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Worksheet Grade 10 Engineering & Design

Grindstone Reservoir Elevated Tank: Volume and Pressure Worksheet

A grade 10 engineering worksheet on a fictional elevated storage tank, calculating tank volume and the water pressure its height delivers to neighborhoods below.

Objectives

  1. Students will calculate an elevated tank's volume in cubic feet and gallons.
  2. Students will convert elevation head to pressure in psi and pressure back to feet of head.
  3. Students will compare delivered pressures to standard distribution-system pressure requirements.

Vocabulary

Key words: elevated tank, head, pressure, psi, service pressure

Teacher overview

Towns store water high above their neighborhoods so gravity can push it to every tap with steady pressure. The fictional Grindstone Reservoir system uses an elevated tank shaped like a cylinder that sits well above the homes it serves. In this worksheet, students find the tank's volume, then use the height of its water to calculate the pressure delivered to two neighborhoods at different elevations. Every foot that water sits above a tap adds pressure, and students use standard conversions to move between feet of height and pounds per square inch.

Grindstone Reservoir Elevated Tank: Volume and Pressure Worksheet — Grade 10 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

At Grindstone Reservoir (a fictional system built for this worksheet), the elevated tank is a cylinder 60 feet in diameter with a water depth of 30 feet. When the tank is full, its water surface sits 140 feet above the service connections of the Lower Meadow neighborhood.

  1. Find the tank's volume in cubic feet. Use Volume = 0.785 × Diameter² × depth.

  2. Convert the tank volume to gallons, using the conversion that 1 cubic foot holds 7.48 gallons.

  3. Find the pressure, in psi, that 140 feet of water height delivers to Lower Meadow, using the conversion that 1 foot of head equals 0.433 psi.

  4. Distribution systems usually run between 40 and 80 psi. Is the Lower Meadow pressure from item 3 inside that range?

  5. Many states require at least 20 psi at every connection. How many feet of head does 20 psi equal, using the conversion that 1 psi equals 2.31 feet of head?

  6. During a large fire flow, friction losses in the mains leave only 55 feet of effective head at Lower Meadow. What pressure, in psi, does that deliver?

  7. Is the pressure from item 6 still above the 20 psi minimum?

  8. The Hilltop neighborhood sits 40 feet higher than Lower Meadow, so a full tank stands only 100 feet above it. Find the pressure, in psi, delivered to Hilltop when the tank is full.

  9. Using your answers from items 3 and 8, how much more pressure does Lower Meadow receive than Hilltop when the tank is full?

  10. Explain why a utility builds its storage tank as high above its neighborhoods as it reasonably can.

  11. Overnight, a pump refills the empty tank at 900 gpm. Using the tank's full volume in gallons from item 2, how many hours does a complete refill take?

  12. Explain why the utility schedules that refill for the overnight hours instead of the afternoon.

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: 84,780 cubic feet.
    Volume = 0.785 × 60² × 30 = 0.785 × 3,600 × 30 = 84,780 cubic feet.

  2. Answer: about 634,154 gallons.
    84,780 cubic feet × 7.48 gallons/cubic foot = 634,154.4, which rounds to about 634,154 gallons.

  3. Answer: 60.62 psi.
    140 feet × 0.433 psi/foot = 60.62 psi.

  4. Answer: Yes.
    A pressure of 60.62 psi is inside the standard 40-to-80 psi range, so Lower Meadow receives normal service pressure.

  5. Answer: 46.2 feet.
    20 psi × 2.31 feet/psi = 46.2 feet of head.

  6. Answer: about 23.8 psi.
    55 feet × 0.433 psi/foot = 23.815, which rounds to about 23.8 psi.

  7. Answer: Yes.
    At about 23.8 psi, the neighborhood is still above the 20 psi minimum, though the margin is small.

  8. Answer: 43.3 psi.
    100 feet × 0.433 psi/foot = 43.3 psi delivered to Hilltop when the tank is full.

  9. Answer: 17.32 psi.
    60.62 psi (Lower Meadow) − 43.3 psi (Hilltop) = 17.32 psi more at Lower Meadow, because it sits 40 feet lower and has more water height above it.

  10. Answer: Accept any answer explaining that greater height means more feet of head, which delivers more pressure by gravity alone, so a taller tank keeps pressure adequate across the system without relying on pumps running all the time.

  11. Answer: about 11.7 hours.
    634,154 gallons ÷ 900 gpm = 704.6 minutes; 704.6 ÷ 60 = 11.74, which rounds to about 11.7 hours.

  12. Answer: Accept any answer explaining that demand is low overnight, so refilling then avoids competing with daytime use, keeps pressure steady when customers need it, and often uses cheaper off-peak electricity for the pumps.

Differentiation

Support (below grade level)

Provide the cylinder-volume formula and both pressure conversions on a reference card with the constants filled in, and work item 1 as a class so students carry the correct volume into item 2 before moving on to the pressure items.

Extension (above grade level)

Ask students to find the lowest tank water level, in feet above Hilltop, that would still deliver the 20 psi minimum to that higher neighborhood, working backward from the feet-to-psi conversion, and explain what that means for how far the tank can be drawn down.

ELL supports

Provide a labeled elevation diagram showing the tank, the 140-foot height, and both neighborhoods, with the words head, pressure, and service connection marked. Allow students to answer items 4, 7, 10, and 12 with a short sentence or a labeled sketch and to show the rest as numbered calculations.