Project Grade 10 Engineering & Design
Quillback Creek Rainwater Cistern: A Grade 10 Design Project
Grade 10 teams size a rainwater cistern for a school garden, priced by tank surface area, to store 4,000 gallons on a 12-foot pad for $6,000 or less.
Objectives
- Students will calculate roof runoff volume and size a cistern to meet a stated storage target.
- Students will design a cistern that fits a footprint and budget, and justify their choice against prioritized criteria.
Vocabulary
- Rainwater harvesting
- Collecting rain, usually from a roof, and storing it in barrels or tanks for later use, like watering gardens. It saves treated drinking water for the uses that really need it.
- Cistern
- A large tank that stores rainwater collected from a roof so it can be used later, usually for watering plants.
Also: runoff, storage volume, surface area, budget constraint
Teacher overview
A school roof sheds thousands of gallons in a single storm, and a rainwater cistern can hold that water to irrigate a courtyard garden instead of sending it to the storm drain. Over four sessions, teams design a cistern for the fictional Foxglove K-8 School, sizing it to capture a target amount of roof runoff while fitting a set footprint and staying inside a materials budget. Because the price sheet charges for the tank by the square foot of steel in its walls, floor, and lid, the shape of the tank changes its cost, and teams have to find dimensions that hold enough water without using too much material. Teams present a scaled drawing and a written proposal to the school district's facilities board. Reference values for checking team designs appear after the rubric.
Project Brief
Driving question: How can we design a rainwater cistern that stores at least 4,000 gallons of roof runoff from a one-inch storm, fits a 12-foot by 12-foot pad, and costs no more than the materials budget?
Scenario: The fictional Quillback Creek School District has asked student teams to propose a rainwater cistern for Foxglove K-8. The cistern will collect runoff from an 8,000-square-foot section of roof and supply the school's courtyard garden.
Constraints (all set for this project):
- The cistern must store at least 4,000 gallons.
- The cistern must fit on a 12-foot by 12-foot gravel pad and stand no taller than 10 feet.
- The materials budget is a fictional $6,000 for the tank, base slab, gutter, pipes, and first-flush diverter, priced from the price sheet below. Every line of the price sheet must appear in the itemized cost.
- The tank may be a vertical cylinder or a rectangular box. Give every dimension to the nearest half foot.
- Runoff is estimated with roof area (square feet) × rainfall (inches) × 0.623 = gallons. The runoff formula gives the most the roof could shed, and real systems collect about 75 to 90 percent of it.
- Tank volume for a cylinder is Volume (cubic feet) = 0.785 × Diameter² × height, and for a rectangular tank Volume (cubic feet) = length × width × height. Convert to gallons with 1 cubic foot holding 7.48 gallons.
Price sheet for this project (all prices are fictional):
| Item | Price | How to find the amount |
|---|---|---|
| Tank shell, welded steel with a food-safe liner | $8.50 per square foot of shell | Shell area is the side wall, the floor, and the lid added together |
| Concrete base slab poured on the gravel pad under the tank | $10.00 per square foot | The area of the tank's footprint, the circle or rectangle it stands on |
| Gutter along the roof edge | $7.00 per foot | The roof section has 160 feet of edge, so 160 feet are required |
| Downspout and inlet pipe from the gutter to the top of the tank | $12.00 per foot | 40 feet are required |
| First-flush diverter, which sends the dirtiest first rain away from the tank | $250 each | One is required |
| Overflow pipe with an insect screen | $150 each | One is required |
Shell area formulas:
- Cylinder: shell area = 3.14 × Diameter × height (the side wall) + 2 × 0.785 × Diameter² (the floor and the lid).
- Rectangular tank: shell area = 2 × (length × width + length × height + width × height).
Final deliverable: A scaled drawing of the cistern on grid paper showing its dimensions and location on the pad, plus a one-page written proposal to the district facilities board explaining how the design meets the storage, footprint, and budget constraints. The proposal includes an itemized cost table with every line of the price sheet.
Milestones
Session 1 — Find the runoff target: Using the runoff formula, teams calculate the most a one-inch storm can shed from the 8,000-square-foot roof section and how much a real system would collect at 80 percent, then confirm the cistern's storage goal of at least 4,000 gallons and discuss whether one storm fills the tank and where the uncollected water goes. Teams also total the four fixed lines of the price sheet (gutter, downspout and inlet pipe, first-flush diverter, and overflow pipe) to find how much of the $6,000 is left for the shell and base. Output: a completed calculation sheet showing the roof runoff, the storage goal, and the money remaining for the tank.
Session 2 — Draft two cistern options: Teams sketch two different cistern options that each fit the 12-foot by 12-foot pad and the 10-foot height limit, at least one of them a cylinder. For each option they calculate the stored gallons with the volume formula, the shell area and footprint area, and the cost of the shell and base slab from the price sheet. Output: two labeled sketches, each with its volume in gallons, its shell area, and its total cost including the fixed lines.
Session 3 — Choose and refine one design: Teams compare their two options against the storage target, the footprint, and the budget, choose one, and refine it into a final scaled drawing with an itemized cost. Each team writes two or three sentences explaining why a very wide, short tank and a very tall, narrow tank of the same volume both need more shell than a tank whose diameter and height are closer together. Output: one final scaled drawing with an itemized cost at or under $6,000 and the written shape explanation.
