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Quiz & test questions Grade 8 Engineering & Design

Oldcastle Mill Race Micro-Hydro: A Design Screening Quiz

A 20-point grade 8 quiz on screening a micro-hydro project, mixing constraint identification with forebay volume, pressure, and flow conversion computations.

Objectives

  1. Students will distinguish a design constraint from a design criterion in a project brief.
  2. Students will calculate the volume of a cylindrical forebay in cubic feet and in gallons.
  3. Students will convert a stream flow between cubic feet per second and gallons per minute.

Vocabulary

Key words: criterion, constraint, forebay, mill race, screening study

Teacher overview

This 30-minute quiz is worth 20 points and covers a screening study for a small hydropower project in a fictional mill town. It uses eight items: two multiple-choice items, two short-answer items, and four computation items. Between them the items cover cylinder volume, a cubic-foot-to-gallon conversion, a pressure figure read from a stated drop, and two flow calculations, all drawn from the same project brief so students carry one scenario through the whole quiz.

Oldcastle Mill Race Micro-Hydro: A Design Screening Quiz — Grade 8 Engineering & Design
Name: ____________________________ Date: ______________

Assessment

Project brief. The town of Oldcastle owns a stone mill race that once turned a grain mill beside Oldcastle Brook. The town is screening whether a small hydropower turbine is worth studying further. Three limits apply: the project cost cannot go above $60,000, at least 3 cubic feet of water each second must stay in the brook for fish, and the turbine must fit inside the existing stone forebay.

  1. (2 points) Which statement is a constraint rather than a criterion?
    • A) The system should produce as much power as possible.
    • B) The project cost cannot go above $60,000.
    • C) The turbine should be simple to maintain.
    • D) The intake screen should be easy to clean.
  2. (2 points) State one constraint from the brief other than the one you chose in item 1, and explain in one sentence how it limits the design.
  3. (3 points) The stone forebay is a cylinder 12 feet across and 6 feet deep. Find its volume in cubic feet. Use 3.14 for pi and show your work.
  4. (3 points) One cubic foot of water holds 7.48 gallons. Convert your answer from item 3 to gallons, rounded to the nearest whole gallon.
  5. (2 points) The mill race drops 14 feet from the intake to the turbine. Water pressure rises by 0.433 psi for each foot of drop. The pressure at the turbine is closest to:
    • A) 6.1 psi
    • B) 14 psi
    • C) 32.3 psi
    • D) 60.6 psi
  6. (3 points) In April the mill race can carry 8 cubic feet of water each second. One cubic foot per second equals 448.8 gallons per minute. Find the race's flow in gallons per minute.
  7. (2 points) In August Oldcastle Brook carries 8 cubic feet of water each second, and the fish rule leaves at least 3 cubic feet each second in the brook. How many cubic feet each second can the race take in August?
  8. (3 points) Explain why a screening study looks at both the driest month and the wettest month before the town spends money on a design.

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: B.
    A constraint is a limit the design must respect, and the cost ceiling is exactly that. Choices A, C, and D describe qualities that make one design better than another, which makes them criteria rather than limits.
  2. Answer: Either the fish flow rule or the forebay size.
    Award full credit for naming the rule that at least 3 cubic feet each second must stay in the brook, with an explanation that the turbine can only use what is left over, or for naming the existing forebay, with an explanation that the turbine has to fit a space the town is not rebuilding.
  3. Answer: 678.24 cubic feet.
    The diameter is 12 feet, so the radius is 6 feet. Volume = 3.14 × 6 × 6 × 6 = 3.14 × 36 × 6 = 678.24 cubic feet. Award 1 point for finding the radius, 1 for the correct setup, and 1 for the arithmetic.
  4. Answer: 5,073 gallons.
    678.24 × 7.48 = 5,073.2352, which rounds to 5,073 gallons. Award partial credit for a correct multiplication using an incorrect volume carried forward from item 3.
  5. Answer: A.
    14 × 0.433 = 6.062, which rounds to 6.1 psi. Choice C comes from dividing by 0.433 instead of multiplying, and choice D comes from using 140 feet instead of 14.
  6. Answer: 3,590.4 gallons per minute.
    8 × 448.8 = 3,590.4 gallons per minute. Accept 3,590 gallons per minute if the student rounds and says so.
  7. Answer: 5 cubic feet per second.
    8 - 3 = 5 cubic feet each second remain available to the race after the fish flow is left in the brook.
  8. Answer: The two months set the low and high limits the design must handle.
    The driest month shows how little water is left for the turbine after the fish flow, which sets the smallest amount of power the project can count on. The wettest month shows the largest flow the intake, screen, and channel have to pass without damage. Award 3 points for naming both ends and what each one decides, 2 points for naming both ends without the reasons, and 1 point for naming only one end.

Differentiation

Support

Provide a reference strip at the top of the page giving the cylinder volume formula, the value 7.48 gallons per cubic foot, and a two-column list headed "criterion" and "constraint" with one example already placed in each column. Allow these students to answer item 2 by circling a limit in the brief and writing a single sentence.

Extension

Suppose the town finds that a larger turbine would need a forebay 16 feet across and 6 feet deep. Ask students to compute that volume, state how many times larger it is than the current forebay, and explain whether the size constraint would still rule the larger turbine out.

ELL supports

Provide a labeled cross-section of the mill race showing the intake, the forebay, the 14-foot drop, and the turbine, with each part named in English and in the student's first language. Give sentence frames for items 2 and 8, such as "This limit changes the design because ___."