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Worksheet Grade 10 Careers & CTE

Crane Hollow Filter Loading Rate: A Water Operator Worksheet

A grade 10 careers worksheet where students act as a filtration operator at the fictional Crane Hollow plant, computing filter loading rates in gpm per square foot.

Objectives

  1. Students will convert a plant flow in MGD to gpm and compute filter surface area.
  2. Students will calculate a filter loading rate in gallons per minute per square foot.
  3. Students will explain how taking a filter offline changes the loading rate on the others.

Vocabulary

Backwash
Backwash is when a treatment plant reverses the flow of water through a filter to flush out the dirt and particles it has trapped. It is like rinsing out a dirty sponge so the filter can keep working well.

Also: filter loading rate, surface area, in service

Teacher overview

A filtration operator keeps track of how fast water passes through each filter, a number called the filter loading rate. It equals the flow through a filter divided by the filter's surface area, in gallons per minute per square foot. Conventional filters run best between 2 and 6 gpm per square foot. This worksheet puts students in the operator's role at the fictional Crane Hollow Water Treatment Plant and has them compute loading rates, including what happens when one filter is pulled offline for cleaning.

Crane Hollow Filter Loading Rate: A Water Operator Worksheet — Grade 10 Careers & CTE
Name: ____________________________ Date: ______________

Student Worksheet

You are the filtration operator at the fictional Crane Hollow Water Treatment Plant. The town of Crane Hollow runs this plant at a flow of 6.0 MGD. It has four identical rapid sand filters, each 20 ft by 20 ft. Use these facts: one MGD equals 694 gpm; conventional filters run best between 2 and 6 gpm per square foot. During cleaning, the plant backwashes a filter at 15 gpm per square foot.

  1. Convert the plant's flow of 6.0 MGD to gpm.
  2. Find the surface area of one filter, in square feet.
  3. Find the total surface area of all four filters.
  4. When all four filters are in service, the flow splits evenly among them. What is the flow through each filter, in gpm?
  5. Calculate the filter loading rate for one filter when all four are in service, in gpm per square foot. Round to the nearest tenth.
  6. Is that loading rate within the recommended range of 2 to 6 gpm per square foot? Explain in one sentence.
  7. One filter is taken offline for backwashing. The full 6.0 MGD now splits evenly among the three filters still in service. What is the flow through each in-service filter, in gpm?
  8. Calculate the loading rate on each in-service filter while one filter is offline, in gpm per square foot. Round to the nearest tenth.
  9. Does taking one filter offline push any in-service filter above the 6 gpm per square foot maximum? Use your answer from item 8 to justify your response.
  10. During cleaning, the plant runs water backward through the offline filter at 15 gpm per square foot. What backwash flow, in gpm, does the one filter being cleaned require?
  11. Explain why the loading rate rises when a filter is taken offline, even though the plant's total flow has not changed.

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: 4,164 gpm. 6.0 MGD x 694 gpm/MGD = 4,164 gpm.
  2. Answer: 400 square feet. 20 ft x 20 ft = 400 sq ft.
  3. Answer: 1,600 square feet. 4 filters x 400 sq ft = 1,600 sq ft.
  4. Answer: 1,041 gpm. 4,164 gpm / 4 filters = 1,041 gpm per filter.
  5. Answer: 2.6 gpm per square foot. 1,041 gpm / 400 sq ft = 2.60, which rounds to 2.6.
  6. Answer: Yes. 2.6 gpm per square foot is between 2 and 6, so it is within the recommended range.
  7. Answer: 1,388 gpm. 4,164 gpm / 3 filters = 1,388 gpm per in-service filter.
  8. Answer: 3.5 gpm per square foot. 1,388 gpm / 400 sq ft = 3.47, which rounds to 3.5.
  9. Answer: No. The loading rate on each in-service filter is about 3.5 gpm per square foot, which is still below the 6 gpm per square foot maximum.
  10. Answer: 6,000 gpm. 15 gpm per square foot x 400 sq ft = 6,000 gpm.
  11. Answer: The plant's total flow stays the same, but it now passes through less filter area, so each in-service filter carries more flow per square foot, which raises the loading rate.

Differentiation

Support

Provide the total filter area (1,600 square feet) and a worked example of a loading-rate calculation on a different filter before students try items 5 and 8. Allow a calculator for every division step.

Extension

Ask students to find the plant flow, in MGD, that would push each of the four in-service filters to the top of the recommended loading-rate range, and to show the calculation that supports their answer.

ELL supports

Provide a labeled diagram of one square filter showing its length and width, with the loading-rate formula written as flow divided by area. Allow items 6, 9, and 11 to be answered with short phrases rather than full sentences.