Math problem set Grade 11 Engineering & Design
Halden Ridge Booster Pumps: Head, Flow, and Pressure Problems
A grade 11 engineering set on the fictional Halden Ridge booster station, where students find total dynamic head, read a pump curve, and check delivered pressure.
Objectives
- Students will calculate total dynamic head as the sum of static lift, friction head, and residual pressure head.
- Students will read a pump-curve table and system requirement to locate the station's operating flow.
- Students will convert head in feet to pressure in psi and judge it against service-pressure standards.
Vocabulary
- Total dynamic head (TDH)
- Total dynamic head is the total amount of lift a pump has to provide to move water where it needs to go, adding up the height it must lift the water, the friction it must overcome in the pipes, and the pressure needed at the far end. Engineers calculate it to pick a pump that is powerful enough for the job.
Also: static lift, friction head, residual pressure, operating point
Teacher overview
Halden Ridge is a fictional hilltop neighborhood served by a booster pump station that lifts water from a storage tank up to homes at a higher elevation. Every booster pump has to supply three things at once: enough head to climb the elevation, enough head to overcome pipe friction, and enough left over to keep pressure at the tap inside a comfortable range. This set has students build that total dynamic head piece by piece, then read a pump-curve table to see how much pressure the station actually delivers at different flows. A common error in this work is treating friction head as a fixed number; friction grows with the square of the flow, so it is small at low demand and large at peak demand.
Problems
Use these facts about the fictional Halden Ridge station for every problem:
- The storage tank water surface sits at elevation 300 feet. The highest customer's ground floor sits at elevation 430 feet.
- Friction head in the supply main follows friction (ft) = 12 × (flow ÷ 600)², with flow in gallons per minute.
- One foot of water height equals 0.433 psi of pressure.
- The utility wants at least 40 psi at the top customer and treats 40 to 80 psi as the comfortable range. State rules require at least 20 psi everywhere to prevent backflow.
The pump curve gives the head the pump produces at each flow:
| Flow (gpm) | Pump head (ft) |
|---|---|
| 300 | 265 |
| 600 | 250 |
| 900 | 225 |
| 1200 | 190 |
- Find the static lift the pump must overcome, in feet, from the tank water surface to the top customer's ground floor.
- Calculate the friction head in feet at a flow of 600 gpm, then at 900 gpm, using the friction formula.
- The head needed just to deliver water to the top customer with no pressure left over equals static lift plus friction head. Find that delivery head at 600 gpm and at 900 gpm.
- Residual head is the pump head minus the delivery head. Find the residual head in feet at 600 gpm, then convert it to residual pressure in psi.
- Find the residual pressure in psi at 900 gpm the same way.
- Between which two tabulated flows does the residual pressure fall below the 40 psi comfort minimum? Use your answers from items 4 and 5.
- The utility must hold at least 40 psi at the top customer during peak demand. Of the four tabulated flows, what is the largest flow at which the station still meets 40 psi?
- At 1200 gpm the delivery head is 178 feet, so the residual head is only 12 feet. Find that residual pressure in psi, explain why it fails the 20 psi state minimum, and name one design change that would raise it.
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: 130 ft. Static lift = 430 − 300 = 130 feet from the tank water surface to the top customer's floor.
- Answer: 27 ft (at 900 gpm). At 600 gpm, friction = 12 × (600 ÷ 600)² = 12 × 1 = 12 feet. At 900 gpm, friction = 12 × (900 ÷ 600)² = 12 × 1.5² = 12 × 2.25 = 27 feet.
- Answer: 157 ft (at 900 gpm). Delivery head = static lift + friction. At 600 gpm: 130 + 12 = 142 feet. At 900 gpm: 130 + 27 = 157 feet.
- Answer: 47 psi. Residual head at 600 gpm = pump head − delivery head = 250 − 142 = 108 feet. Residual pressure = 108 × 0.433 = 46.8 psi, which rounds to about 47 psi.
- Answer: 29 psi. Residual head at 900 gpm = 225 − 157 = 68 feet. Residual pressure = 68 × 0.433 = 29.4 psi, which rounds to about 29 psi.
- Answer: Between 600 and 900 gpm. At 600 gpm the residual is about 47 psi, above the 40 psi minimum; at 900 gpm it is about 29 psi, below it. The pressure crosses 40 psi somewhere between those two flows.
- Answer: 600 gpm. At 600 gpm the residual is about 47 psi, still at or above 40 psi. At 900 gpm it has already dropped to about 29 psi, so 600 gpm is the largest tabulated flow that still meets the comfort minimum.
- Answer: 5 psi. Residual pressure = 12 × 0.433 = 5.196, about 5 psi, which is below the 20 psi state minimum. When pressure drops that low, groundwater or other contamination can be drawn into the main through leaks or cross-connections. Adding a second pump in parallel, installing a larger pump, or enlarging the supply main to cut friction head would each raise the residual pressure at high flow.
Differentiation
Support
Provide the friction formula already evaluated for all four flows (3, 12, 27, and 48 feet) so students can concentrate on assembling total dynamic head and converting feet to psi. Give a printed strip stating "feet → psi: multiply by 0.433."
Extension
Ask students to estimate the operating flow where the pump head exactly equals the delivery head plus a 40 psi (92-foot) residual, by interpolating between the tabulated rows, and to explain why that flow is the practical peak the station can serve while holding comfortable pressure.
ELL supports
Pre-teach "head," "lift," "friction," and "residual" with a labeled cross-section of the tank, the pump, and the hilltop home showing each term as a vertical distance. Allow students to record item 8's design change as a labeled sketch with a short caption rather than a full paragraph.