Article #39: Parallel and Series Operation of Pumps, and Operating against Multiple Systems

In most training exercises or general discussions of pump-system interactions, great simplifications are made. The two most common examples presented are usually two pumps operating in parallel, or two pumps operating in series. Rarely, discussion involves more then two pumps, and even less frequently operation of a single pump against a multi-branched system is discussed. Yet, real installations rarely resemble such isolated and greatly simplified situations. Usually, in practice, multiple pumps operate against multiple branches of a system, or several interconnected complex systems operated with pumps coming on and off line, valves adding multiple new branches, or shutting off parts of the system.

Such multi-branched, multi-pump systems can no longer be analyzed with a graph and calculator in hand, but an entire computerized network of the plant piping, tanks, pumps, reflecting proper sizes, friction, elevations, and so on, need to be carefully modeled.

However, before the complexities of the entire plant modeling are attempted, the fundamentals of the multi-pump, multi-branch systems must be first understood. When such examination is reviewed, it becomes clear that the entire complex network is essentially a combination of the following three cases:

1. Several pumps in parallel, against a single system
2. Several pumps in series, against a single system
3. A single pump against two-branched system, or against a multi-branched system

This article presents the fundamentals of such three main building blocks of the complex network.

1-a: (2) pumps in parallel against (1) system                  1-b: (2) pumps in series – against (1) system              1-c: (1) pump – against (2) system branches

1-a: (2) pumps in parallel against (1) system

Method of construction of multiple (combined) pump curve: at constant head line (200’) double the flow (250 gpm x 2) for a point on a 2-pump curve. Repeat at several other constant head lines, such as at 400’ double the flow (200 gpm x 2). For 3-pump operation, triple the flow at constant head lines. Continue in the same fashion for more pumps. Intersections between one, two, three, or more pumps, with a given system curve establishes operating point (resultant head and flow) for multiple pumps.

1-b: (2) (or more) pumps (or pump stages) in series – against (1) system

Method of construction of multiple (combined) pump curve: at series of constant flows, add pump (or pump stages for multiple pumps) heads. Intersections between the result pump curve (stages curve) and a system curves establishes operating point (resultant head and flow).

1-c: (1) pump – against (2) system branches

Method of construction: instead of combining pump curves, add flows (at constant head) for systems (can be more then two). Intersection of the resultant system curve with a given pump curve produces operating point (resultant flow and head)

This process can be computerized as illustrated in a simplified example of a positive displacement pump operating against two systems (two branches). Underlying programming formulas are:

(1) H = h1 + k1 x Q12 – general equation for a system of branch (1), including static head h1 and friction with system friction resistance k1

(2) H = h2 + k2 x Q22 – general equation for a system of branch (2), including static head h2 and friction with system friction resistance k2

(3) Q = Q1 + Q2 – what leaves the pumps splits into branches

Known/given: Q, k1, k2, h1, h2

Need to find: Q1, Q2 and pump head h

Programming procedure:

1. Guess h
2. Calculate Q1 from (1)
3. Calculate Q2 from (2)
4. Calculate Q=Q1+Q2 and compare with given Q
5. If calculated flow is different then given, re-guess h and repeat the process until error is small

Only when these fundamental basics of the pump(s)-to-system(s) principles are understood, you are ready to take the next step – a computerized analysis of complex pumping systems.