Worksheet Grade 9 Engineering & Design
Kestrelmoor Plating Rinse: Sizing a Neutralization Tank
A grade 9 worksheet sizing a pH neutralization tank for a fictional plating shop, covering detention time, tank geometry, caustic use, cost, and a permit check.
Objectives
- Students will size a treatment tank from a flow rate and a required detention time.
- Students will convert a tank volume between cubic feet and gallons and solve for a missing dimension.
- Students will compare a measured pH against a permit range and interpret the logarithmic pH scale.
Vocabulary
- Detention time
- Detention time is how long water stays inside a tank or basin before flowing out. Water must stay long enough for each treatment step, like settling or disinfecting, to finish its job.
Also: neutralization, pretreatment, permit limit, order of magnitude
Teacher overview
Kestrelmoor Plating is a fictional metal-finishing shop in the town of Sedbury. Its rinse tanks send a steady stream of acidic water toward the town sewer, and the shop's discharge permit sets a pH range that water must fall inside before it leaves the property. To meet that range the shop mixes the rinse water with a caustic solution in a tank sized to hold the flow long enough for the reaction to finish. This worksheet has students size that tank, price the chemical, and then compare two ways to improve the system. The error worth watching for is treating pH as a linear scale, so that a change from pH 2.5 to pH 7.0 looks like a small adjustment rather than a drop of four and a half orders of magnitude in acid strength.
Student Worksheet
Kestrelmoor Plating and the town of Sedbury are fictional. Use only the figures given here.
The shop's rinse tanks discharge 12 gpm for 8 hours each working day. The raw rinse water sits at pH 2.5. The neutralization tank must hold the flow for at least 30 minutes. The tank the shop built is a rectangle 4.0 feet long, 3.0 feet wide, and 4.5 feet deep. Bench tests show the shop needs 0.85 gallons of caustic for every 100 gallons of rinse water. Caustic costs $3.20 per gallon. The shop runs 250 days a year. The discharge permit allows pH between 6.0 and 9.0. Use 1 cubic foot = 7.48 gallons.
The shop discharges 12 gpm for 8 hours a day. How many gallons is that in one working day?
The tank must hold the flow for at least 30 minutes. At 12 gpm, how many gallons must the tank hold?
A tank 4.0 feet long and 3.0 feet wide has a floor area of 12 square feet. What water depth, in feet, would hold the volume you found in item 2? Round to the nearest hundredth.
The shop built the tank 4.0 feet long, 3.0 feet wide, and 4.5 feet deep. How many gallons does it hold when full? Round to the nearest tenth.
Using the full volume from item 4 and the flow of 12 gpm, what is the actual detention time in minutes? Round to the nearest tenth.
The shop needs 0.85 gallons of caustic for every 100 gallons of rinse water. Using your daily flow from item 1, how many gallons of caustic does the shop use in one day?
The shop runs 250 days a year. Using your answer from item 6, how many gallons of caustic does it use in a year?
Caustic costs $3.20 per gallon. Using your answer from item 7, what is the yearly caustic cost?
The pH scale is logarithmic, so each whole step is a tenfold change in acid strength. Going from pH 2.5 to pH 7.0 is a change of how many orders of magnitude?
A grab sample from the discharge line reads pH 5.4. The permit allows pH between 6.0 and 9.0. Is that sample inside the permit range? Answer yes or no and name the limit involved.
The shop installs counterflow rinse tanks and cuts the rinse flow from 12 gpm to 8 gpm. Using the full tank volume from item 4, what is the new detention time in minutes? Round to the nearest tenth.
Cutting the rinse flow also raises the detention time in the tank the shop already has. Explain in two or three sentences why reducing the rinse flow is a better first move than building a larger neutralization tank.
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: 5,760 gallons per day.
8 hours x 60 minutes per hour = 480 minutes of discharge. Then 480 minutes x 12 gpm = 5,760 gallons in a working day.Answer: 360 gallons.
12 gpm x 30 minutes = 360 gallons of storage needed to hold half an hour of flow.Answer: 4.01 feet.
Convert the volume to cubic feet: 360 gallons divided by 7.48 gallons per cubic foot = 48.128 cubic feet. Then divide by the floor area: 48.128 divided by 12 square feet = 4.0107 feet, which rounds to 4.01 feet.Answer: 403.9 gallons.
4.0 x 3.0 x 4.5 = 54 cubic feet. Then 54 x 7.48 = 403.92 gallons, which rounds to 403.9 gallons.Answer: 33.7 minutes.
403.92 gallons divided by 12 gpm = 33.66 minutes, which rounds to 33.7 minutes. That clears the 30-minute requirement with a small margin.Answer: 48.96 gallons per day.
The ratio is 0.85 gallons per 100 gallons, or 0.0085 gallons of caustic per gallon of rinse water. Then 5,760 x 0.0085 = 48.96 gallons of caustic each day.Answer: 12,240 gallons per year.
48.96 gallons per day x 250 days = 12,240 gallons in a year.Answer: $39,168 per year.
12,240 gallons x $3.20 per gallon = $39,168 for the year's caustic.Answer: 4.5 orders of magnitude.
7.0 minus 2.5 = 4.5. Each whole pH unit is a factor of ten, so the hydrogen ion concentration falls by 4.5 orders of magnitude, which is more than thirty thousand times.Answer: No, it is below the lower limit.
The permit's lower limit is pH 6.0, and 5.4 is below it, so the sample fails. Students should note that the sample is still acidic, which means the caustic feed or the mixing was short that day.Answer: 50.5 minutes.
403.92 gallons divided by 8 gpm = 50.49 minutes, which rounds to 50.5 minutes. The same tank now holds the water half again as long (50 percent longer), because less water passes through it each minute.Answer: Cutting the flow raises detention time without building a new tank.
Accept any answer making at least two of these points: a smaller flow raises detention time in the tank the shop already owns, so no new tank is needed; the shop uses and discharges less water each year; a smaller flow leaves the existing pumps and piping in place; and a larger tank would still have to neutralize the same acid load and would not reduce water use. Strong answers add that source reduction is cheaper to maintain than added equipment.
Differentiation
Support
Give these students item 3 with the conversion already carried out, so the remaining step is one division. Provide a labeled sketch of the fictional Kestrelmoor tank showing length, width, and depth as separate measurements, since students often substitute the depth for the width. Print a pH strip beside item 9 with the permit range shaded, and allow a calculator on every item.
Extension
Ask students to find the largest rinse flow, in gallons per minute, that the existing tank at this fictional shop could handle while still holding water for 30 minutes. Then have them calculate what that flow would cost in caustic over 250 operating days and write a two-sentence recommendation on whether the shop should run at that limit or keep a margin.
ELL supports
Pre-teach detention time, neutralize, and permit limit with a drawing showing water entering a tank, mixing, and leaving. Provide the sentence frame "The tank holds ___ gallons, and the flow is ___, so the water stays ___ minutes" for item 5. Allow item 12 to be answered as a two-column list of advantages rather than a paragraph.
Extensions
Have students research how a municipal pretreatment program works and write a short summary of what a shop like the fictional Kestrelmoor Plating must report to the town each month. Ask them to explain why a wastewater plant sets limits on industrial dischargers rather than treating whatever arrives, naming at least one effect a slug of strong acid would have on the biological treatment process downstream.