Water for Schools
Menu

Math problem set Grade 7 Math

Caldervale's Hydrant Flow Test: A Grade 7 Rate Set

A grade 7 problem set where students find flow rates from fractional fill times during a fictional town's hydrant test and compare them with a target.

Objectives

  1. Students will compute a flow rate in gallons per minute from a fractional fill time.
  2. Students will combine two flow rates and scale the total to a two-hour demand.
  3. Students will find a pressure drop and a drain time from stated readings.

Vocabulary

Key words: hydrant, flow test, static pressure, residual pressure, unit rate

Teacher overview

Before a town approves a new building, its water department runs a hydrant flow test to learn how much water the pipes on that street can actually deliver and how far the pressure falls while the water is moving. The reading taken before the hydrants open is the static pressure, and the lower reading taken while they are flowing is the residual pressure. Distribution systems normally run between 40 and 80 psi, and state rules generally require the pressure to stay at or above 20 psi even during heavy use. This set follows one afternoon of testing on a fictional street, where the crew timed how long each hydrant took to fill a tank of known size. The misconception to correct is that dividing by a fraction always makes an answer smaller; filling 150 gallons in three quarters of a minute works out to a rate above 150 gallons per minute rather than below it.

Caldervale's Hydrant Flow Test: A Grade 7 Rate Set — Grade 7 Math
Name: ____________________________ Date: ______________

Problems

Suppose the fictional town of Caldervale tested two hydrants on Marsh Street. The crew filled a tank of known size from each hydrant and timed it with a stopwatch.

  1. Hydrant A filled a 150-gallon tank in 3/4 of a minute. What is Hydrant A's flow rate in gallons per minute?
  2. Hydrant B filled a 240-gallon tank in 2/3 of a minute. What is Hydrant B's flow rate in gallons per minute?
  3. If both hydrants run at once at those rates, what is the combined flow in gallons per minute?
  4. How many gallons would both hydrants together deliver in 2 hours, which is 120 minutes?
  5. Caldervale's target for this street is 90,000 gallons over those 2 hours. How many gallons short of the target is the combined flow?
  6. The gauge read 62 psi before the test and 38 psi while both hydrants were flowing. What was the pressure drop?
  7. Caldervale's storage tank holds 336,000 gallons. At the combined flow rate, how many minutes would it take to empty the tank?
  8. How many hours is that draining time?

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: 200 gpm. Divide gallons by minutes: 150 divided by 3/4 is the same as 150 times 4/3, which equals 200 gallons per minute.
  2. Answer: 360 gpm. Divide gallons by minutes: 240 divided by 2/3 is the same as 240 times 3/2, which equals 360 gallons per minute.
  3. Answer: 560 gpm. Add the two rates: 200 plus 360 equals 560 gallons per minute.
  4. Answer: 67,200 gallons. Multiply the combined rate by the minutes: 560 times 120 equals 67,200 gallons.
  5. Answer: 22,800 gallons. Subtract the delivered amount from the target: 90,000 minus 67,200 equals 22,800 gallons short.
  6. Answer: 24 psi. Subtract the flowing pressure from the starting pressure: 62 minus 38 equals 24 psi.
  7. Answer: 600 minutes. Divide the tank volume by the combined rate: 336,000 divided by 560 equals 600 minutes.
  8. Answer: 10 hours. Divide the minutes by 60: 600 divided by 60 equals 10 hours.

Differentiation

Support

Give these students the two fractional divisions rewritten as multiplications, 150 times 4/3 and 240 times 3/2, and a printed reminder that dividing by a fraction less than 1 gives a larger result. Allow calculators and let them treat 3/4 as 0.75 and 2/3 as about 0.667 if that is easier.

Extension

Ask students to find what third hydrant flow the fictional town would need to add to reach its 90,000-gallon target in the same 2 hours, and to explain in writing why the answer is not simply the shortfall divided by 2.

ELL supports

Pre-teach "hydrant," "flow rate," "static pressure," and "residual pressure" with a drawing of a hydrant, a tank, and a gauge labeled before and during the test. Provide the frame "___ gallons in ___ of a minute equals ___ gallons in one minute" for problems 1 and 2.