## A Simplified Method for Monitoring Pump Performance

### Selecting the Optimum Field Test Method

Monitoring performance in the field has always been a challenge due to an absence of field-mounted instrumentation, the time required for testing, and imprecision from the cumulative uncertainty of all performance variables involved.

Last month I reviewed a practical, cost-effective, and environmentally-friendly pump performance assessment method to determine the pump’s health and whether repairs are economically justified. That simplified method, as researched by D. Budhram, M. Russek, and myself, advocates using only motor power and flow measurements to determine if a pump is healthy or worn.1

The purpose of this column is to refine some of that original research and introduce a new means of determining which field analysis method is best for your situation. Centrifugal pump users have several pump assessment methods to choose from. Each one has its own advantages and disadvantages. Here are the most common.

## Single-Variable Method

*Head at shut-in conditions*– Using this method, you run the pump dead headed and measure the pump’s differential pressure. This method requires a pump curve and the willingness to shut the pump in long enough to gather the data.

## Two-Variable Methods

*Head vs. Flow*– With this method, you can test the pump at any flow rate. You measure the output flow (*Q*_{M}) and compare it to the apparent flow (*Q*_{A}). The apparent flow is the test curve flow that corresponds to the field-measured differential pressure. This method requires a test curve from the manufacturer.*Power vs. Flow*– Using this method, you can also test the pump at any flow rate. With this method, you measure the output flow (*Q*) and compare it to the apparent flow (Q_{M}_{A}). The apparent flow is the test curve flow that corresponds to the field-measured horsepower. This method requires a test curve from the manufacturer.- The two-variable methods assume that the apparent lost flow (
*Q*) is due to internal leakage and can be reestablished by renewing internal clearances._{A}-Q_{M}

## Three-Variable Method

*Head, Flow, and Power*– With this method, you can test the pump at any flow rate. This method doesn’t require a test curve. By measuring head, flow, and power you can determine the pump’s hydraulic efficiency directly.

(Note: I consider *H*, *Q*, and *P* to be primary (measured) quantities and hydraulic efficiency to be a secondary (calculated) quantity. This is because efficiency has the greatest percent error of all test stand results due to the fact that errors in all the primary testing quantities, i.e. *H*, *Q*, *P1*, *P2*, and S.G., “stack-up” during the calculation of η. For this reason, efficiency is not the best choice for trending pump condition under field conditions.)

## A New Method

The original research recommended the Power vs. Flow method for pumps with low specific speeds (< 3000) to ensure the horsepower vs. flow slope is both positive and easy to resolve into reasonably small horsepower increments.

I now realize this was a rather vague guideline without a clear technical basis. A major goal of this column is to better quantify when head vs. flow method should be used, and when the power vs. flow method should be used.

I first began my analysis by approximating a general performance curve with a straight line (see Figure 1). The line has the general form H = Ho + mQ, where Ho is where the tangent line at the best efficiency point (BEP) intersects the abscissa and m is the slope of the tangent line. I assume the efficiency is constant over the flow range of interest, which is a good assumption at BEP. (Note: Ho should not be confused with the pump’s shut-in pressure.)

**Figure 1. Typical pump curve with simplified performance line.**

- Starting with this approximation, my aim was to determine whether pressure or power measurements would lead to higher uncertainty in apparent flow (
*Q*). What good is an accurate measured flow (_{A}*Q*) if the_{M}*Q*is excessive? The desired result of a field assessment is to determine the Δ_{A}*Q*value, which is equal to*Q*. The uncertainty in the flow discrepancy (Δ_{A}-Q_{M}*Q*) is:

Uncertainty in the flow discrepancy = ((Uncertainty in *Q*_{A})^{2} – Uncertainty in *Q*_{M})^{2})^{0.5}

To reduce the uncertainty in Δ*Q* to useful levels, we must ensure the uncertainty in both *Q _{A}* and

*Q*are also at useful levels.

_{M}I will not include the derivation of what I call the flow error ratio (*Ø*) parameter here, but anyone interested can find it in the appendix. I will only present only the results here. The *Ø* parameter, which is the ratio of apparent flow error (Δ*Q _{H}*) expected when using the head vs. flow method to the apparent flow error (Δ

*Q*) expected when using the power vs. flow method is given by the following equation:

_{P}