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Name: James
Status: student
Grade: 9-12
Location: TX 
Country: N/A
Date: 7/22/2005

I was designing a water system for cattle (4H). Basically I am going to tap into a water pipeline, and run a much smaller pipe to a storage tank. The pressure would remain constant in the big pipe since it is a huge pipe. I could find the pressure in it also (250 psi). I know: length of my pipe running off of the main line (2 miles); the diameter (2 inches), a textbook told me the viscosity (.01 kg/m/s), and the rise in the elevation 200 feet. I found an equation but it talks about the velocity of the water and I do not know how to add that into my equation. I would like to know how much volume I will get at the end of the line.

Civil engineering covers hydraulics, and maybe while in school I could have dealt with the problem, now I would go to our hydraulics or mechanical people.

For whatever help here are my thoughts, there are many factors affecting the flow, there will be friction losses in the 2 mile pipe. Overcoming gravity for a 200 foot rise will impact the flow. It sounds like the pipe is exposed, so that can add thermal impacts. Any loss in the jointing, that is not one stretch of pipe. Being a "take off" from the main pipe, can add some flow effects that could affect the initial pressure. There are tutorials on the web for designing pumps. It may be an approach to work backwards, find the pump and therefore the pressure to get the gallons per minute to the destination.

James Przewoznik

Hi James,

You wish to know what flow rate, in gallons per minute, you can expect to discharge from the end of your new pipe. Flow moves through pipe due to a difference in pressure between each end. You have a driving force of 250 psi. If we convert this to feet of water, (multiply by 2.31) we get a driving force of about 577.5 feet.

Now, flow through the 2" pipe will be resisted by basically two main effects (let us keep this simple OK?). You have the change in elevation, and you have the friction loss in the pipe due to the water flowing through it. The elevation change is simple, it is 200 feet and since we are going uphill, we subtract this directly from the driving force. So, now our driving force is 377.5 feed of "head" as we call it.

Friction loss is a little more tricky, I use an empirical formula called Hazen-Williams for the calculation. This formula is

H(friction) = 0.002083 * L * (100/C)^1.85 * ( gpm^1.85/d^4.8655)

Friction loss is equal to a constant times L which is the equivalent length of straight pipe. C is a roughness factor of the pipe in use. If you are using new steel pipe or smooth plastic, use 120 here for the value of C. Little d is the inside diameter of your pipe in inches. Gpm is your chosen flow rate.

So, let us figure some of this out. Equivalent length of pipe equals the total length of pipe plus conversion of fittings to pipe length. For example, a 2 inch 90 degree elbow has the same friction loss as 5 feet of straight pipe. In your case, you have two miles of piping and I will assume not a lot of turns, etc. Two miles is about 11,000 feet of pipe so not counting a few fittings really will not make too much of a difference.

Little d for 2 inch steel pipe is 2.067 inches


L = 11,000 feet
C = 120
d = 2.067

Now, we cannot calculate the friction loss without the flow and we cannot get the flow without the friction loss. So, we will make a graph of flow vs. friction loss in feet of water. Here is what you do, choose a flow rate, say 10 gpm. Plug it into the equation with all of the above values and get a friction loss. Repeat at 20, 30, 40, 50, etc. Once you reach 100 gpm, make a graph with flow on the x axis and friction loss in feet on the y-axis. Plot the points and you will see that it makes a curve. This is called the system curve and tells you how your pipeline flow will react to changes in resistance.

Once you have your curve, find 377.5 feet on the y-axis and make a straight horizontal line across the graph. At the point it intersects the system curve, move straight down to the X-axis and read the flow. This will be the flow you can expect from your system.

Good luck, and contact me again to let me know what your answer is or if you have any difficulties.

Bob Hartwell

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