Lab / experiment Grade 9 Engineering & Design
Nethercote Service Lines: A Bench Test of Length and Flow
A grade 9 lab where students hold head constant and measure how tubing length and inner diameter change delivered flow, then apply the result to a fictional town.
Objectives
- Students will hold head constant while varying one pipe property at a time.
- Students will calculate flow rates in milliliters per second from their own timed collections.
- Students will report a measured flow rate to a number of digits the instruments support.
Vocabulary
- Flow rate
- Flow rate measures how much water moves past a point in a certain amount of time, like gallons per minute through a garden hose. Bigger pipes and stronger pushes give bigger flow rates.
- Friction loss
- Friction loss is the pressure water loses as it rubs against the inside of a pipe on its way to you. Longer, narrower, and rougher pipes cause more of this pressure loss.
- Service line
- A service line is the small pipe that connects the water main under the street to the plumbing inside one home or building. It is the last leg of the trip water makes to your tap.
Also: head, inner diameter
Teacher overview
Nethercote is a fictional town replacing the small service lines that run from the street main to each house. Residents on one long street complain that two fixtures cannot run at once, and the district suspects the length and the bore of the old lines are the cause rather than the pressure in the main. This investigation asks students to hold the water height constant and change one property of the tubing at a time, so the effect of length and of inner diameter can be separated. The classroom rig is a simplified analog of a service line, not a pressure test, and the numbers it produces describe this bench setup rather than any real pipe.
Procedure
Put on your safety goggles. Work over the catch tub, and wipe up spills right away so the floor stays dry.
Push one end of the 30 cm quarter-inch tubing through the hole in the bottle drilled for it. Seal around it with clay or tape so no water leaks past the tubing.
Set the bottle on a stack of books at the edge of the table. Point the free end of the tubing into the catch tub. Keep that free end at the same height for every run.
Draw a fill line on the bottle about 4 cm below the top. This line sets your head. Head is the height of water above the tubing outlet, and it must stay the same all day.
Pinch the tubing closed. Fill the bottle to the line. Have one partner ready with the pitcher.
Release the tubing and start the stopwatch at the same moment. Hold the graduated cylinder under the outlet. While water runs, the partner pours from the pitcher to keep the bottle exactly at the fill line.
Stop collecting at 15 seconds. Read the volume in the cylinder to the nearest 5 mL. Record it as Trial 1.
Empty the cylinder into the catch tub. Repeat twice more, so this tubing has three trials.
Swap in the 90 cm quarter-inch tubing. Keep the same bottle, the same fill line, and the same outlet height. Run three trials.
Swap in the 180 cm quarter-inch tubing and run three trials the same way.
Move to the bottle drilled for the wider tubing and push the 30 cm three-eighths-inch tubing through its hole. Seal it, set the bottle on the same stack, draw its fill line at the same height, and keep the outlet at the same height. Run three trials. This run changes the bore, not the length.
Do not drink any of the water. Dry the tubing, wipe the table, and wash your hands when you finish.
Data & Analysis
Record each trial as the milliliters collected in 15 seconds. Average the three trials, then divide the average by 15 to get a flow rate in milliliters per second.
| Tubing | Inner diameter | Length (cm) | Trial 1 (mL) | Trial 2 (mL) | Trial 3 (mL) | Average (mL) | Flow (mL/s) |
|---|---|---|---|---|---|---|---|
| 1 | 1/4 inch | 30 | |||||
| 2 | 1/4 inch | 90 | |||||
| 3 | 1/4 inch | 180 | |||||
| 4 | 3/8 inch | 30 |
Use your own data for tubing 1. Show the division that turns your average volume into a flow rate in milliliters per second.
Suppose a group collected 210 mL in 15 seconds from a 30 cm run and 140 mL in 15 seconds from a 180 cm run. By what percent did the collected volume drop? Round to the nearest tenth of a percent.
Use the 210 mL figure from question 2. What flow rate in milliliters per second does that represent?
Compare your own tubing 1 and tubing 4. Both are 30 cm long, and only the bore differs. Which delivered more water, and how much more?
In your own data, which change moved the flow rate more, going from 30 cm to 180 cm or going from a quarter-inch bore to a three-eighths-inch bore? Name the two numbers from your table that support your answer.
Your stopwatch reads to 0.1 second and the cylinder is marked every 5 mL. How many digits should you report in a flow rate, and why?
