11-05-2016, 07:29 PM

Association of Pumps in Parallel. [ PH<Q>, PQ<H> ]

From the author’s Engineering Collection, included in the ETSII4 module (ETI4 on the CL Library)

With these programs the combined head (H) and capacity (Q) values for centrifugal pumps associated in parallel are calculated using the individual head/capacity curves for each pump – modeled as second degree polynomials.

The H<Q> program will check for minimal capacity error condition if one of the pumps would run into stall mode with the given combined flow.

In addition to the driver programs with automated data entry, two subroutines QH and HQ can be used for manual operation or other checks.

Let H1 and H2 be the head-capacity curves for each of the associated pumps, P1 and P2. The general expressions are modeled as second degree curves, with a2<0, b2<0 for the case of pumps:

H1(Q) = a0 + a1 Q + a2 Q^2 ;

H2(Q) = b0 + b1 Q + b2 Q^2 ;

The program PH<Q> calculates the combined head for a given capacity, and PQ<H> does the reciprocal job, i.e. obtaining the combined capacity for a given head. The programs use the MCODE function QROOT (also included in the ETSII4 module for your convenience) to calculate the roots of the quadratic equations, and provide logic to select the meaningful roots for the physical problem.

Example.

Obtain the combined flow provided by two pumps in parallel with the height-capacity equations given below, when the combination generates a total head of 20 m

H1(Q) = 30 + 2Q – 0.096 Q^2; Q in l/s

H2(Q) = 20 + 0.3 Q – 0.015 Q^2; with Q in l/s

The solution using PQ<H> is: Q=25,0000 l/s

PS/ Updated MOD file attached - with corrections and improvements.

From the author’s Engineering Collection, included in the ETSII4 module (ETI4 on the CL Library)

With these programs the combined head (H) and capacity (Q) values for centrifugal pumps associated in parallel are calculated using the individual head/capacity curves for each pump – modeled as second degree polynomials.

The H<Q> program will check for minimal capacity error condition if one of the pumps would run into stall mode with the given combined flow.

In addition to the driver programs with automated data entry, two subroutines QH and HQ can be used for manual operation or other checks.

Let H1 and H2 be the head-capacity curves for each of the associated pumps, P1 and P2. The general expressions are modeled as second degree curves, with a2<0, b2<0 for the case of pumps:

H1(Q) = a0 + a1 Q + a2 Q^2 ;

H2(Q) = b0 + b1 Q + b2 Q^2 ;

The program PH<Q> calculates the combined head for a given capacity, and PQ<H> does the reciprocal job, i.e. obtaining the combined capacity for a given head. The programs use the MCODE function QROOT (also included in the ETSII4 module for your convenience) to calculate the roots of the quadratic equations, and provide logic to select the meaningful roots for the physical problem.

Example.

Obtain the combined flow provided by two pumps in parallel with the height-capacity equations given below, when the combination generates a total head of 20 m

H1(Q) = 30 + 2Q – 0.096 Q^2; Q in l/s

H2(Q) = 20 + 0.3 Q – 0.015 Q^2; with Q in l/s

The solution using PQ<H> is: Q=25,0000 l/s

PS/ Updated MOD file attached - with corrections and improvements.