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Worksheet Grade 6 Engineering & Design

Wembrey Ombry Street Leak Sensor Spacing Worksheet

Eleven items where students space leak sensors along an old water main in a fictional town, price the sensor set, and compare what the leaks cost with finding them.

Objectives

  1. Students will divide a pipe length by a sensor's listening range to find how many sensors a design needs.
  2. Students will calculate the daily and yearly cost of leaking water from a price per thousand gallons.
  3. Students will compare the cost of a sensor set with the savings it produces.

Vocabulary

Water main
A big underground pipe that carries drinking water beneath the streets to a neighborhood. Smaller service lines branch off it to reach each building.

Also: acoustic sensor, leak, coverage

Teacher overview

Wembrey is a fictional town, and every length, price, and flow on this worksheet was invented for it. The town's oldest cast-iron water main runs under Ombry Street and leaks somewhere along its length, though nobody knows where. Acoustic leak sensors clamp onto valves and hydrants and listen at night for the hiss a leak makes underground. This worksheet has students work out how many sensors cover the street, what the set costs, and how long the repaired leaks take to pay for the sensors, which is the same comparison a utility makes before it buys leak detection equipment.

Wembrey Ombry Street Leak Sensor Spacing Worksheet — Grade 6 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

Every number below belongs to the fictional Wembrey scenario.

  1. Ombry Street has 8,400 feet of old iron water main. One sensor listens to 600 feet of pipe. How many sensors cover the whole street?
  2. Each sensor costs $310. What do the sensors from item 1 cost in all?
  3. Wembrey set aside $5,000 for sensors. How many dollars under that amount is your answer to item 2?
  4. Each sensor needs a new battery after four years. One battery costs $28. What does one battery for every sensor cost?
  5. The sensors find five leaks. Together the five leaks lose 8,000 gallons a day. What is the average loss for one leak?
  6. Cleaning and pumping water costs the town $2.50 for every 1,000 gallons. What do the five leaks cost the town each day?
  7. How much do the leaks cost over 365 days?
  8. Repairing the leaks saves the town the daily amount you found in item 6. How many days of that saving equal the sensor cost from item 2?
  9. A newer sensor listens to 840 feet of pipe. How many of those sensors would cover the 8,400 feet of main?
  10. Suppose Wembrey buys only 10 of the 600-foot sensors. What percent of the 8,400 feet would they cover? Round to the nearest whole percent.
  11. Use your answer to item 10. Explain why buying only 10 sensors would not meet the town's requirement to listen to the whole main.

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: 14 sensors. The main is 8,400 feet long and one sensor covers 600 feet, so 8,400 / 600 = 14 sensors.
  2. Answer: $4,340. Fourteen sensors at 310 dollars each give 14 x 310 = 4,340 dollars.
  3. Answer: $660. The set-aside is 5,000 dollars, so 5,000 - 4,340 = 660 dollars under.
  4. Answer: $392. Fourteen batteries at 28 dollars each give 14 x 28 = 392 dollars.
  5. Answer: 1,600 gallons per day. The five leaks lose 8,000 gallons a day together, so 8,000 / 5 = 1,600 gallons for the average leak.
  6. Answer: $20.00. The leaks lose 8,000 gallons, which is 8 groups of 1,000 gallons, so 8 x 2.50 = 20 dollars a day.
  7. Answer: $7,300. At 20 dollars a day for 365 days, 20 x 365 = 7,300 dollars.
  8. Answer: 217 days. The sensors cost 4,340 dollars and the saving is 20 dollars a day, so 4,340 / 20 = 217 days.
  9. Answer: 10 sensors. Each newer sensor covers 840 feet, so 8,400 / 840 = 10 sensors.
  10. Answer: 71 percent. Ten sensors cover 10 x 600 = 6,000 feet, and 6,000 / 8,400 = 0.714, which rounds to 71 percent.
  11. Answer: Ten sensors cannot cover the whole main, so about 29 percent of it would have no sensor listening to it. Ten of the 600-foot sensors cover 6,000 of the 8,400 feet, leaving 2,400 feet unwatched, and a leak in that stretch would go on losing water. Accept any answer that names the uncovered length or the uncovered percent and connects it to leaks that would not be found.

Differentiation

Support

Give these students a printed number line of the fictional street marked every 600 feet, so item 1 can be answered by counting the marks before the division is written. Provide the reminder that 8,000 gallons is 8 groups of 1,000 gallons beside item 6.

Extension

Ask students to decide which sensor the fictional town should buy if the newer 840-foot sensor sells for 460 dollars each, comparing the total price of each full set and stating which set leaves more of the set-aside for batteries.

ELL supports

Provide a simple street map showing the main as a long line with sensor symbols spaced along it and the words "sensor," "leak," and "main" labeled on the drawing. Allow students to answer item 11 by shading the uncovered part of the line and writing one sentence.

Extensions

Have students estimate the length of the water main under their own street by pacing the block, then calculate how many 600-foot sensors that length would need. Ask them to write one sentence about why a utility would start leak detection on its oldest pipes rather than its newest ones.