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Worksheet Grade 6 Math

Halbury's Water Tower: Feet of Head and Pounds of Pressure

A grade 6 worksheet on one town's water tower: students multiply and divide decimals to turn feet of water into pounds per square inch and back again.

Objectives

  1. Students will multiply a whole number of feet by a decimal rate to find water pressure.
  2. Students will divide a pressure reading by a decimal rate to find the height of water above a gauge.
  3. Students will compare computed pressures against a stated normal range and a stated minimum.

Vocabulary

Key words: pressure, head, gauge, unit rate

Teacher overview

Water pressure in a town's pipes comes mostly from height. Each foot of water standing above a point pushes down with 0.433 pounds per square inch, so the water level in a tower sets the pressure at every house below it. This worksheet uses the fictional town of Halbury, whose single tower serves houses at three different elevations. Students who expect pressure to depend on the width of the pipe or the size of the tank will find that only the height above a point changes the answer, and the three-place decimal rate gives them multiplication and division worth practicing.

Halbury's Water Tower: Feet of Head and Pounds of Pressure — Grade 6 Math
Name: ____________________________ Date: ______________

Student Worksheet

The fictional town of Halbury has one water tower. Use these facts for every item.

  • Each foot of water height gives 0.433 pounds per square inch, written psi.
  • Water systems usually run between 40 and 80 psi.
  • Most states require at least 20 psi at all times.

Round decimal answers to the nearest hundredth when they do not come out even.

  1. The tower's water level sits 100 feet above the Miller house. What is the pressure at that house, in psi?
  2. The tower's water level sits 150 feet above the pump house. What is the pressure there, in psi?
  3. The tower's water level sits 60 feet above a house on the hilltop. What is the pressure at that house, in psi?
  4. Which of the three pressures you found in items 1, 2, and 3 fall inside the usual 40 to 80 psi range?
  5. Does the hilltop house from item 3 meet the 20 psi minimum? Answer yes or no and give the number that shows it.
  6. Subtract to find the difference between the largest and the smallest of the three pressures from items 1, 2, and 3, in psi.
  7. A gauge on a hydrant reads 51.96 psi. How many feet of water stand above that gauge? Divide by 0.433.
  8. A gauge in a basement reads 21.65 psi. How many feet of water stand above that gauge? Divide by 0.433.
  9. During the morning rush the tower level drops 0.35 feet each hour for 6 hours. How many feet does it drop in all?
  10. That drop of 2.1 feet lowers the pressure at every house. By how many psi does the pressure drop?

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: 43.3 psi.
    100 feet times 0.433 psi per foot is 43.3 psi.
  2. Answer: 64.95 psi.
    150 feet times 0.433 psi per foot is 64.95 psi.
  3. Answer: 25.98 psi.
    60 feet times 0.433 psi per foot is 25.98 psi.
  4. Answer: The 43.3 psi and 64.95 psi readings.
    Both fall between 40 and 80. The hilltop house at 25.98 psi falls below that range.
  5. Answer: Yes.
    The hilltop house is at 25.98 psi, and 25.98 is greater than the 20 psi minimum, so it passes.
  6. Answer: 38.97 psi.
    The largest pressure is 64.95 psi and the smallest is 25.98 psi. Subtracting gives 38.97 psi.
  7. Answer: 120 feet.
    51.96 divided by 0.433 is 120. Multiplying back, 120 times 0.433 is 51.96, which checks.
  8. Answer: 50 feet.
    21.65 divided by 0.433 is 50. Multiplying back, 50 times 0.433 is 21.65, which checks.
  9. Answer: 2.1 feet.
    0.35 feet per hour times 6 hours is 2.1 feet.
  10. Answer: 0.91 psi.
    2.1 feet times 0.433 psi per foot is 0.9093, which rounds to 0.91 psi.

Differentiation

Support

Give these students a two-column conversion card with "feet to psi: multiply by 0.433" on one side and "psi to feet: divide by 0.433" on the other. Assign items 1, 2, 3, 5, and 9 first, and add items 7 and 8 once the multiplication items are correct.

Extension

Ask these students to find the lowest tower water level, in feet above a house, that still keeps the fictional Halbury system at or above the 20 psi minimum, and to explain why an operator would keep the level well above that number rather than right at it.

ELL supports

Pre-teach pressure, gauge, and head with a labeled diagram of the Halbury tower showing the water surface, a house, and the vertical distance between them. Provide this sentence frame for item 5: "The pressure is ___ psi, and the minimum is ___ psi, so the house ___ the rule."

Extensions

Have students find the elevation of their own school and of a nearby hilltop on a topographic map, then compute the pressure difference those elevations would create if both were served by one tower. The result explains why a town on hilly ground needs more than one pressure zone.