Worksheet Grade 9 Engineering & Design
Granite Ridge Transmission Main: Material and Pressure Class
A grade 9 engineering worksheet where students screen three pipe options for a transmission main against ranked requirements for pressure, schedule, and cost per year.
Objectives
- Students will test three pipe options against a minimum pressure rating, a road-closure limit, and a cost-per-year requirement.
- Students will name the option the district installs and the yearly cost it accepts to meet its higher-ranked requirements.
Vocabulary
Key words: pressure class, surge allowance, service life, design requirement, trade-off, corrosion protection
Teacher overview
Choosing the pipe for a transmission main is a purchasing decision made against written requirements rather than a search for the lowest price. A utility settles the minimum pressure rating first, because pipe that cannot hold the pressure it will see is not a candidate at any price. A schedule limit usually comes next, since the trench runs down a street the town needs back. Cost then decides among whatever options are still standing, and the cost that matters is the cost per year of expected service rather than the price on the invoice. This worksheet gives students three pipe options for one fictional main and asks them to apply the requirements in the order the district ranked them, then to state what the surviving option costs each year compared with the one it displaced.
Student Worksheet
The Granite Ridge Water District (a fictional utility used for this worksheet) will build a new 24-inch transmission main, 6,000 feet long, running from the treatment plant to the tank at Kirkmoor Gap. Along 2,000 feet of that route the trench crosses wet clay that corrodes bare iron. The district has written three requirements and ranked them in this order:
- Pressure rating: the pipe's pressure class must be at least the working pressure at the lowest point on the route plus a 40 psi surge allowance.
- Schedule: the road may stay closed no longer than 45 working days.
- Cost: among the options that meet the first two requirements, the district takes the lowest cost per year of expected service.
Use these design values:
- The tank at Kirkmoor Gap sits 260 feet above the lowest point on the route, and each foot of elevation adds 0.433 psi.
- Ductile iron laid in the 2,000-foot clay stretch needs a polyethylene wrap at $14 per foot. PVC needs no wrap.
- The three options the district priced:
| Option | Pipe | Pressure class | Installed cost per foot | Expected service life | Crew rate |
|---|---|---|---|---|---|
| A | Ductile iron | 250 psi | $246 | 75 years | 120 feet per day |
| B | PVC | 165 psi | $178 | 50 years | 160 feet per day |
| C | PVC | 150 psi | $166 | 50 years | 160 feet per day |
The tank sits 260 feet above the lowest point on the route, and each foot of elevation adds 0.433 psi. Find the working pressure at that low point, rounded to the nearest tenth of a psi.
The district adds a 40 psi surge allowance to the working pressure of 112.6 psi. Find the minimum pressure class rating the pipe must carry, then name which of the three options meet it.
Option C is rated for 150 psi against that 152.6 psi minimum. Find how far short the rating falls, and state what the district does with Option C even though its $166 per foot is the lowest price of the three.
Find the installed cost of Option A: 6,000 feet at $246 per foot, plus polyethylene wrap at $14 per foot across the 2,000 feet of clay.
Find the installed cost of Option B: 6,000 feet at $178 per foot, with no wrap needed.
Option A costs $1,504,000 installed and is expected to serve 75 years. Find its cost per year of expected service, rounded to the nearest dollar.
Option B costs $1,068,000 installed and is expected to serve 50 years. Find its cost per year of expected service, rounded to the nearest dollar, then state which of the two options costs less for each year it serves.
Option A's crew lays 120 feet per day. Find the working days the 6,000-foot main needs, and state whether that meets the district's 45-working-day closure limit.
Option B's crew lays 160 feet per day. Find the working days the 6,000-foot main needs, and how many days that saves against Option A's 50 days.
Apply the three requirements to Options A, B, and C in their ranked order. Name the option the district installs, and find how much more it costs each year than the option it displaced, comparing $21,360 per year with $20,053 per year.
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: 112.6 psi.
260 feet x 0.433 psi per foot = 112.58 psi, which rounds to 112.6 psi. This is the pressure the pipe holds at the low point when the tank is full and no water is moving.Answer: 152.6 psi.
112.6 psi of working pressure + 40 psi of surge allowance = 152.6 psi. Option A at 250 psi and Option B at 165 psi both carry ratings above that minimum, and Option C at 150 psi does not.Answer: 2.6 psi.
152.6 psi - 150 psi = 2.6 psi short of the minimum. Because the rating requirement is ranked first, the district drops Option C from the comparison before any cost is weighed, and the lowest price per foot does not earn it a second look.Answer: $1,504,000.
Pipe: 6,000 feet x $246 per foot = $1,476,000. Wrap: 2,000 feet x $14 per foot = $28,000. Installed cost = $1,476,000 + $28,000 = $1,504,000.Answer: $1,068,000.
6,000 feet x $178 per foot = $1,068,000. PVC does not corrode in the clay, so the district adds no wrap cost to this option.Answer: $20,053 per year.
$1,504,000 / 75 years = $20,053.33 per year, which rounds to $20,053 per year of expected service.Answer: $21,360 per year.
$1,068,000 / 50 years = $21,360 per year. Option A costs less for each year it serves, even though it costs $436,000 more to install, because the district expects 25 more years of service from it.Answer: 50 days.
6,000 feet / 120 feet per day = 50 working days. That is 5 days past the 45-working-day closure limit, so Option A fails the second requirement.Answer: 37.5 days.
6,000 feet / 160 feet per day = 37.5 working days, which is 12.5 days fewer than Option A needs and inside the 45-day limit.Answer: $1,307 per year.
Option C fails the pressure rating and Option A fails the closure limit, so the district installs Option B. $21,360 - $20,053 = $1,307 per year, which is what the district pays for handing the road back inside 45 days. A student who ranked cost first would have chosen Option A and closed the road for 50 days, and one who read price alone would have bought pipe rated below the pressure the main will see.
Differentiation
Support
Give students the working pressure (112.6 psi) and the minimum rating (152.6 psi) already computed so they can start at problem 3, and hand out the fictional district's option table with the two cost lines set up but not multiplied: 6,000 x $246 and 6,000 x $178. Allow a calculator throughout, and let students mark each option "meets" or "fails" beside each requirement before they write anything.
Extension
Ask students to run the same ranked comparison for the fictional district under a 60-working-day closure limit, which no longer rules out Option A, and to write two sentences naming what the district trades for the yearly saving. Students who finish early can find the service life Option B would need before its cost per year matched Option A's.
ELL supports
Gloss the six column headings of the fictional district's option table in the students' first language, and pre-teach "pressure class," "service life," and "closure limit" against one labeled sketch of the route showing the plant, the tank, the low point, and the clay stretch. Students may answer problems 3, 8, and 9 with a number plus the word "meets" or "fails" rather than a full sentence.