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Quiz & test questions Grade 12 Math

Marston Regional Water: Hydraulics and Distribution Test

A grade 12 unit test mixing multiple-choice, short-answer, and computation items on pressure, head, tank volume, and pipe flow for a fictional regional water system.

Objectives

  1. Students will convert between pressure and head and compute tank volume and pipe flow.
  2. Students will interpret distribution pressures against standard service requirements.

Vocabulary

Key words: head, static pressure, continuity, pressure-reducing valve

Teacher overview

This 40-minute unit test is worth 38 points and covers distribution hydraulics for Marston Regional Water System. It mixes three multiple-choice items, two short-answer items, and six computation items, ranging from recalling a service standard to computing tank volume and pipe flow. Students may use a calculator and the conversion facts printed at the top of the test.

Marston Regional Water: Hydraulics and Distribution Test — Grade 12 Math
Name: ____________________________ Date: ______________

Assessment

Marston Regional Water System (a fictional system) supplies a town from one elevated tank. Use these facts: 1 psi = 2.31 feet of head; 1 foot of head = 0.433 psi; a cylinder's volume (cu ft) = 0.785 x diameter squared x depth; 1 cubic foot = 7.48 gallons; 1 cfs = 448.8 gpm; 1 MGD = 694 gpm; and flow Q = area x velocity.

  1. (2 points) The water surface in Marston's tower stands 150 feet above a home. Using 1 foot = 0.433 psi, the static pressure at that home is closest to:
    • A) 65 psi
    • B) 35 psi
    • C) 150 psi
    • D) 347 psi
  2. (4 points) A gauge at the pump station reads 52 psi. Convert that pressure to feet of head.
  3. (2 points) Most states require a minimum distribution pressure of at least:
    • A) 5 psi
    • B) 20 psi
    • C) 80 psi
    • D) 120 psi
  4. (3 points) A low-lying neighborhood in Marston records 84 psi, while utilities aim for 40 to 80 psi. State whether that reading is within the target range and name the device used to lower pressure in low areas.
  5. (5 points) The tower tank is a cylinder 45 feet in diameter and 32 feet deep. Find its volume in cubic feet.
  6. (4 points) Convert the tank volume from item 5 to gallons.
  7. (5 points) A main with a 16-inch (1.333-foot) diameter carries water at 4.0 feet per second. Using Q = area x velocity with area = 0.785 x diameter squared, find the flow in cfs.
  8. (4 points) Convert the flow from item 7 to gallons per minute.
  9. (4 points) The system delivers an average of 3.0 MGD. Convert that to gallons per minute.
  10. (3 points) Explain why the static pressure at a home depends on the height of the water surface above it, not on how wide the tower tank is.
  11. (2 points) The tank is drained for painting. Refilling at 2,082 gpm, about how long will it take to add 380,000 gallons?
    • A) about 3 hours
    • B) about 30 minutes
    • C) about 12 hours
    • D) about 3 days

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: A) 65 psi.
    150 feet x 0.433 psi per foot = 64.95, about 65 psi. Choice D, 347 psi, comes from multiplying 150 by 2.31 (346.5) by mistake, the classic wrong-constant error.

  2. Answer: 120 ft.
    52 psi x 2.31 feet per psi = 120.12, about 120 feet of head.

  3. Answer: B) 20 psi.
    Most states require at least 20 psi at every connection to keep contaminants from being drawn into the mains.

  4. Answer: Above the range; a pressure-reducing valve.
    84 psi is above the 40-to-80-psi target, so the neighborhood needs a pressure-reducing valve to bring service pressure down.

  5. Answer: 50,868 cubic feet.
    Volume = 0.785 x 45 squared x 32 = 0.785 x 2,025 x 32 = 0.785 x 64,800 = 50,868 cubic feet.

  6. Answer: 380,493 gallons.
    50,868 cubic feet x 7.48 gallons per cubic foot = 380,492.64, about 380,493 gallons.

  7. Answer: 5.58 cfs.
    Area = 0.785 x 1.333 squared = 0.785 x 1.7769 = 1.395 square feet. Flow = area x velocity = 1.395 x 4.0 = 5.58 cfs.

  8. Answer: 2,504 gpm.
    5.58 cfs x 448.8 gpm per cfs = 2,504.3, about 2,504 gallons per minute.

  9. Answer: 2,082 gpm.
    3.0 MGD x 694 gpm per MGD = 2,082 gallons per minute.

  10. Answer: Pressure depends on the height of water above the point.
    Static pressure comes from the weight of the water column above a point, which is set by the height of the water surface, not by the tank's width. A tall, narrow tank and a short, wide tank at the same water-surface height give the same pressure below.

  11. Answer: A) about 3 hours.
    380,000 gallons / 2,082 gpm = 182.5 minutes, which is about 3.0 hours.

Differentiation

Support

Provide the conversion facts on a separate reference card and allow students to use a formula sheet that shows the cylinder-volume and continuity formulas already arranged. Break item 7 into two graded parts, area then flow, so partial credit is clear.

Extension

Ask students to find the water-surface height, in feet, that would deliver exactly the 40-psi lower end of the target range to the home in item 1, and to explain what that means for how low the tank level can drop.

ELL supports

Provide a labeled cross-section of the tower and a home showing the water-surface height, and gloss "head," "static pressure," and "pressure-reducing valve." Allow short-answer items 4 and 10 to be answered with a labeled sketch plus a short sentence.

Extensions

Have students measure or estimate the height of a local water tower or standpipe, compute the static pressure it would deliver at ground level, and compare that value with the 40-to-80-psi service target.