# Pressure drop in elbows & bends in a pipe

1. Aug 9, 2007

### bajaj_383

hi!
i want to calculate pressure drops in a pipe having various elbows ,bends & valves.whts equation should be used to calculate the pressure drop.

thanks
gaurav

2. Aug 10, 2007

### Q_Goest

Hi bajaj,
Attached is a nice summary of how it's done throughout industry. Each elbow, valve, section of pipe or other fluid restriction is given a resistance coefficient, K. All resistance coefficients can be summed up and put into the Darcy Weisbach equation as shown in equation 2 of the attached.

#### Attached Files:

• ###### Pipe-Flo Pro.pdf
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3. Aug 10, 2007

### FredGarvin

Perhaps one of the mentors could sticky your post Q. There seem to be a big need.

4. Aug 11, 2007

### Q_Goest

Hi Fred,
Ya know it's kinda strange that the standard method for calculating flow through piping systems isn't taught very well in undergraduate college. At least, it wasn't at my school. Seems colleges like to focus on the most fundamental, theoretical methods. That isn't to say the standard method of doing pressure drop/flow calculations through pipe isn't based on theoretical concepts, but at least it's been refined almost to the point of being a cook-book, hasn't it?

We've often talked about creating a thread that might discuss this method for calculating pipe flow, but the more I thought about it, the more it seemed we needed a whole paper that discussed at length how this is done that we could post. I didn’t want to have to write everything myself – too much work, not enough pay :grumpy:. lol Anyway, I eventually found this paper. It comes from a company that sells software for pipe flow and this paper documents the basic method. I haven't read through it in detail, but everything I've seen thus far looks good. Have you looked it over yet? Seen any obvious problems?

Let’s use this thread to talk about what should go into a post regarding how to do pipe flow analysis. Then we could create a new thread, starting off with a good introduction to pipe flow, and present material such as this paper or any other references such as for expansion joints (convoluted metal hose) or other restrictions that aren’t covered by this paper such as mitered elbows at various angles, orifices, etc... We might consider putting in a spreadsheet calculator too. Quark sent me one that might be good. Speaking of whom, where is Quark? I’d like to get his involvement in here too.

I think we need to start off from the perspective of someone in college or who had just graduated. Why would someone like that want to read the post or learn about pipe flow? What are we going to present and where does it come from (ie: references)? What are the limitations? Why not use CFD or NS equations for pipe flow? Where does the standard Bernoulli equation limit us in calculating pipe flow? Why use Darcy-Weisbach, why not Poiseuille or others? What limitation is there on low pressure or vacuum (introduce Knudsen number since this method is also applicable to vacuum systems down to a relatively low pressure, typically ~ 0.1 Torr)? Etc…

Hmm… that’s about it for now. I like the idea of coming up with a thread that could be used for reference on pipe flow (he says for the umpty-squat time), but I think we should talk about the best way to do that and what it needs to contain.

Comments from students and others here would be great too! I think we should hear from everyone.

5. Aug 11, 2007

### Astronuc

Staff Emeritus
Great idea!

In my undergrad program, the Fluid Mechanics course did provide both theoretical concepts and practical application, and we would be expected to derive the practical from the theoretical. In the graduate program, it was more complex and to the point of developing numerical solutions/programs for CFD.

I think pipe-flow is largely cook-book now. Many companies, which provide piping or which build fluid transport systems, have manuals, which give equations and tables for pipe flow (including resistance coefficients for piping and fittings), pump performance, and other useful engineering information.

Thank you Q_Goest for that useful pdf attachment.

Last edited: Aug 12, 2007
6. Aug 11, 2007

### bajaj_383

can u focus something on how pipes in parallel will work in comparison to the same pipes in series.i want to calculate pressure drop across 4 parallel pipes emerging from a tank & entering inside the other tank . pipes of sam dia,& same length.
thnks

7. Aug 12, 2007

### Q_Goest

Hi bajaj,
I see you posted your question up in the classical physics forum and got a responce. Here's just a few more thoughts. Note that putting two or more pipes in parallel will result in some flow rate between points 1 and 2, but when these pipes are put in series with the same pressure drop, the flow rate can't be directly calculated from the parallel case. Although pressure drop is a function of the square of the flow rate, the friction factor can change dramatically with velocity. The Darcy-Weisbach equation looks a lot like:
dP = C * Q^2
where dP = pressure drop
C = a constant for any given piping system
Q = flow rate
But the C in the equation is a function of friction factor, f, which varies with flow. So it's not so simple.

