Worksheet Grade 8 Engineering & Design
Verity Springs Pressure Zone: Elevation and House Pressure
A grade 8 worksheet where students compute house pressures from elevation differences, read 0.433 as the slope, and pick a fix for the house that falls short.
Objectives
- Students will calculate water pressure at a house from the elevation difference to the tank.
- Students will identify the slope of a proportional relationship between elevation and pressure.
- Students will choose a design fix for a low-pressure house under a stated constraint.
Vocabulary
- Pressure zone
- A pressure zone is a section of a water system that a utility manages separately because it sits at a different elevation than the rest of the town. Utilities create pressure zones so that water pressure stays safe and steady for everyone, whether they live at the bottom of a hill or near the top.
Also: elevation, head, booster pump, slope
Teacher overview
Water pressure in a town's pipes comes mostly from height. Every foot of water standing above a tap adds 0.433 psi of pressure, which is why utilities build tanks on the highest ground they can find. That height of water above a tap is called head, and the group of houses a single tank can serve within an acceptable pressure range is called a pressure zone. Verity Springs is a fictional hillside town with one tank and four houses at four different elevations, and this worksheet has students compute the pressure at each one. Distribution systems usually run between 40 and 80 psi, and most states set a floor of 20 psi to keep contamination from being drawn into a pipe. Students frequently divide by 0.433 instead of multiplying, which turns a 140-foot drop into an impossible reading, so item 2 is worth checking before the class continues.
Student Worksheet
The town of Verity Springs stores its water in a tank whose water surface sits at an elevation of 780 feet. Four houses sit below it. Use 0.433 psi of pressure for each foot of elevation difference, and round each pressure to the nearest tenth.
| House | Ground elevation (feet) |
|---|---|
| A | 640 |
| B | 660 |
| C | 590 |
| D | 745 |
The town wants every house to receive between 40 and 80 psi. The state sets a minimum of 20 psi at all times.
- How many feet is the tank's water surface above House A?
- What is the water pressure at House A?
- How many feet is the tank's water surface above House B?
- What is the water pressure at House B?
- What is the water pressure at House C?
- What is the water pressure at House D?
- Which houses fall outside the town's target range of 40 to 80 psi?
- Which house falls below the state minimum of 20 psi?
- On a graph of pressure against elevation difference, what is the slope of the line?
- Explain why that line passes through the point (0, 0).
- How many feet of elevation difference does a house need to receive 40 psi?
- The tank sits on the highest ground the town owns and cannot be raised. House D sits only 35 feet below the tank's water surface. Which fix meets that constraint, a taller tank or a booster pump for House D's street?
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: 140 feet.
780 - 640 = 140 feet of elevation difference. - Answer: 60.6 psi.
140 × 0.433 = 60.62, which rounds to 60.6 psi. This sits inside the town's target range. - Answer: 120 feet.
780 - 660 = 120 feet of elevation difference. - Answer: 52.0 psi.
120 × 0.433 = 51.96, which rounds to 52.0 psi. - Answer: 82.3 psi.
The elevation difference is 780 - 590 = 190 feet, and 190 × 0.433 = 82.27, which rounds to 82.3 psi. - Answer: 15.2 psi.
The elevation difference is 780 - 745 = 35 feet, and 35 × 0.433 = 15.155, which rounds to 15.2 psi. - Answer: Houses C and D.
House C reads 82.3 psi, which is above the 80 psi top of the range. House D reads 15.2 psi, which is below the 40 psi bottom of the range. Houses A and B fall inside the range. - Answer: House D.
At 15.2 psi, House D sits below the 20 psi state minimum, so the town has to correct it rather than simply prefer a higher reading. - Answer: 0.433 psi per foot.
Pressure rises by 0.433 psi for each additional foot of elevation difference, so that constant rate is the slope of the line. - Answer: A house level with the tank's water surface receives no pressure from height.
When the elevation difference is 0 feet, there is no column of water above the tap, so the pressure from elevation is 0 psi. That makes (0, 0) a point on the line and the relationship proportional. - Answer: 92.4 feet.
40 ÷ 0.433 = 92.379, which rounds to 92.4 feet. A house needs to sit at least that far below the tank's water surface to reach 40 psi from elevation alone. - Answer: A booster pump for House D's street.
Reaching 40 psi at House D would take 92.4 feet of elevation difference, and only 35 feet is available. The tank cannot be raised, so added height is ruled out by the constraint. A booster pump adds pressure without changing the tank, which is how real utilities serve homes close to a tank's elevation.
Differentiation
Support
Give students the elevation differences for all four houses already computed, so the worksheet begins at the multiplication step. Provide a worked example using a fifth house at 700 feet, where the difference is 80 feet and the pressure is 34.6 psi, printed at the top of the page.
Extension
Suppose the town builds a second tank for the high ground near House D, with a water surface at 850 feet. Ask students to recompute the pressure at all four houses from the new tank and explain which houses would then need a pressure-reducing valve to stay under 80 psi.
ELL supports
Provide a hillside sketch showing the tank, the four houses, and a vertical arrow labeled "elevation difference" for one house. Give a sentence frame for items 10 and 12, such as "House D needs a booster pump because ___."