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Worksheet Grade 12 Engineering & Design

Pindrock Meter Test Bench: Accuracy and Lost Revenue Worksheet

A grade 12 worksheet where students grade water meters on a fictional utility's test bench, compute percent accuracy, and trace under-registration into lost revenue.

Objectives

  1. Students will compute a water meter's percent accuracy from bench test data.
  2. Students will apply an accuracy acceptance band to decide which meters pass.
  3. Students will translate meter under-registration into annual lost revenue and a replacement payback period.

Vocabulary

Key words: test bench, percent accuracy, under-registration, apparent loss, payback period

Teacher overview

Every gallon a utility sells passes through a meter, and meters lose accuracy as they age. A worn meter usually runs slow, recording less water than actually passed through it, so the customer is billed for less than they used. Utilities call the difference an apparent loss, water that was delivered yet never billed. This worksheet puts students at the fictional Pindrock Water Utility's meter test bench, where a known volume is run through each meter and the reading is compared against it, and then follows the arithmetic from one slow meter to a fleet-wide revenue decision.

Pindrock Meter Test Bench: Accuracy and Lost Revenue Worksheet — Grade 12 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

The fictional Pindrock Water Utility tests meters by running exactly 100.0 gallons from a calibrated tank through each meter and recording what the meter registers. Percent accuracy = registered volume ÷ actual volume × 100. Pindrock accepts a meter if its accuracy falls between 98.5 and 101.5 percent. The retail water rate is $4.20 per 1,000 gallons.

  1. Meter A registers 96.5 gallons on the 100.0-gallon test. Compute its percent accuracy.
  2. Does Meter A over-register or under-register, and which party, the customer or the utility, loses money because of it? Explain in one sentence.
  3. Meter B registers 101.8 gallons on the same test. Compute its percent accuracy.
  4. Meter C registers 99.2 gallons. Using the 98.5 to 101.5 percent acceptance band, state which of the three meters pass.
  5. Why does the bench use exactly 100.0 gallons from a calibrated tank rather than an ordinary garden-hose fill? Answer in one sentence.
  6. A household served by Meter A actually uses 9,000 gallons in a month. Using Meter A's accuracy, how many gallons does the meter register for billing?
  7. How many gallons of that household's monthly use go unbilled?
  8. At $4.20 per 1,000 gallons, how much revenue does the utility lose on that household in one month?
  9. Pindrock has 1,400 aging meters that behave like Meter A, each with about 315 unbilled gallons per month. How many gallons per year go unbilled across that fleet?
  10. What is the fleet's total lost revenue per year at $4.20 per 1,000 gallons?
  11. Replacing one meter costs $95 installed and restores full accuracy, recovering that meter's lost revenue of about $15.88 per year. Compute the simple payback period in years, to the nearest tenth.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key
  1. Answer: 96.5 percent. 96.5 ÷ 100.0 × 100 = 96.5 percent accuracy.
  2. Answer: It under-registers, and the utility loses money. The meter records less than the water actually delivered, so the customer is billed for less than they received.
  3. Answer: 101.8 percent. 101.8 ÷ 100.0 × 100 = 101.8 percent accuracy.
  4. Answer: Only Meter C passes. Meter A (96.5 percent) falls below 98.5, Meter B (101.8 percent) sits above 101.5, and Meter C (99.2 percent) is inside the band.
  5. Answer: The test needs a known true volume. Accuracy is a comparison against the actual amount delivered, so the reference volume must itself be measured to a tighter standard than the meter being tested.
  6. Answer: 8,685 gallons. 9,000 × 0.965 = 8,685 gallons registered for billing.
  7. Answer: 315 gallons. 9,000 − 8,685 = 315 unbilled gallons that month.
  8. Answer: $1.32. 315 gallons is 0.315 thousand gallons, and 0.315 × $4.20 = $1.323, about $1.32 of lost revenue.
  9. Answer: 5,292,000 gallons. 315 gallons × 12 months × 1,400 meters = 5,292,000 unbilled gallons per year.
  10. Answer: $22,226.40. 5,292,000 gallons is 5,292 thousand gallons, and 5,292 × $4.20 = $22,226.40 per year.
  11. Answer: 6.0 years. $95 ÷ $15.88 per year = 5.98, which rounds to a payback of about 6.0 years.

Differentiation

Support

Provide the accuracy formula with the fictional bench's 100.0-gallon divisor already in place, so items 1 and 3 reduce to reading the registered value, and give a worked model for item 6 using a different meter accuracy such as 98.0 percent on 5,000 gallons.

Extension

Ask students whether the fictional utility should also replace the newer meters that behave like Meter C, using the same $95 replacement cost against the much smaller loss a 99.2 percent meter produces on 9,000 gallons per month, and to defend the resulting policy in two sentences. (The loss is about 72 gallons per month, roughly $3.63 per year, so the payback stretches past two decades.)

ELL supports

Provide a labeled photo-style diagram of a test bench: calibrated tank, meter under test, and the two numbers being compared. Offer sentence frames for items 2 and 4: "Meter A reads ___ than the true amount, so the ___ loses money," and "Meter ___ passes because ___ is between 98.5 and 101.5."