Worksheet Grade 8 Engineering & Design
Marlin Quay Storm Inlet Screens: Choosing a Bar Spacing
A grade 8 worksheet using five tested inlet screen designs: students model flow as a linear function of bar spacing, then pick the one design meeting all three criteria.
Objectives
- Students will find the rate of change of flow with respect to bar spacing from a test table.
- Students will use a linear model to predict a tested quantity and compare it to a measured value.
- Students will apply three stated criteria to five designs and recommend the one that meets all three.
Vocabulary
Key words: storm inlet, bar spacing, criterion, rate of change, linear model, trade-off
Teacher overview
Screens over storm drain inlets catch litter and leaves before they reach a harbor, yet the same bars that catch litter also slow the water down, and a screen that blocks too much flow pushes stormwater into the street. This worksheet uses a five-design test set from the fictional town of Marlin Quay, where public works tested bar spacings from 10 mm to 30 mm on one inlet and recorded litter capture, the flow passed before water backed up, and crew cleaning time. Students first treat flow as a linear function of bar spacing, then check every design against three stated criteria. The habit this worksheet is built to interrupt is choosing the design that wins the column students care about most; here no design wins all three columns, and only one meets all three thresholds.
Student Worksheet
Public works in the fictional town of Marlin Quay tested five screen designs on the same storm inlet. Each design used a different bar spacing. The crew recorded three things for every design.
| Design | Bar spacing | Litter captured | Flow passed before backup | Cleaning time per inlet |
|---|---|---|---|---|
| A | 10 mm | 92 percent | 180 gpm | 14 min |
| B | 15 mm | 84 percent | 240 gpm | 11 min |
| C | 20 mm | 74 percent | 300 gpm | 8 min |
| D | 25 mm | 66 percent | 340 gpm | 6 min |
| E | 30 mm | 55 percent | 380 gpm | 5 min |
Marlin Quay set three criteria. A screen must capture at least 70 percent of the litter. It must pass at least 250 gpm before water backs up. Crews must be able to clean it in 10 minutes or less.
- Design A has a bar spacing of 10 mm and Design E has a bar spacing of 30 mm. By how many millimeters does the bar spacing increase from Design A to Design E?
- Design A captured 92 percent of the litter and Design E captured 55 percent. By how many percentage points does litter capture fall from Design A to Design E?
- Design A passed 180 gpm and Design E passed 380 gpm. How much more flow does Design E pass than Design A?
- Design A passes 180 gpm at a 10 mm bar spacing, and Design E passes 380 gpm at a 30 mm bar spacing. Find the average rate of change in flow passed per millimeter of bar spacing between these two designs.
- Use a rate of change of 10 gpm per millimeter and Design A's measured 180 gpm at a 10 mm bar spacing. What flow does this linear model predict for a screen with a 22 mm bar spacing?
- Use the same model, starting from 180 gpm at a 10 mm bar spacing with a rate of change of 10 gpm per millimeter. What flow does the model predict at a 20 mm bar spacing?
- The model predicts 280 gpm at a 20 mm bar spacing, and Design C measured 300 gpm at that spacing. By how much does the measured value exceed the prediction?
- List every design that meets the litter criterion of at least 70 percent capture.
- List every design that meets the flow criterion of at least 250 gpm.
- List every design that meets the cleaning criterion of 10 minutes or less.
- Which single design meets all three criteria?
- Marlin Quay has 36 storm inlets. Design C takes 8 minutes to clean per inlet. How many minutes of crew time does one full cleaning round take with Design C?
- Design B takes 11 minutes to clean per inlet and Design C takes 8 minutes per inlet. For 36 inlets, how many more minutes does one full cleaning round take with Design B than with Design C?
- A resident says Marlin Quay should pick Design E because it is the fastest to clean. Use the three criteria to explain why the town should not pick Design E.
- Using two columns of the table, explain why widening the bar spacing improves one criterion while making another one worse.
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: 20 mm
Subtract the two bar spacings: 30 mm minus 10 mm equals 20 mm.
Answer: 37 percentage points
Subtract the two capture values: 92 minus 55 equals 37 percentage points.
Answer: 200 gpm
Subtract the two flow values: 380 gpm minus 180 gpm equals 200 gpm.
Answer: 10 gpm per mm
Divide the change in flow by the change in bar spacing: 200 gpm divided by 20 mm equals 10 gpm for each millimeter of added spacing. Accept a student who writes the slope as a fraction equal to 10.
Answer: 300 gpm
From 10 mm to 22 mm is an increase of 12 mm. Multiply 12 mm by 10 gpm per mm to get 120 gpm, then add it to the starting 180 gpm for 300 gpm.
Answer: 280 gpm
From 10 mm to 20 mm is an increase of 10 mm. Multiply 10 mm by 10 gpm per mm to get 100 gpm, then add it to the starting 180 gpm for 280 gpm.
Answer: 20 gpm
Subtract the prediction from the measurement: 300 gpm minus 280 gpm equals 20 gpm. The straight line is a good but imperfect model of the test data.
Answer: Designs A, B, and C
Their capture values are 92, 84, and 74 percent, all at or above 70 percent. Design D at 66 percent and Design E at 55 percent fall short.
Answer: Designs C, D, and E
Their flows are 300, 340, and 380 gpm, all at or above 250 gpm. Design B passes only 240 gpm and Design A only 180 gpm.
Answer: Designs C, D, and E
Their cleaning times are 8, 6, and 5 minutes, all at or below 10 minutes. Design B takes 11 minutes and Design A takes 14 minutes.
Answer: Design C
Design C is the only design appearing in the answers to items 8, 9, and 10, so it is the only one that meets the litter, flow, and cleaning criteria together.
Answer: 288 minutes
Multiply the cleaning time by the number of inlets: 8 minutes times 36 inlets equals 288 minutes.
Answer: 108 minutes
Design B takes 11 minutes times 36 inlets, which is 396 minutes, and Design C takes 288 minutes. The difference is 108 minutes. Students may also multiply the 3 minute difference per inlet by 36 inlets.
Answer: Design E fails the litter criterion
Design E captures 55 percent, which is below the 70 percent the town requires. Cleaning speed is only one of three criteria, and a design that fails any one of them is out regardless of how well it does on the others.
Answer: Wider bars pass more flow but catch less litter
Accept any response that names the flow column rising from 180 gpm to 380 gpm as spacing widens while the litter column falls from 92 percent to 55 percent, and that explains the cause: wider gaps let more water through and also let more debris through.
Differentiation
Support
Give these students the table with the three criteria thresholds already written at the top of each relevant column, and let them shade every cell that meets its threshold before answering items 8 through 11. Items 1 through 3 can be modeled aloud as one worked example.
Extension
Ask students to write the linear model from items 4 through 6 as an equation in the form of flow as a function of bar spacing, then use it to find the spacing at which this fictional test set would predict a flow of 400 gpm. Strong responses also state one reason the model should not be trusted far outside the tested range.
ELL supports
Provide a labeled cross-section of a storm inlet showing curb, grate, bars, and pipe, with the bar spacing marked. Pair the word criterion with the plain phrase "a rule the design must pass," and offer sentence frames such as "Design ___ meets the ___ criterion because ___" and "As the bars get wider, ___ goes up and ___ goes down."
Extensions
Have students measure the grate openings on a storm inlet near the school, with adult supervision and without stepping into the street, and compare the measured spacing to the five tested designs. Students can then write one sentence predicting which of the three criteria that real inlet is most likely to fail, which turns the worksheet into a field question.