Suppose a group recorded flow rates of 14.0, 11.5, and 9.3 milliliters per second for its 30 cm, 90 cm, and 180 cm runs. Is the relationship between length and flow rate linear? Use the differences to support your answer.
The fictional Nethercote district must pick a size for its new service lines. Write one criterion for that choice. State a quantity and a unit that someone could measure after the work is done.
Name one constraint on the choice of service line size, and explain in one sentence why it limits the 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
Answer: Accept the group's own average divided by 15 seconds.
The work should show the three trial volumes, their sum divided by 3, and that average divided by 15 seconds. Most 30 cm quarter-inch runs at a small head land somewhere between 8 and 20 milliliters per second, though the rig's exact head and hole size shift that range. Score the method rather than the exact number.Answer: 33.3 percent.
210 minus 140 = 70 mL of difference. Then 70 divided by 210 = 0.3333, or 33.3 percent less collected by the longer run.Answer: 14.0 milliliters per second.
210 mL divided by 15 seconds = 14.0 milliliters per second.Answer: Accept the wider bore delivering more, with the group's own difference.
Tubing 4 should deliver noticeably more than tubing 1 at the same length and head, because a larger bore has more cross-sectional area and less wall surface per unit of flow. Accept any difference the group's data supports, stated in milliliters per second or in milliliters collected. If a group's wider tubing delivered less, check whether the seal leaked or the fill line drifted.Answer: Accept either answer when two numbers from the group's own table support it.
In most setups the bore change moves the flow more than the length change, because area grows with the square of the diameter while friction grows with length. The scored part is the evidence: the response must name the two flow rates being compared and say which pair of runs they came from.Answer: Two or three significant digits, argued from the instruments.
The cylinder is the coarser instrument. Reading to the nearest 5 mL out of about 200 mL is roughly a 1 to 2 percent uncertainty, so a flow rate reported as 14 or 14.0 milliliters per second is honest while 14.06 is not. Accept two or three significant digits when the student argues from the instrument marks rather than from the calculator display.Answer: No, the relationship is not linear.
From 30 cm to 90 cm the rate falls 2.5 milliliters per second across 60 cm, which is about 0.042 per centimeter. From 90 cm to 180 cm it falls 2.2 milliliters per second across 90 cm, which is about 0.024 per centimeter. The drop per centimeter is not constant, so the relationship is not linear. Accept any answer that compares the two rates of change rather than only the two differences.Answer: Accept any measurable service line criterion.
Correct answers state a quantity and a unit that can be checked, such as delivering at least a stated flow in gallons per minute at the farthest fixture, holding a stated pressure at the meter while two fixtures run, or keeping the delivered flow within a stated percent of the flow at the nearest house. Reject goals with no measurable quantity, such as good water pressure.Answer: Accept any genuine constraint with a reason.
Common correct answers include the width of the existing trench or bore path, the size of the tap the main will accept, the cost of larger pipe and fittings across many houses, the diameter the meter and the setter are built for, the depth required to stay below frost, and the disruption a wider trench causes to driveways and trees. The reason must explain how the limit bounds the choice rather than restating it.
Differentiation
Support
Give these students the data table with the flow rate column already labeled with its division, and pre-cut all four tubing lengths so setup time goes to measuring rather than assembly. Assign one student to watch the fill line and call out when it drifts, since a falling head is the most common source of scattered trials. Allow them to run two trials instead of three.
Extension
Ask these students to add a fifth run using two quarter-inch lengths joined by a coupling, then compare it with a single length of the same total length to see what the fitting costs in flow. Have them plot flow rate against length for the quarter-inch runs and describe the curve, then predict the flow at 360 cm and test the prediction if tubing allows.
ELL supports
Pre-teach head, bore, and flow rate with a labeled diagram of the rig showing the fill line, the height of the outlet, and the tubing. Provide the sentence frame "The flow rate is ___ milliliters per second because we collected ___ milliliters in ___ seconds" for question 1. Allow questions 8 and 9 to be answered with the frames "A criterion is ___" and "A constraint is ___ because ___."
Extensions
Have students repeat one run with the bottle raised twice as high, holding the tubing length and bore fixed, and describe what the added head does to the flow rate. Ask them to explain why a utility cannot simply raise pressure to solve a flow complaint at a house, naming at least one thing higher pressure does to old plumbing and to the rate at which a leak loses water. Students can then write a short recommendation to the fictional Nethercote district that names the change they would make first.