Math problem set Grade 11 Math

Larkmoor Junction Transmission Main: Flow, Velocity, and Pipe Geometry

A grade 11 problem set modeling a fictional transmission main as a cylinder, converting MGD to gpm and cfs, and using Q = A x V for velocity, volume, and travel time.

Grade: Grade 11
Subject: Math
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator

Standards

HSG-MG.A.1 Common Core Math

Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

How this material aligns: Problems 3, 6, and 7 model the pipe's circular cross-section and full length as a cylinder to compute cross-sectional area and pipe volume from measured dimensions.

All materials for HSG-MG.A.1 →

HSN-Q.A.1 Common Core Math

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

How this material aligns: Problems 1, 2, and 4 carry units through a multi-step conversion chain from MGD to gpm and cfs, then keep area and flow in matching units inside the continuity formula Q = A x V.

All materials for HSN-Q.A.1 →

Download Word file

This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will convert a design flow among MGD, gpm, and cfs while tracking units.
Students will apply Q = A x V and cylinder geometry to find velocity, pipe volume, and travel time in a transmission main.

Vocabulary

Key words: transmission main, continuity, velocity, cross-sectional area

Teacher overview

A transmission main is a large pipe that carries treated water from a plant toward a city before it branches into smaller distribution lines. Engineers size these pipes so the water moves fast enough to stay fresh but slow enough to avoid pressure loss and pipe wear. This set walks through a fictional main at Larkmoor Junction using the continuity formula Q = A x V and simple cylinder geometry. A common misconception is plugging a flow in MGD straight into Q = A x V; the formula needs flow and area in matching units, so the flow must first become cubic feet per second to pair with an area in square feet.

Larkmoor Junction Transmission Main: Flow, Velocity, and Pipe Geometry — Grade 11 Math

Name: ____________________________ Date: ______________

Problems

The Larkmoor Junction water system (a fictional system used for this set) runs a straight transmission main that is 24 inches (2.0 feet) in diameter and 12,000 feet long. Its design flow is 5.0 MGD. Use these relationships throughout:

1 MGD = 694 gpm
1 MGD = 1.547 cfs
1 cubic foot = 7.48 gallons
Area of a circle = 0.785 x diameter squared
Continuity: Q = A x V (flow = area x velocity)

Convert the 5.0 MGD design flow to gallons per minute.
Convert the 5.0 MGD design flow to cubic feet per second.
Model the pipe's cross-section as a circle and find its area in square feet, using diameter = 2.0 feet.
Using Q = A x V with Q = 7.735 cfs and A = 3.14 square feet, find the water velocity in feet per second.
Operators like transmission velocities between 2 and 5 feet per second. Does this main fall inside that range?
Model the whole main as a cylinder 2.0 feet in diameter and 12,000 feet long, and find its volume in cubic feet.
Convert the pipe's volume from item 6 to gallons.
How many minutes does a parcel of water take to travel the full 12,000-foot main at 2.46 feet per second?

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: 3,470 gpm. 5.0 MGD x 694 gpm per MGD = 3,470 gpm.
Answer: about 7.74 cfs. 5.0 MGD x 1.547 cfs per MGD = 7.735 cfs, which rounds to 7.74 cfs.
Answer: 3.14 square feet. Area = 0.785 x 2.0 squared = 0.785 x 4 = 3.14 square feet.
Answer: about 2.46 feet per second. V = Q / A = 7.735 / 3.14 = 2.463, which rounds to 2.46 feet per second.
Answer: Yes. The velocity of 2.46 feet per second is inside the 2 to 5 feet per second range operators prefer.
Answer: 37,680 cubic feet. Volume = area x length = 3.14 square feet x 12,000 feet = 37,680 cubic feet.
Answer: about 281,800 gallons. 37,680 cubic feet x 7.48 gallons per cubic foot = 281,846 gallons, which rounds to about 281,800 gallons.
Answer: about 81 minutes. Time = length / velocity = 12,000 / 2.46 = 4,878 seconds; 4,878 / 60 = 81.3 minutes, or about 81 minutes.

Differentiation

Support

Provide a labeled diagram of the pipe showing diameter, radius, and length as separate measurements, and give the area from item 3 already computed so students can move directly into the velocity and volume steps.

Extension

Ask students to confirm the travel time from item 8 a second way, by dividing the pipe volume in gallons by the design flow in gallons per day and converting the result to minutes, then to explain why both methods should agree.

ELL supports

Pre-teach "diameter," "velocity," "cross-section," and "transmission main" with a labeled sketch of a pipe cut open. Provide a conversion strip listing the four relationships as arrow rules so students can see which direction each conversion runs.