Worksheet Grade 8 Science

Falkirk Heights Pressure Zones: Solving for Head and Pressure

A grade 8 science worksheet where students convert head to pressure on a fictional hillside system and solve linear equations for an unknown tank elevation.

Grade: Grade 8
Subject: Science
Material: Worksheet
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

8.EE.C.7 Common Core Math

Solve linear equations in one variable, including equations with variables on both sides, and recognizing equations with one solution, infinitely many solutions, or no solutions.

How this material aligns: Items 5 and 7 require students to write and solve a one-variable linear equation for an unknown tank elevation and an unknown pressure reduction, exactly the equation-solving this standard names.

All materials for 8.EE.C.7 →

8.F.B.4 Common Core Math

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description, a table, or a graph, and interpret them in terms of the situation modeled.

How this material aligns: Students use the constant 0.433 psi per foot as the rate of change of pressure with head to convert head to pressure in items 2 and 3, then interpret and apply that rate of change in the hillside situation in items 8 and 10, the rate-of-change reasoning this standard names.

All materials for 8.F.B.4 →

MS-ETS1-1 NGSS

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

How this material aligns: Items 4 and 6 test each zone against the district's 20 psi legal minimum and its 40 to 80 psi target band, and items 5 and 7 size a tank elevation and a valve setting to those constraints using the head-to-pressure principle item 10 has students explain.

All materials for MS-ETS1-1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will calculate water pressure from head using the rate 0.433 psi per foot.
Students will solve a linear equation to find an unknown tank elevation or pressure adjustment.

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: head, pressure, elevation, pressure-reducing valve

Teacher overview

The fictional Falkirk Heights Water District serves homes at different heights on a hillside from one tank near the top. The pressure at any home depends on its head, which is the height of the tank's water surface above that home. This worksheet has students convert head to pressure using the rate 0.433 psi per foot, then solve linear equations to size a tank elevation and a pressure adjustment. A common error is mixing up the two conversions; head-to-pressure multiplies by 0.433, while pressure-to-head multiplies by 2.31.

Falkirk Heights Pressure Zones: Solving for Head and Pressure — Grade 8 Science

Name: ____________________________ Date: ______________

Student Worksheet

In the fictional Falkirk Heights Water District, the tank's water surface sits at an elevation of 820 feet. Three homes sit at different elevations on the hill. For every foot of head (the height of the tank's water surface above a home), pressure rises by 0.433 psi. To go the other way, each psi requires 2.31 feet of head. Suppose state rules require at least 20 psi at every home, and the district aims for 40 to 80 psi.

Location	Elevation (ft)
Tank water surface	820
Zone A home	700
Zone B home	620
Zone C home (hilltop)	780

Find the head at the Zone A home. (Head = tank water-surface elevation − home elevation.)
Find the water pressure at the Zone A home, using 0.433 psi per foot.
Find the head and the pressure at the Zone C hilltop home.
Does the Zone C home meet the 20 psi minimum? By about how many psi does it clear or miss it?
The district wants exactly 40 psi at the Zone C home (elevation 780 ft). Write and solve a linear equation of the form 0.433 × (H − 780) = 40 to find the tank water-surface elevation H it would need.
Find the pressure at the Zone B home. Is it inside the 40 to 80 psi target, and by how much is it over or under?
A pressure-reducing valve should bring the Zone B home down to exactly 70 psi. Write and solve the equation (Zone B pressure) − r = 70 to find how many psi the valve must remove.
Every extra foot of head adds 0.433 psi. If a new home sits 25 feet lower than the Zone A home, how much higher is its pressure than the Zone A home's?
A gauge at a fourth home reads 45 psi. Use 2.31 feet per psi to find the head of water above that home.
Explain why homes lower on the hill have higher water pressure than homes near the tank, using the idea of head.

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: 120 ft.
820 − 700 = 120 feet of head.
Answer: 52 psi.
0.433 × 120 = 51.96, which rounds to about 52 psi.
Answer: 17 psi (head 40 ft).
Head = 820 − 780 = 40 feet; 0.433 × 40 = 17.32, about 17 psi.
Answer: No, about 3 psi under.
The Zone C pressure of about 17 psi is below the 20 psi minimum; 20 − 17.32 = 2.68, so roughly 3 psi short.
Answer: 872 ft.
0.433 × (H − 780) = 40, so H − 780 = 40 ÷ 0.433 = 92.4, and H = 780 + 92.4 = 872.4, about 872 feet.
Answer: 87 psi (over by about 7 psi).
Head = 820 − 620 = 200 feet; 0.433 × 200 = 86.6, about 87 psi, which is over the 80 psi ceiling by about 6.6 psi.
Answer: 16.6 psi.
86.6 − r = 70, so r = 86.6 − 70 = 16.6 psi (about 17 psi) that the valve must remove.
Answer: 10.8 psi.
0.433 × 25 = 10.825, so about 10.8 psi higher because the lower home has 25 more feet of head.
Answer: 104 ft.
2.31 × 45 = 103.95, about 104 feet of head above that home.
Answer: Lower homes have more head.
Pressure depends on the height of the tank's water surface above a home. A home lower on the hill has more feet of water stacked above it, so its head, and therefore its pressure, is larger than a home near the tank.

Differentiation

Support

Give students an arrow-rule strip that reads "feet to psi: multiply by 0.433" and "psi to feet: multiply by 2.31," and start with items 1 through 4 before the equation-solving in items 5 and 7. Provide the subtraction for head already set up for each location.

Extension

Ask students to find the single tank water-surface elevation that would put the Zone A, Zone B, and Zone C homes all within the 40 to 80 psi target at once, or to explain why one tank elevation cannot satisfy all three, using their pressure results.

ELL supports

Provide a labeled hillside diagram showing the tank, the three homes, and the head as a vertical arrow between the water surface and each home. Pre-teach "head," "pressure," and "elevation" with the diagram, and allow item 10 to be answered with a labeled sketch plus a short phrase.