velocity is only a unit of measure to calculate penetration of surroundings after discharge.. It Doesn't matter what "X" is, as long as I have a stated starting point from which to adjust.

ie: Velocity =X (given these parameters).

These are the considerations I used when I gave #1 the good answer. But Please continue, I find this absolutely fascinating! The factors that you take into consideration when making your conclusions are truly en lighting.

Thank you!

P.S. I posted this question on another "expert" discussion page and even with a "Bounty" of $10. Received not 1 single reply. BRAVO! CR4 members.

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#12

Re: How can I calculate water discharge velocity?

04/25/2008 10:33 AM

US gallon = 231.009 cubic inches

1 inch circle = 0.785 sq inches

one gallon in pipe = 294.279 inches

10 gallon = 2942.79 inches of pipe or 2942.79 inches per minute

2942.79 IPM = 49 feet per second

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#22
In reply to #12

Re: How can I calculate water discharge velocity?

06/20/2012 5:03 AM

So, if it comes out of a 1/8in hole instead of a 1in open end, the velocity will be 82 x 49fps which is 3136fps or Mach 2.8, which is rubbish. So something is wrong.

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#23
In reply to #22

Re: How can I calculate water discharge velocity?

06/21/2012 10:47 AM

I'm not sure how or why this thread has been re-opened after four years, but it gives me an opportunity to re-assess the question. The reality of the situation described by the questioner is that he obviously has the ability to measure some of the perameters he has given. The pressure has been defined and the flow has been defined. Therefore, the question he is asking can be easily answered thusly:

We have pressure that drives the water. We have friction that regulates the pressure. The flow of 10 GPM will ALWAYS yield a velocity of .02228 feet per second in a standard 1" schedule 40 steel pipe having an internal diameter of 1.049" (standard for the industry). Therefore, the exit velocity will always yield that number if the flow is 10 GPM in the pipe and the pressure remains the same. If the restricted exit aperture (1/8" gap around the circumference of a 1.048" pipe) causes the exit velocity to change, there would be a corresponding change in the flow within the 1" pipe because that is what is driving the water. However, if the flow within the pipe remains the same, there would have to be a corresponding change in the pressure driving the water through the pipe. Now, the actual velocity through the aperture around the 1" pipe could be defined by the realtionship of the area of the pipe and the area of the resultant aperture around the pipe. The velocity through the aperture would be directly proportional to the area of the aperture to the area of the pipe opening.

Ap = Area of 1" pipe Vp = Velocity in the 1" pipe

Aa = Area of the 1/8" aperture Va = Velocity through the 1/8" aperture

So the formula Ap/Aa = Vp/Va would solve the question.

To determine the area of the aperture, we need to subtract 1/4" from the inside diameter of the pipe diameter and solve for the area of that, then subtract that from the full area of the 1" diameter pipe. The result would be the area of the aperture. Of course, all values would need to be converted to like terms ie., sq.ft., sq. in, cu. ft., cu. in., etc. Taking all this into consideration, it can be determined that the velocity in the aperture as well as the velocity in the pipe would be equal - 3.72 feet per second. This is not surprising given (as someone noted inan earlier reply) "...a gallon in equals a gallon out." If the flow in the pipe is 10 gpm, it must exit at the same flow. It can't disappear. The corresponding velocity (Flow/Area of conduit) would be the same no matter what the area of the final opening is.

The pressure driving the water through the pipe would be regulated by the opening size. The smaller the opening, the higher the pressure required to maintain the same flow through the pipe. Sounds conplicated, but it is not.

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Commentator

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#13

Re: How can I calculate water discharge velocity?

04/25/2008 11:47 AM

Seems to me the 1" pipe is irrelevant, it's 10 gpm at 1000 psi coming out a 1/8" hole, the math for that was explained in a couple of other posts, yes it's just an average and doesn't take the friction into account but given the parameters, I wouldn't think it would be all that much or very critical to be off a little bit.

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Guru

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#14
In reply to #13

Re: How can I calculate water discharge velocity?

04/25/2008 12:22 PM

1/8" gap 360 deg. open for discharge;

OK but its not a 1/8" hole it would be equal to a 0.3925 area

thus the flow would be 40/.3925 or 101.9108 FPS

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#15
In reply to #14

Re: How can I calculate water discharge velocity?

04/25/2008 12:57 PM

JEEZ!!

101.9108 feet per second translates to be

366,878.88 feet per hour which is

69.5 miles per hour...

Given a 1/8 inch stream, I don't think I would want to stand in front of it. It might drill holes in your body.

Bill

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#18
In reply to #13

Re: How can I calculate water discharge velocity?

04/26/2008 3:34 AM

It only comes into play when the volume of water greatly increaces (250 gpm @ 1/2" gap) I think could be wrong.

Also the conduit and the release chamber vary in size. In my use.

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Guru
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#16

Re: How can I calculate water discharge velocity?

04/26/2008 3:10 AM

There is a very interesting site includes all what you need related to piping: Piping Guide: Piping & Instrumentation Diagram in addition to the topics of fluid mechanics such as:

LIQUID PIPE FLOW: PIPE DIAMETER CALCULATION

REYNOLDS NUMBER AND FRICTION FACTORS

SIZING OF PIPELINES

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Associate

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#17
In reply to #16

Re: How can I calculate water discharge velocity?

04/26/2008 3:30 AM

Thank you I will put this to good worK!

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Anonymous Poster
#19
In reply to #17

Re: How can I calculate water discharge velocity?

04/26/2008 5:41 AM

If you want to create a glass-like umbrella-shaped flow, the flow must be laminar, not turbulent. You can predict if the flow is laminar by calculating the Reynolds number. Since Reynolds number is a function of fluid velocity, pipe dimension, and fluid viscosity, you will have to do iterations with different velocities and pipe dimensions that would result to a Reynolds number less than 2000. Once you get the velocity you need for laminar flow, you can estimate the diameter of the resulting umbrella-shaped flow using trajectory equations. Then you may have to repeat your calculations until you get the umbrella diameter you want.

The GPM can be calculated based on the velocity and area of the nozzle. The pressure is calculated based on what is needed to overcome the elevation, friction losses and entrance/exit losses.

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Anonymous Poster
#21

Re: How can I calculate water discharge velocity?

02/17/2011 4:08 PM

What pipe diameter flowing 1/2 full is required to carry 600 gpm at 2.5 ft/sec. How is the constant/ or standard number of 449 used in the formula.?l

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