Session 4 — Write and present the proposal: Teams write the one-page proposal and present the drawing and proposal to the class acting as the district facilities board. Output: a completed written proposal and a short team presentation.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Rubric
| Criterion | Emerging | Developing | Proficient | Advanced |
|---|---|---|---|---|
| Storage-capture design | The design does not show it can store 4,000 gallons | The drawing names the 4,000-gallon target but the volume math does not clearly support it | The volume calculation clearly shows the cistern stores at least 4,000 gallons | The cistern meets the 4,000-gallon target with a stated margin and explains the reasoning |
| Budget constraint | The itemized cost is over $6,000 or missing | The cost is near $6,000 but leaves out a price sheet line or miscalculates the shell or base area | The itemized cost includes every price sheet line, uses correct shell and footprint areas, and is at or under $6,000 | The itemized cost is correct and at or under $6,000, and the team explains one trade-off made to stay in budget |
| Geometry and footprint | The cistern does not fit the 12-by-12 pad or 10-foot height | The drawing fits the pad but is not drawn to a consistent scale | The scaled drawing fits the pad and height limit with correct dimensions | The scaled drawing fits the limits and the team explains, with shell-area figures, why its proportions use less steel than a wider or taller tank of the same volume |
| Proposal and presentation | The proposal is incomplete or hard to follow | The proposal covers the design but skips one constraint | The proposal clearly shows how all three constraints are met | The proposal meets all constraints and answers a likely question from the facilities board |
Teacher reference values. The roof runoff from a one-inch storm is 8,000 × 1 × 0.623 = 4,984 gallons, and at 80 percent collection a real system would gather about 3,987 gallons, so one storm of this size would nearly fill a 4,000-gallon tank. The four fixed lines total $1,120 + $480 + $250 + $150 = $2,000, which leaves $4,000 for the shell and base slab. The table below shows sample designs teams are likely to try, with gallons rounded to the nearest gallon and costs that include the $2,000 of fixed lines.
| Design | Gallons | Shell area (sq ft) | Footprint (sq ft) | Total cost | Meets all constraints? |
|---|---|---|---|---|---|
| Cylinder, 9 ft diameter, 9 ft tall | 4,281 | 381.51 | 63.585 | $5,878.69 | Yes |
| Cylinder, 10 ft diameter, 7 ft tall | 4,110 | 376.80 | 78.5 | $5,987.80 | Yes |
| Cylinder, 8.5 ft diameter, 9.5 ft tall | 4,030 | 366.99 | 56.716 | $5,686.56 | Yes |
| Cylinder, 8 ft diameter, 10 ft tall | 3,758 | 351.68 | 50.24 | $5,491.68 | No, too little storage |
| Cylinder, 11 ft diameter, 6 ft tall | 4,263 | 397.21 | 94.985 | $6,326.14 | No, over budget |
| Cylinder, 12 ft diameter, 5 ft tall | 4,228 | 414.48 | 113.04 | $6,653.48 | No, over budget |
| Rectangular, 8.5 ft by 7 ft by 9 ft tall | 4,006 | 398 | 59.5 | $5,978.00 | Yes, by a narrow margin |
| Rectangular, 8 ft by 8 ft by 8.5 ft tall | 4,069 | 400 | 64 | $6,040.00 | No, over budget by $40 |
| Rectangular, 10 ft by 10 ft by 6 ft tall | 4,488 | 440 | 100 | $6,740.00 | No, over budget |
A rectangular tank can meet every constraint only narrowly, because a box needs more shell area than a cylinder of the same volume; the 8.5-by-7-by-9 design is the least expensive passing box with half-foot dimensions. The least expensive passing design of any shape is the cylinder 8.5 feet in diameter and 9.5 feet tall, whose diameter and height are close to each other. Wide, short tanks also pay more for the base slab because their footprint is larger. Teams that find a passing design not listed here should be checked against the same formulas.
Differentiation
Support (below grade level)
Provide the Session 1 runoff calculation and the fictional $2,000 fixed-line total already worked out, so teams start from a known storage target and a known $4,000 for the shell and base. Give a cost worksheet with the cylinder shell-area formula written out in steps (side wall, then floor and lid) and limit teams to cylinders in whole-foot dimensions. Pre-mark the 12-by-12 pad on grid paper at a set scale.
Extension (above grade level)
Ask teams to calculate what share of the roof's one-inch-storm runoff their cistern actually captures, and to propose one change that would let the design store more water within the same footprint and budget, showing the volume and cost math that supports it. Teams can also make a table of shell area for several cylinders that each hold about 4,000 gallons and describe how the shell area changes as the ratio of height to diameter changes.
ELL supports
Provide a labeled diagram of a rainwater cistern showing the roof, gutter, first-flush device, tank, overflow pipe, and garden line, with the terms runoff, storage volume, footprint, and surface area defined beside it. Allow the written proposal to combine short sentences with labeled sketches.
Extensions
Teams can compare a rainwater cistern with a rain garden of the same footprint, listing which one stores water for reuse, which one slows runoff to the storm drain, and when a school might prefer each. Teams that want an authentic audience can share their proposal with the school's facilities staff and ask what a real cistern for the building would need to consider.