How Do I Calculate the Change in Head When Reducing Discharge Line Size?

[RNPNR]

I have a pump running at 400rpm with 8" inlet and outlet with head 30 ft 500 gpm. Now I am planning to reduce the discharge line to 6" . Assuming the flow rate and speed constant the velocity in the pipe will increase. How do I calculate the change in head?

 

[russ_watters]

I have a pump running at 400rpm with 8" inlet and outlet with head 30 ft 500 gpm. Now I am planning to reduce the discharge line to 6" . Assuming the flow rate and speed constant the velocity in the pipe will increase. How do I calculate the change in head?

You nee to know the full details of the system and what you are changing. How long is the discharge pipe and what is it connected to? If the entire system is just one 3600 ft, 8" pipe (about what it takes to dissipate 30' of head), changing the pipe size without changing the flow rate (unlikely unless you increse the pump speed) increases the pressure required to 136'. That's from Bernoulli's principle or the affinity laws: pressure is a square function of velocity.

...but I suspect this answer isn't actually going to be useful to you...

 

[RNPNR]

You nee to know the full details of the system and what you are changing. How long is the discharge pipe and what is it connected to? If the entire system is just one 3600 ft, 8" pipe (about what it takes to dissipate 30' of head), changing the pipe size without changing the flow rate (unlikely unless you increse the pump speed) increases the pressure required to 136'. That's from Bernoulli's principle or the affinity laws: pressure is a square function of velocity.

...but I suspect this answer isn't actually going to be useful to you...

Thanks Russ. I am going to add a sketch here. As you have mentioned that I need to know the pipe length. The flow rate and head I am referring to is from a pump curve with 8" inlet and outlet

. I need to calculate the flow at different heads when using 6" pipe.

 

[russ_watters]

Ok, that helps. There are online calculators that will tell you the pressure loss of the pipe in question. You need the material, diameter, length and the details fo the fluid and flow:

http://www.pressure-drop.com/Online-Calculator/

The head loss due to the elevation gain will obviously not be changing, only the component due to friction in the pipe you are changing.

Edit: wait, does that say 9-11 meters elevation change? 9m is 29.5' and your pump only generates 30' of head...

 

[RNPNR]

Ok, that helps. There are online calculators that will tell you the pressure loss of the pipe in question. You need the material, diameter, length and the details fo the fluid and flow:

http://www.pressure-drop.com/Online-Calculator/

The head loss due to the elevation gain will obviously not be changing, only the component due to friction in the pipe you are changing.

Edit: wait, does that say 9-11 meters elevation change? 9m is 29.5' and your pump only generates 30' of head...

Pump generates 36' head max. the point I am looking at 500 gpm at 30 ft head. I need to calculate the change in flow with 6" pipe for 9,10 and 11 m head. It is not the gain. Sorry for confusions.

 

[russ_watters]

Pump generates 36' head max. the point I am looking at 500 gpm at 30 ft head. I need to calculate the change in flow with 6" pipe for 9,10 and 11 m head. It is not the gain. Sorry for confusions.

Ok, that's kind of what I figured. The difficulty here is that there are multiple variables and a real-world pump with a unique performance curve. Since you have one performance point fully spec'd, you can use that to predict the others, but you will need a way to map the calculations to the pump curve. To do that, I'd create a spreadhseet that models the piping system, calculating total system pressure drop from flow rate.

When you model the altered system (with the smaller pipe), you'll get a higher pressure than your pump is actually capable of handling. So then you adjust the flow rate in the new system until you reach a combination of flow and pressure that is back on the pump curve.

One potential problem I see is that since you are close to the maximum head of the pump, you are likely to find that small changes in lift result in huge changes in flow rate. The piping loss is a relatively small factor.

 

[RNPNR]

Here is what I calculated. We are changing diameter after the pump discharge. So I am assuming pressures change due to velocity change. After calculating pressure loss, I used affinity law to calculate new flow and head to make up for the pressure loss. One of the end condition is velocity cannot go below 4fps at any point in the pipe.

 

[russ_watters]

Here is what I calculated. We are changing diameter after the pump discharge. So I am assuming pressures change due to velocity change. After calculating pressure loss, I used affinity law to calculate new flow and head to make up for the pressure loss. One of the end condition is velocity cannot go below 4fps at any point in the pipe.

That's a great effort -- I'd actually whipped-one up myself this morning that was a lot simpler (though you have some information there you didn't share earlier...). Did you make that based on my direction or had you already made it? (Either way, I'm impressed.)

A few things:
1. The change in pressure due to change in speed should be ignored. It isn't a loss, it is conserved (that's the whole point of Bernoulli's principle; you get it back at the end of the pipe or if you increase the pipe size later). What is lost is just what is due to friction (and fittings). I assume you took column L from the link I posted? I get different numbers, but may have used different materials/friction (steel: 0.15). Still, even with 6" pipe at 500 gpm I only got 0.69 ft of loss. Clearly your lift height matters more.
2. You hid some columns where you calculated the loss through the reducer. I'm guessing you figured out they didn't have a significant loss so you decided to ignore them? Nice.
3. Your pump curves concern me; did you generate them from scratch, from the affinity laws? (they are just in an image file - I'm not seeing where they came from). They don't look anything like real pump curves; they should be...curved. Do you have a pump make and model in mind that you can get a real pump curve from?

What you should be finding is that the numbers you calculated in your tables feed into a curve that is shaped like the first quarter of a circle -- and you'll be near the top of that. So a small change in pressure loss will result in a large change in flow.

 

[RNPNR]

These pumps are single vane impeller pumps used to transfer live fish from one tank to the other. These are not traditional centrifugal pumps. Hence the curves.
Regarding calcs yes I used one incorrect value and I have corrected it now.
I built this spreadsheet after your suggestions.

 

[russ_watters]

These pumps are single vane impeller pumps used to transfer live fish from one tank to the other. These are not traditional centrifugal pumps. Hence the curves.

Fair enough. Odd curves, but I'll take them for what they are.

I built this spreadsheet after your suggestions.

I'm legitimately impressed with your effort. Want a job?

The effort is great, but I don't think you quite got how it works. The system curves and pump curves are not related to each other. The system curve is curve of the losses inherent in the piping system for a range of flows, whereas the pump curve is the pressure associated with the flow a pump can generate. As the pump flow goes up, the pressure it can generate goes down, but as the system flow goes up, the pressure required to push through it goes up. So picking one pump curve and matching two system curves...see attached.

The bottom line I'm finding is that since almost all of your pump head is chewed-up with your elevation gain, the pipe size has very little impact.

Caveat: I'm not sure my system curves match your realities. Your OP mentions a specific flow, pressure and RPM that don't match what you gave in the spreadsheet. I would have expected that was a real measurement. So some adjustment may be needed...