I don't understaand. You have system #1 feeding in to #2?

System Curve and Pump Performance Curve

Yes sir, here system 1 feeds system 2. Here can i add both pumps curves and both system curves based on series law then get a operating point?

Basically you put both pump curves on the same graph and read off the intersection point.

But, "Both systems are having so many bends and valves, etc." will complicate things considerably.

Sir, my doubt here is, since i've two pump curves and two system curves separately, how to get a single operating point of the whole system?

By iterative methods.

Either that, or switch it on and read the required information from pressure gauges.

Assuming the 2 pumps cover similar flow ranges, (otherwise you're going to have problems) you can get a combined pump curve by adding the 2 heads at each flow.

Ditto for the 2 systems, and plot the combined pump and system curves on the same graph.

As #4, check the pressure at relevant points in the combined system.

In multistage / serial pumping the pressure contribution of each stage is added together. in your case the booster pump can be anywhere provided that there is always a positive pressure in the pipe system.

Sir -

In each piping system, convert your bends and fittings to equivalent lengths of straight pipe and you will simplify your concerns over these considerably. If your two systems are of the same diameter and coeffecient you may combine them to calculate the systems curve as a single system without issue. If they differ in parameters it is easier to calculate their respective head losses at given flow rates and simply combine the resulting pressure losses and draw a single combined system curve.

Regarding your pumps, at each given flow rate, add the pressure provided by each pump to reach a new pressure of the combined pumping at that same flow rate. Use these new flow/pressure values to draw a new pump curve that represents the combined impact of both pumps running together.

He's already worked out the system characteristics, said so in original post.

How to combine the two systems

Start with system #2 and assume a inlet pressure of say 5m. and choose your pump.

deduct the 5m (or whatever) from the duty point - that pump is only responsible for the boosted pressure)

Then you add a working pressure of the chosen 5m to system #1 and choose your pump.

The above is based om a constant delivery and pump 2 is a booster.

Lets keep it simple. If you have one, two or three pumps, multi-stage and of different number of stages (impeller & defuser) per pump, then the pump curve for all the pumps should be the same. That is, same efficiency, same lift, same flow rate and same HP required per stage.

So then you ADD together the LIFT per STAGE for ALL pumps and HP per STAGE for the TOTAL number of stages you have(this will give you the required Motor HP to drive the pumps if you have them all connected together). REMEMBER the FLOW RATE remains the same. That is the simple way to do it.... Pumps first!

But I suspect you have different pumps, in different positions (not mechanically joined together) with different flow rates etc and you want to use them to move fluid. Lets start at the source of your fluid you wish to pump. You would put your largest pump in terms of flow rate closest to the source, then the next size down and finally the smallest pump would be your last. Your system flow rate(or flow rate at the final destination of the fluid) would be that of the smallest pump. Once you have that configuration set, you can then work out your TDH per section per pump.

Slightly more info is needed

Are there take off points on system 1? That then prevent all the water pumped against the final head of system 2.

Is the intention to save on pipe class?

Are the 2 pumps the same?

This is water?

What is done often is to lift the water from a river by submersible and then pump it further with the booster.

Sir,

I've attached below the look of my system and the approach i'm following. Please correct me.

From Figure 2, i've arrived Figure 3 by adding system curves and Pumps curves separately and overlapping on the same graph. Is my operating point correct?

If so, then how i arrive my operating point?

I assume you mean you've added the pump heads for a range of flows (and again for the system).It looks that way from the curves. If so, that's OK, and your operating point??? is correct.

Are you sure the system has no static head?

Thank you sir, for the reply.

As you've told, i've added the pump heads for a range of flows (and again for the system also) and arrived the final system curve and pump curve. And as in circuit there is no static head and so my system curve starts from zero.

I've one more doubt sir,

If i've a Centrifugal pump and then a positive displacement pump (Gear pump) in series, how to get the operating point for the system downstream of the two pumps. Since this is the case in my gas turbine engine.

The combined pump curve is a vertical straight line, flow determined by that of the PD pump. Head is where that line intersects the system curve. The centrif flow is the same, generated head determined by where that flow is on the pump curve. But you need to be a bit careful about the 2 system losses to ensure no negative pressure anywhere. I would draw the circuit and add the pressures at various points.

greetings again.

(I have to point out, today is America's day to yet once again prove how dumb we can be; today is election day and today we are casting our votes for our new government leaders based on hype, lies and sound-bites.)

Now, on to your question...

From your diagrams and sketch I have some assumptions I'd like you to confirm or correct and some questions - lastly some more input.

First, you last sketch is correct, in the theory.

Assumption 1 - I do not see multiple sources of flow or multiple discharges that would alter the flow thru the systems (both 1 and 2) Resultant question - is your goal to have uniform flow across the entire combined system, from input flow at pump 1 to the discharge of system 2?

Assumption 2 - I am not sure why you have placed the control valve in system 1, if you need to boost the pressure by installing pump 2, then I see no need for the flow control valve located between the two pumps. resultant questions - what are you setting the flow control valves at? If you are using them, can you tell me their Cv factor, the diameter and length of the two systems?

finally, You show pump 1 has a lower pump curve than pump 2. Is this true and your existing conditions (or just how you chose to represent it in a drawing)?

if you imagine system 1 and 2 are a single system by removing pump 2 from the drawing, you can calculate the system curve as one single system. in this process, the math does not care where pumps 1 and 2 are located, we as designers do, but the math does not, so just imagine the system as one length, with the pumps removed. This gives you exactly what you have drawn in the final system curve sketch.

again, the math does not care; add the pump curves just as you have done in the last of your pump curve drawings and you will have your equivalent combined pump curve.

Now some design concerns. always, ALWAYS install your pumps with the largest pump upstream and smallest pumps downstream, this prevents a large pump from pulling the flow away from the smaller pump faster than the small pump can supply and causing damage inside the small pump. although it is not uncommon to combine different pumps in series, there are risks, if the larger pump is operating such that it cause the system to flow at a rate that is too far out to the right on the smaller pump, this will have the same impact as if you were running the smaller pump alone without adaquate system head and you will burn up the motor on the pump.

if you plan on running the small pump at low flow/head demand conditions, then turning it off and running the larger pump at medium demands and both pumps in series for your high demand conditions, then you should consider installing a loop of pipe around each pump with a check valve and installing shaft brakes to prevent the 'off duty' pump from spinning due to the flows generated by the 'on duty' pump. You should never allow a pump that is free spinning to be turned on, this can cause shaft and bearing damage to occur.

Try to always have the smallest diameter pipe upstream and progress to larger pipe if you must change sizes, this decelerates the flow at the transition. Try to never pump into a large pipe first where the flow is forced to neck down into a smaller diameter conduit, this could turn the first multiple of diameters of the smaller into a nozzle and errodes the transition and pipe walls to premature failure. Additionally when there is a sudden stop of the flow, you risk damage and/or blowout when the large pipe flows towards the smaller pipe

His later post #16 says the 2nd pump is PD. That contradicts his sketch #14, and it would have helped if he'd given the right data at the start. But it alters the situation.

Incidentally I've known of PD (piston type) pumps, giving about 100 bar discharge pressure, that needed suction pressure 5 barg to avoid cavitation. Suction pressure usually provided by a centrif.