Hi Astronuc,
Thanks for the kind words. I'll see if I can write up a rough draft for the thread in the next day or so. Hope to hear from you and get comments.

8. Aug 14, 2007

### FredGarvin

I do see Quark poke his head in from time to time. I do agree it would be nice to get his input as well with it.

I'll start with a quick attempt at an outline and some major points. I'll PM you when I get it together.

9. Jul 16, 2010

### mzp

Please use this handbook with extreme caution & doublecheck the equations/formulas.
E.g.: there is a vicious typo in equations 1&2. dP is labelled as a _pressure_ drop instead of a head loss.
The difference is pressure=pascals=N/m2
head loss = meters

Its always a good idea to check the units of any posted equation.

mz

10. Jul 19, 2010

### stewartcs

Pressure drop can certainly be expressed in meters of head just as it can be in Pascals.

CS

11. Jul 19, 2010

### mzp

While that is certainly true, head loss is typically labeled "h" with units of length, and "P" is typically expressed in terms of Pa, psi, etc.

There is another typo that I've found just recently: the sudden expansion and contraction equations should be divided by beta^4; beta=dSmall/dLarge.

12. Jul 19, 2010

### stewartcs

Not really, over the years I've seen it both ways equally. Just depends on the application.

They do not need to be diveded by beta^4 since the velocity is based on that of the smaller diameter pipe. However, if the velocity is based on that of the larger diameter pipe, then one would divide by beta^4.

CS

13. Mar 15, 2011

### QPAS

I wonder if there is no table or graph with which I can make a quick estimation of the pressure drop in function of pipe diameter and flowrate ( for 90° bends only ) ... can anyone help me with that ??

14. May 27, 2011

### vivaldoblue

What do you want to tell him?

15. May 27, 2011

### mombarre

this is a useful thread. I am waiting to hear more ..please keep it alive.

16. May 30, 2011

### spanky489

bernoulli's equation(which is in fact posted in the pdf our colleague posted up higher), i just handed in my lab report last week on this topic.

of course some parameters must be known in order to calculate the losses in bends.

so basically this is what bernoullis equation looks like:

$\frac{p_{1}}{\rho\cdot g} + \frac{v^{2}_{1}}{2\cdot g} + \ z_{1} + \ h_{pump} = \frac{p_{2}}{\rho\cdot g} + \frac{v^{2}_{2}}{2\cdot g} + \ z_{2} + \ h_{losses}$

$\ h_{losses} =\ _{i=1}^{n}\sum{\frac{v^{2}_{i}}{2 \cdot g} \left[\xi_{valve} + \xi_{bend} + \xi_{friction} \right]}$

now if your water flow sistem doesnt use a pump you take it out of the 1st equation and continue calculating with the already stated variables.
Of course you will need to know a few things before you can start. 1st you need to know both pressures of the points you are referring to, then you need to know both of the velocities(if you know one velocity and the corresponding flux, you can calculate the 2nd), $\ z_{2} - z_{1} =$ height difference.

regarding losses, they are the sum of all elements with a particular velocity.

lets say there are 2 valves inbetween point 1 and 2, and 1 valve and 1 bend inbetween points 2 and 3.
now if im trying to find global losses in my system i will use the bernoulli equation for points 1 and 3. ill give an example how to calculate the losses in between.
$\ h_{losses 1-3} =\frac{v^{2}_{1-2}}{2 \cdot g} \left[2 \cdot \xi_{valve} + \xi_{friction 1-2} \right] + \frac{v^{2}_{2-3}}{2 \cdot g} \left[1 \cdot \xi_{valve} + 1 \cdot \xi_{bend} + \xi_{friction 2-3} \right]$

i hope this will help you guys with your problems.
if you need any help regarding this topic in the future feel free to ask.

Last edited: May 30, 2011
17. Oct 18, 2011

### bhavikkp

Can anybody show how to develop a model for the flow through pipe with all fitting

18. Oct 20, 2011

### stewartcs

What kind of model? The equations have already been given in the earlier threads.

CS