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Lesson plan Grade 7 Science

Sizing the Rennick Canal: A Flow, Area, and Velocity Lesson

A 50-minute grade 7 science lesson where students use flow equals area times velocity to size a fictional canal and reason about how area and speed change flow.

Objectives

  1. Students will use the relationship flow equals area times velocity to calculate the flow in an open channel.
  2. Students will explain how changing a channel's cross-sectional area or the water's speed changes the flow, using proportional reasoning.

Vocabulary

Key words: flow, velocity, cross-sectional area, continuity, proportional

Teacher overview

Engineers who size a channel or pipe use one compact rule: the flow equals the cross-sectional area of the water times how fast the water is moving. This lesson has students apply that rule to a fictional supply canal that carries water to a treatment plant, then reason about what happens to the flow when the channel is made deeper or the water is sped up. A common misconception this lesson addresses is that a wider channel always means more flow; the flow depends on the area and the speed together, so a wide but slow channel can carry the same flow as a narrow, fast one.

Procedure

Hook (5 min): Project a photo or sketch of a concrete-lined canal. Ask students to guess what two things they would need to measure to know how much water is passing a point each second. Write guesses on the board without judging them, then reveal the two answers: the area of the water and its speed.

Direct instruction (12 min): Introduce the rule flow equals area times velocity. Model one example on the board for the fictional Rennick Canal: a water area of 6 square feet and a speed of 4 feet per second gives a flow of 6 times 4, or 24 cubic feet per second. Show the units lining up: square feet times feet per second gives cubic feet per second. Emphasize that the area is the width of the water times its depth.

Guided practice (13 min): Work two problems together. First, if the same canal's water speeds up to 8 feet per second while the area stays at 6 square feet, the flow becomes 48 cubic feet per second, which is double. Then ask what the flow becomes if the area doubles to 12 square feet while the speed stays at 4 feet per second. Guide students to see that both changes double the flow, because flow is proportional to each factor.

Independent practice (15 min): Students complete the six-item handout on their own or in pairs, calculating flows and reasoning about proportional changes. Circulate and check that students are multiplying area by velocity, not adding them.

Closure and exit ticket (5 min): On an index card, each student answers: "A canal has a water area of 5 square feet and a speed of 3 feet per second. What is its flow?" Collect the cards. If fewer than 80 percent write 15 cubic feet per second, reteach the rule at the start of the next class.

Sizing the Rennick Canal: A Flow, Area, and Velocity Lesson — Grade 7 Science
Name: ____________________________ Date: ______________

Student Handout

The Rennick Canal is a fictional concrete channel that carries water to a treatment plant. Use flow equals area times velocity. Area is the water's width times its depth. Give flow in cubic feet per second.

  1. The canal's water area is 6 square feet and the water speed is 4 feet per second. What is the flow?
  2. At one point the water is 3 feet wide and 2 feet deep. What is the cross-sectional area of the water?
  3. The water speeds up to 8 feet per second while the area stays 6 square feet. What is the new flow, and how does it compare to your answer for item 1?
  4. Instead, the area is made 12 square feet while the speed stays 4 feet per second. What is the flow?
  5. Explain, using the idea of proportional relationships, why doubling the speed and doubling the area each have the same effect on the flow.
  6. Farther downstream the canal narrows to an area of 2 square feet, but it must still carry the 24 cubic feet per second from item 1. What water speed is needed there? Use speed equals flow divided by area.

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: 24 cubic feet per second.
    6 square feet times 4 feet per second = 24 cubic feet per second.
  2. Answer: 6 square feet.
    3 feet wide times 2 feet deep = 6 square feet.
  3. Answer: 48 cubic feet per second.
    6 times 8 = 48 cubic feet per second, which is double the 24 from item 1.
  4. Answer: 48 cubic feet per second.
    12 times 4 = 48 cubic feet per second.
  5. Answer: Flow is proportional to both area and speed.
    The area is the constant of proportionality when speed changes, and the speed is the constant when area changes. Doubling either factor doubles the product, so the flow doubles either way.
  6. Answer: 12 feet per second.
    Speed = flow divided by area = 24 divided by 2 = 12 feet per second. The narrower section must move the water faster to carry the same flow.

Differentiation

Support

Give students a filled-in example strip showing the units lining up (square feet times feet per second equals cubic feet per second). Let them use the area 6 square feet from item 1 directly in item 3 without recomputing it.

Extension

Ask students to design a canal section that carries exactly 30 cubic feet per second and stays at or below a safe speed of 5 feet per second to limit erosion, stating the area they chose and showing that it meets both the flow criterion and the speed constraint.

ELL supports

Pre-teach "flow," "area," "velocity," and "proportional" with a labeled cross-section diagram showing width, depth, and an arrow for speed. Provide a sentence frame for item 5: "Doubling the ___ doubles the flow because ___."