Math problem set Grades 6–7 Math
Water Tower Height and Pressure: Unit-Rate Problems
Eight problems that turn the town water tower into unit-rate practice, converting height to pressure with the real 0.433 psi-per-foot rule operators use.
Objectives
- Convert water height in feet to pressure in psi using the rate 0.433 psi per foot.
- Convert pressure in psi to feet of water height using the rate 2.31 feet per psi.
- Interpret answers against the real service standards water utilities must meet.
Teacher overview
Towns throughout the world have water towers, yet many of us do not know why. This problem set explains the reason using the same two numbers a licensed water operator uses: every foot of water height adds 0.433 psi of pressure, and every psi requires 2.31 feet of height. These are two forms of one unit rate, which makes the water tower a concrete, physical setting for ratio reasoning.
Run it as independent practice or as a paired problem-solving session. Problems 1 through 5 are one-step unit-rate conversions in both directions; problem 6 is a ratio table; problems 7 and 8 ask students to reason about a change and a range. Real service standards appear throughout: most states require at least 20 psi at every connection, and utilities aim for roughly 40 to 80 psi at the tap.
A common misconception to watch for: students multiply by the wrong constant when converting. Height to pressure uses 0.433, while pressure to height uses 2.31. A quick estimation habit catches the error, because pressure in psi should always be a smaller number than height in feet. Suppose a student converts 120 feet and gets 277 psi; that student used 2.31, and the size of the answer should signal the mistake.
Problems
The town of Cedar Falls has one water tower. The water surface inside the tank currently stands 120 feet above the level of Maple Street. Use these facts for all problems:
- Each foot of water height adds 0.433 psi of pressure.
- Each psi of pressure requires 2.31 feet of water height.
- State rules require at least 20 psi at every connection. Utilities aim for 40 to 80 psi at the tap.
What is the water pressure at a fire hydrant on Maple Street? Round to the nearest whole psi.
The Hilltop neighborhood sits 60 feet above Maple Street. How far is the water surface above Hilltop, and what is the water pressure there? Round to the nearest whole psi.
Does Hilltop meet the state minimum of 20 psi? By about how many psi does it clear or miss the requirement?
A pressure gauge at the fire station reads exactly 45 psi. How many feet above the fire station is the water surface? Round to the nearest foot.
The town is building a new school and wants 65 psi at its ground floor. How many feet above the school's ground floor must the water surface be? Round to the nearest foot.
Complete the ratio table. Round pressures to the nearest tenth of a psi.
Height of water above a house (ft) Pressure at the house (psi) 10 50 100 200 The utility runs a pump overnight and raises the water surface in the tank by 15 feet. By about how many psi does the pressure increase at every house below? Round to the nearest tenth.
Challenge. A house gets its most comfortable service when pressure stays between 40 and 80 psi. Between which two heights, in feet of water above the house, does the water surface need to stay? Round each to the nearest foot. Explain what happens to homes far below the tank on a steep hill.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
Answer: 52 psi.
120 ft × 0.433 psi/ft = 51.96 psi, which rounds to 52 psi. Students who answer 51.96 or 52.0 are correct; the rounding instruction asks for a whole psi.Answer: 26 psi.
Hilltop is 60 ft above Maple Street, so the water surface is 120 − 60 = 60 ft above Hilltop. 60 ft × 0.433 psi/ft = 25.98 psi ≈ 26 psi.Answer: yes, by about 6 psi.
Hilltop's pressure (about 26 psi) is above the 20 psi minimum: 25.98 − 20 = 5.98, so roughly a 6 psi margin. Worth discussing: this is a thin margin, which is exactly why utilities watch hilltop neighborhoods closely.Answer: 104 ft.
45 psi × 2.31 ft/psi = 103.95 ft ≈ 104 ft above the fire station.Answer: 150 ft.
65 psi × 2.31 ft/psi = 150.15 ft ≈ 150 ft. The tank's water surface must stay at least about 150 feet above the school's ground floor.Answer: 4.3, 21.7, 43.3, 86.6 psi.
Each height × 0.433: 10 ft → 4.33 ≈ 4.3 psi; 50 ft → 21.65 ≈ 21.7 psi (21.6 also accepted if students truncate); 100 ft → 43.3 psi; 200 ft → 86.6 psi. The table doubles as a check on proportional thinking: doubling the height doubles the pressure.Answer: 6.5 psi.
15 ft × 0.433 psi/ft = 6.495 ≈ 6.5 psi. Every customer below the tank sees the same increase, because pressure depends only on the height of water above each point.Answer: between about 92 ft and 185 ft.
40 psi × 2.31 = 92.4 ft and 80 psi × 2.31 = 184.8 ft, so the water surface should stay roughly 92 to 185 feet above the house. Homes far below the tank on a steep hill can sit more than 185 feet below the water surface, pushing pressure above 80 psi, which is why utilities install pressure-reducing valves in low neighborhoods.
Differentiation
Support (below grade level)
Give students the two conversions as labeled arrow rules — "feet → psi: multiply by 0.433" and "psi → feet: multiply by 2.31" — on a printed strip. Start with problem 6 (the ratio table) before problems 1 through 5, so the proportional pattern is visible first. Reduce the rounding load by accepting unrounded calculator answers.
Extension (above grade level)
Ask students to derive one rule from the other: if 1 psi = 2.31 ft, show that 1 ft must equal 1 ÷ 2.31 ≈ 0.433 psi. Then pose problem 8 in reverse for a house 220 feet below the water surface: what pressure results (about 95 psi), and what percent above the 80 psi comfort ceiling is that?
ELL supports
Pre-teach the words pressure, height, surface, and hydrant with a simple diagram of a water tower labeled in both English and students' home languages where possible. The phrase "feet of head," which appears in industry materials, is intentionally avoided in the student pages; introduce it orally as a bonus vocabulary item once the concept is solid.
Extensions
Walk or map your own town's water tower or standpipe. Estimate its height from photos, then have students compute the pressure it can deliver to the school building and compare with a real gauge reading if your facilities team can share one. Many public works departments will answer a class letter asking how tall the tank is and what pressure the school's neighborhood gets, and the reply gives students real local figures to compare with their answers.