Worksheet Grade 10 Math
Copperline Water Authority Flow Conversion Worksheet
A grade 10 worksheet chaining unit conversions for a fictional river withdrawal: MGD to gpm to cfs, gallons to acre-feet, and pipe area from the continuity equation.
Objectives
- Students will convert a river withdrawal among MGD, gpm, cfs, gallons, cubic feet, and acre-feet.
- Students will apply the continuity equation to find the cross-sectional area and diameter of an intake pipe.
Vocabulary
- Acre-foot
- The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.
Also: MGD, cfs, continuity
Teacher overview
The fictional Copperline Regional Water Authority withdraws water from the Sage River and needs the same flow reported in several different units for planning, permits, and pipe design. This worksheet walks students through converting one withdrawal rate across the unit chain that operators and engineers use, then applying the continuity equation to size the intake pipe. Each answer feeds the next, so a slip early on shows up later.
Student Worksheet
The Copperline Regional Water Authority (a fictional authority used for this worksheet) withdraws 5.0 MGD from the Sage River. Use these conversions where needed: 1 MGD = 694 gpm; 1 MGD = 1.547 cfs; 1 cfs = 448.8 gpm; 1 MGD = 1,000,000 gallons per day; 1 acre-foot = 325,851 gallons; 1 cubic foot = 7.48 gallons; and flow Q (cfs) = area (sq ft) × velocity (ft/s). For a circular pipe, area = 0.785 × diameter².
Convert the 5.0 MGD withdrawal to gallons per minute using 1 MGD = 694 gpm.
Convert the 5.0 MGD withdrawal to cubic feet per second using 1 MGD = 1.547 cfs. Round to the nearest hundredth.
Check your work by converting the cfs answer from item 2 back to gpm using 1 cfs = 448.8 gpm. It should be close to item 1. Explain the small difference in one sentence.
How many gallons does the authority withdraw in one full day at 5.0 MGD?
Convert the daily withdrawal from item 4 to acre-feet using 1 acre-foot = 325,851 gallons. Round to the nearest tenth.
Over a 30-day month, how many acre-feet does the authority withdraw? Round to the nearest whole acre-foot.
The intake carries the flow at a velocity of 3.0 ft/s. Using Q = area × velocity with Q from item 2, find the required cross-sectional area in square feet. Round to the nearest hundredth.
The intake pipe is circular. Using area = 0.785 × diameter², find the pipe diameter in feet from the area in item 7. Round to the nearest hundredth.
Convert the daily withdrawal from item 4 to cubic feet using 1 cubic foot = 7.48 gallons.
Explain in two or three sentences why an engineer sizing the intake pipe would want the flow in cfs, while a planner tracking the yearly water budget would want it in acre-feet.
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 × 694 gpm per MGD = 3,470 gpm.
Answer: 7.74 cfs. 5.0 MGD × 1.547 cfs per MGD = 7.735, which rounds to 7.74 cfs.
Answer: about 3,471 gpm (3,474 gpm if the rounded 7.74 cfs is used). 7.735 cfs × 448.8 gpm per cfs = 3,471.4. The small gap from item 1 comes from the conversion factors themselves being rounded (1.547 × 448.8 = 694.3, not exactly 694), and rounding the cfs value adds a little more.
Answer: 5,000,000 gal. 5.0 MGD × 1,000,000 gallons per MGD = 5,000,000 gallons in one day.
Answer: 15.3 acre-feet. 5,000,000 gallons / 325,851 gallons per acre-foot = 15.34, which rounds to 15.3 acre-feet.
Answer: 460 acre-feet. 15.34 acre-feet per day × 30 days = 460.3, about 460 acre-feet in the month.
Answer: 2.58 sq ft. Area = Q / velocity = 7.735 cfs / 3.0 ft/s = 2.578, which rounds to 2.58 square feet.
Answer: 1.81 ft. From area = 0.785 × diameter², diameter² = 2.58 / 0.785 = 3.287, so diameter = 1.813, about 1.81 feet.
Answer: 668,449 cu ft. 5,000,000 gallons / 7.48 gallons per cubic foot = 668,449 cubic feet.
Answer: The engineer needs cfs because the continuity equation pairs a flow in cubic feet per second with a pipe area in square feet and a velocity in feet per second, so the units match. The planner needs acre-feet because a reservoir's yearly supply is measured and permitted in acre-feet, which makes the season's total easy to compare against the allowed budget.
Differentiation
Support
Give students a conversion reference card listing each factor already lined up, and mark item 1 as a worked example so they can copy its structure. Let students use the fictional authority's rounded 7.74 cfs in items 3, 7, and 8 rather than tracking the longer 7.735 value.
Extension
Ask students to find what pipe diameter would be needed if the intake velocity were held to a gentler 2.0 ft/s instead of 3.0 ft/s, then explain why a lower velocity calls for a larger pipe at the same flow.
ELL supports
Provide a flow-conversion chain drawn as labeled arrows (MGD to gpm to cfs) with the multiplying factor written on each arrow. Allow students to record answers as a filled-in chain diagram before writing them as sentences.
Extensions
Have students look up the permitted withdrawal of a real nearby water supplier, often listed in acre-feet per year, and convert it into MGD to compare with the fictional Copperline rate. A short paragraph can note whether the real supplier withdraws more or less than 5.0 MGD and what that means for the river it draws from.