Water for Schools
Menu

Math problem set Grade 10 Engineering & Design

Sawtooth Ridge Booster Pump Station: Flow and Pressure Problems

A grade 10 engineering math set sizing a booster pump station for a fictional hillside subdivision, chaining flow, pipe-velocity, and pressure-head conversions.

Objectives

  1. Convert a peak flow rate through gpm and cfs using standard water-industry conversions.
  2. Apply the continuity equation to find water velocity inside a supply pipe.
  3. Calculate the total pressure a booster pump must add to overcome elevation and meet a minimum service-pressure requirement.

Vocabulary

Pump station
A pump station is a building full of powerful pumps that push water through pipes or lift it uphill. Pumps give water the extra push that gravity alone cannot provide.
Centrifugal pump
A centrifugal pump is the most common kind of water pump, using a spinning wheel called an impeller to fling water outward and build up pressure. Treatment plants, pump stations, and even most home well pumps use this design.
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.
Hydraulic head
Hydraulic head is the height of water pushing down on a spot, which tells you how much pressure it creates. The taller the column of water above you, the harder it pushes.

Teacher overview

Sawtooth Ridge, a fictional hillside subdivision invented for this problem set, sits above the reach of its town's gravity-fed distribution system, so engineers are sizing a booster pump station to serve it. This set walks students through converting the station's peak flow through several water-industry units, finding the velocity of water inside the supply pipe, and calculating the total pressure the pump must add to overcome elevation and still meet the minimum pressure homes require. A common misconception in this math is treating psi and feet of head as interchangeable numbers instead of converting between them with the correct constant; watch for that error in items 6 through 8.

Sawtooth Ridge Booster Pump Station: Flow and Pressure Problems — Grade 10 Engineering & Design
Name: ____________________________ Date: ______________

Problems

The booster pump station at Sawtooth Ridge (a fictional site created for this problem set) must serve a subdivision whose highest point sits 210 feet above the pump station. During peak morning demand, the station's supply line carries a flow of 0.75 MGD. The suction pipe feeding the station has an inner diameter of 12 inches (1 foot).

  1. Convert the peak flow of 0.75 MGD to gallons per minute (gpm), using the conversion that 1 MGD equals 694 gpm.

  2. Convert your answer from item 1 to gallons per second, using 60 seconds per minute.

  3. The suction pipe's cross-sectional area, in square feet, can be found with the same circular-area relationship used for tank volume: Area = 0.785 × Diameter², with the diameter in feet. Find the pipe's cross-sectional area.

  4. Convert your answer from item 2 to cubic feet per second (cfs), using the conversion that 1 cubic foot holds 7.48 gallons.

  5. Using the continuity equation, Q = Area × Velocity, solve for the water's velocity inside the suction pipe in feet per second, using your answers from items 3 and 4.

  6. Using the conversion that 1 foot of water height equals 0.433 psi, calculate the pressure, in psi, created by the 210-foot elevation difference between the pump station and the subdivision's highest point.

  7. Most states require at least 20 psi of pressure at every connection to prevent backflow contamination. What total pressure, in psi, must the pump station deliver so the subdivision's highest point still receives at least that 20 psi minimum, on top of overcoming the elevation from item 6?

  8. Convert the 20 psi minimum service-pressure requirement to feet of head, using the conversion that 1 psi equals 2.31 feet of head, and add it to the 210-foot elevation to find the pump's total required head in feet. Confirm that this feet-of-head total is consistent with your psi answer from item 7.

  9. If the pump station operates at the peak flow of 0.75 MGD for a full 24-hour day, how many total gallons pass through the station, using the definition that 1 MGD equals one million gallons per day?

  10. Explain why an engineer sizing this booster pump must plan for the peak flow of 0.75 MGD rather than the subdivision's lower average daily demand.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

  1. Answer: 520.5 gpm.
    0.75 MGD × 694 gpm/MGD = 520.5 gpm.

  2. Answer: 8.675 gal/sec.
    520.5 gpm ÷ 60 sec/min = 8.675 gallons per second.

  3. Answer: 0.785 sq ft.
    Diameter = 1 ft, so Diameter² = 1, and Area = 0.785 × 1 = 0.785 square feet.

  4. Answer: 1.16 cfs.
    8.675 gal/sec ÷ 7.48 gal/cu ft ≈ 1.1598, which rounds to about 1.16 cubic feet per second.

  5. Answer: 1.48 ft/sec.
    Velocity = Q ÷ Area = 1.16 ÷ 0.785 ≈ 1.4777, which rounds to about 1.48 feet per second.

  6. Answer: 90.93 psi.
    210 ft × 0.433 psi/ft = 90.93 psi.

  7. Answer: 110.93 psi.
    90.93 psi (elevation) + 20 psi (minimum service pressure) = 110.93 psi, roughly 111 psi.

  8. Answer: 256.2 ft total head.
    20 psi × 2.31 ft/psi = 46.2 ft, and 210 ft (elevation) + 46.2 ft (pressure requirement) = 256.2 feet of total head. This matches item 7's answer, since 110.93 psi × 2.31 ft/psi ≈ 256.2 ft as well, within rounding.

  9. Answer: 750,000 gallons.
    Because 1 MGD means one million gallons per day, 0.75 MGD equals 0.75 × 1,000,000 = 750,000 gallons in a 24-hour day.

  10. Answer: Accept any answer explaining that the pump must be able to meet the highest expected demand, such as a morning peak, without the subdivision's pressure dropping below the required minimum; sizing the pump only for average demand would leave the subdivision under-pressured during peak hours, risking backflow contamination and inadequate service exactly when demand is highest.

Differentiation

Support (below grade level)

Provide the unit-conversion chain as a labeled flowchart (MGD → gpm → gal/sec → cfs) with each constant already written next to its arrow, and allow students to complete items 1 through 4 with a calculator and the flowchart in hand before attempting items 5 through 8 independently.

Extension (above grade level)

Ask students to recalculate the pump station's required total head (item 8) if the subdivision's highest point were instead 260 feet above the pump station, and to explain how that change would affect the total pressure the pump must deliver.

ELL supports

Provide a labeled diagram of the pump station, the 210-foot elevation, and the subdivision, with the key terms "elevation," "pressure," and "flow" marked directly on the diagram. Allow students to show their work numerically for items 1 through 9 and answer item 10 with a short spoken explanation instead of writing.