Simple flow through a pipe question.
Simple flow through a pipe question.
(OP)
Hey Everyone,
I have what I think should be a relatively simple problem, unfortunately I cannot find a good formula to help me do the calculations. Each formula I find does not resonates well in my head because I can't seem to grasp the basic principals..any input would be greatly appreciated!
Lets say I have a 1/2 in. copper tube of some length X connected to a large water main which has essentially constant pressure (50 PSI) and infinite water flow capacity.
If this copper pipe was capped at its end so that it had no flow through it, I know I could stick a gauge at every inch of this copper tube length and measure 50 PSI, that part is clear in my head. However, if I was to remove the cap and let water flow, what formula could I use to calculate the pressure within the copper tube at various lengths say 0.25X, 0.5X, 0.75X and 0.9999X (right before exit). I'd love to know the formula for this so that it can help me visual what is actually happening inside that pipe and at it's exit.
The above theory is just so that I can learn how to calculate how much water (GPM) will actually come out of the copper tube assuming its just open without the cap given that the source of the water is 50 PSI constantly.
Help with any of the above would be of great help.
Thanks in advance!
I have what I think should be a relatively simple problem, unfortunately I cannot find a good formula to help me do the calculations. Each formula I find does not resonates well in my head because I can't seem to grasp the basic principals..any input would be greatly appreciated!
Lets say I have a 1/2 in. copper tube of some length X connected to a large water main which has essentially constant pressure (50 PSI) and infinite water flow capacity.
If this copper pipe was capped at its end so that it had no flow through it, I know I could stick a gauge at every inch of this copper tube length and measure 50 PSI, that part is clear in my head. However, if I was to remove the cap and let water flow, what formula could I use to calculate the pressure within the copper tube at various lengths say 0.25X, 0.5X, 0.75X and 0.9999X (right before exit). I'd love to know the formula for this so that it can help me visual what is actually happening inside that pipe and at it's exit.
The above theory is just so that I can learn how to calculate how much water (GPM) will actually come out of the copper tube assuming its just open without the cap given that the source of the water is 50 PSI constantly.
Help with any of the above would be of great help.
Thanks in advance!





RE: Simple flow through a pipe question.
Unless I'm missing something...
RE: Simple flow through a pipe question.
Look at this site:-
http://www.princeton.edu/~asmits/Bicycle_web/Berno...
RE: Simple flow through a pipe question.
The D-W formula, including the resistance coefficients is
ΔP = ( (ƒD x L/D) + ΣK) x (ρ.V2/2)
Unfortunately there are 2 unknowns - ƒ and V. But ƒ is only a function of the pipe and fluid properies and the velocity so it is not really independent. You guess an ƒ, solve for V and then test that V to see if it gives the correct ƒ. If not, correct ƒ and re-solve for V. Repeat until ƒ doesn't change any more.
The tricky part is getting the units right. There are plenty of online calculators and downloadable spreadsheets and calculators that will do this for you.
Katmar Software - AioFlo Pipe Hydraulics
http://katmarsoftware.com
"An undefined problem has an infinite number of solutions"
RE: Simple flow through a pipe question.
David Simpson, PE
MuleShoe Engineering
Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat
RE: Simple flow through a pipe question.
I tend to lump "Bernoulli" and "Darcy" together...which, as you state, is technically wrong. The formula provided by Katmar is indeed what I had in mind, but I messed up.
Too long on the tractor yesterday.
RE: Simple flow through a pipe question.
David Simpson, PE
MuleShoe Engineering
Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat
RE: Simple flow through a pipe question.
Use the "modified Bernoulli equation" that incorporates fL and it works even better than D'arcy alone. Facts are that you can't ignore either one at the expense of the other and understand what the heck is going on in anything except a horizontal pipe with flow, or a pipe at any orientation but with no flow at all.
I hate Windowz 8!!!!
RE: Simple flow through a pipe question.
I see I can use the Darcy-Weisbach formula to calculate pressure loss per length of pipe, but that assumes I know velocity of the liquid going through the pipe right? How do I get this velocity?
I figure also that once I know velocity, I can calculate the flow rate..
RE: Simple flow through a pipe question.
Seems like I can also just use Hazen-Williams equation right and where it requires pressure drop, I just substitute gauge - atmospheric. Am I correct with that?
http://en.wikipedia.org/wiki/Hazen%E2%80%93William...
RE: Simple flow through a pipe question.
Hazen Williams is not as accurate as D-W. H-W is a simplified solution where the roughness coefficient is not a function of Reynolds number (i.e. unaffected by velocity). This is not true in reality, but H-W is useful in water reticulation systems where the Reynolds numbers fall in a relatively narrow band.
You could use Hazen Williams as a first estimate to start the trial and error solution with D-W, or if your need for accuracy is not too great you could accept the HW solution. In your case, a major shortcoming of H-W is that it does not have a good way to deal with the "minor losses" due to the pipe fittings - the inlet and outlet in this instance. Because you have a short piece of pipe the minor losses are likely to be significant and whether or not you include them depends only on how accurate you want to be. As mentioned by SNORGY earlier, your ΣK will be 1.5 (0.5 for the inlet and 1.0 for the outlet).
Katmar Software - AioFlo Pipe Hydraulics
http://katmarsoftware.com
"An undefined problem has an infinite number of solutions"
RE: Simple flow through a pipe question.
I hate Windowz 8!!!!
RE: Simple flow through a pipe question.
David Simpson, PE
MuleShoe Engineering
Law is the common force organized to act as an obstacle of injustice Frédéric Bastiat