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Worksheet Grade 7 Engineering & Design

Hemlock Bend RO Pilot: Sizing Recovery Rate and Reject Volume

A grade 7 worksheet where students use a stated recovery rate to size a reverse-osmosis pilot's clean water output and reject volume against a service constraint.

Objectives

  1. Students will calculate the clean water output and reject volume of a reverse-osmosis design at a stated recovery rate.
  2. Students will solve backward from a demand constraint to find a minimum required recovery rate.

Vocabulary

Key words: recovery rate, reject water, intake, constraint

Teacher overview

Hemlock Bend, a fictional rural district used in this worksheet, is piloting a reverse-osmosis unit to treat brackish well water. The pilot is designed to recover a stated percentage of its intake as clean drinking water, and the rest becomes a concentrated reject stream that must be disposed of safely. This worksheet has students size the pilot's output at its current design, check it against the district's minimum service constraint, and then work backward to find the recovery rate a larger future demand would require.

Hemlock Bend RO Pilot: Sizing Recovery Rate and Reject Volume — Grade 7 Engineering & Design
Name: ____________________________ Date: ______________

Student Worksheet

This pilot is fictional. Assume the reverse-osmosis unit takes in 2,000 gallons of brackish water per day. Brackish water is saltier than fresh water but not as salty as seawater. The unit is designed to recover 65 percent of that intake as clean product water. The rest of the intake becomes concentrated reject water.

  1. How many gallons of clean product water does the pilot produce each day at its current 65 percent recovery rate?

  2. How many gallons of concentrated reject water does the pilot produce each day?

  3. Check your answers to items 1 and 2 by adding them together. Do they equal the 2,000-gallon intake?

  4. The district needs at least 1,200 gallons of clean water per day to meet its minimum service constraint. Does the pilot's current design (item 1) meet this constraint? By how many gallons does it exceed or fall short?

  5. Engineers are considering a higher recovery rate of 75 percent. The intake stays at 2,000 gallons per day. How many gallons of clean water would this redesign produce each day?

  6. Compare your answers to items 5 and 1. How many more gallons of clean water per day does the 75 percent redesign produce than the original 65 percent design?

  7. A higher recovery rate leaves a smaller reject stream. That stream is also more concentrated, so it can be harder to dispose of safely. Explain one reason the district might not simply choose the highest possible recovery rate. Use the idea of competing criteria and constraints.

  8. The pilot runs for a 30-day test month at the original 65 percent recovery rate. How many total gallons of clean water does it produce over the month?

  9. Challenge. Suppose the district's demand grows to 1,500 gallons of clean water per day. The intake source can supply up to 2,400 gallons per day. What minimum recovery rate, as a percent, would the pilot need to meet that demand? Round to the nearest whole percent.

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: 1,300 gallons. 65% of 2,000 gallons = 1,300 gallons.

  2. Answer: 700 gallons. 2,000 − 1,300 = 700 gallons of reject water.

  3. Answer: Yes. 1,300 + 700 = 2,000 gallons, which matches the total intake.

  4. Answer: Yes, it exceeds the constraint by 100 gallons. 1,300 gallons (item 1) − 1,200 gallons (minimum) = 100 gallons more than required.

  5. Answer: 1,500 gallons. 75% of 2,000 gallons = 1,500 gallons.

  6. Answer: 200 more gallons per day. 1,500 − 1,300 = 200 gallons.

  7. Answer: Accept any explanation noting that a higher recovery rate leaves a smaller volume of more concentrated reject water, which can be more difficult and costly to dispose of safely, or that reaching a higher recovery rate can require more energy or larger equipment, so the district must balance the clean-water criterion against these disposal and cost constraints rather than maximizing recovery alone.

  8. Answer: 39,000 gallons. 1,300 gallons/day × 30 days = 39,000 gallons.

  9. Answer: About 63%. The pilot needs 1,500 gallons of clean water from an intake of 2,400 gallons: 1,500 ÷ 2,400 = 0.625, or 62.5%. Because 62% would fall short (62% of 2,400 = 1,488 gallons, less than 1,500), the rate must round up to 63% to meet the demand.

Differentiation

Support

Provide item 1's calculation already set up as "65% of 2,000 = ___" and allow a calculator for every item. Give students a printed strip showing the relationship "clean water + reject water = intake" to reference for items 2 and 3.

Extension

Ask students to find how many gallons of intake water the pilot would need per day, at the original 65 percent recovery rate, to produce exactly 2,000 gallons of clean water, working backward from the recovery rate.

ELL supports

Provide a simple labeled diagram showing intake water splitting into two paths, clean water and reject water, with the 65 percent and 35 percent shares marked. Allow item 7's explanation to be written as one sentence using a provided frame: "A higher recovery rate makes the reject water more ___, which is harder to ___."