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Worksheet Grade 12 Art & Music

Orrin Gap Main Profile Poster: Choosing a Vertical Exaggeration

Grade 12 students set scales for a fictional pipeline profile poster, find vertical exaggeration and pressure head, and design how the hydraulic grade line reads.

Objectives

  1. Students will choose a vertical scale that fits a fixed poster band and calculate the resulting vertical exaggeration.
  2. Students will calculate pressure head from hydraulic grade line and pipe elevations and identify where a main runs under suction.
  3. Students will make line, color, and labeling decisions that make the key hydraulic relationship the first thing a viewer reads.
  4. Students will explain how to disclose vertical exaggeration so a public audience is not misled.

Vocabulary

Key words: profile, vertical exaggeration, hydraulic grade line, pressure head, station, scale bar, direct labeling

Teacher overview

Engineers describe a pipeline route with a profile, a side view that plots elevation against distance along the pipe. Because a main can run for miles while rising and falling only a few hundred feet, a profile drawn at true scale is a nearly flat line, so profiles are drawn with the vertical scale stretched. Choosing how much to stretch it is a design decision, and the designer is obliged to tell readers how much stretch was applied. In this worksheet students design a public-meeting poster for a fictional main over a ridge called Orrin Gap. They set the scales, find the exaggeration, compute the pressure head that the drawing has to show, and decide how line weight, color, and labels make the key relationship legible. Two misconceptions are addressed directly. The first is that an exaggerated profile is a dishonest drawing; exaggeration is standard practice, and the problem arises only when it is hidden. The second, from hydraulics, is that water in a pipe cannot flow uphill; a pressurized main can carry water over a rise as long as the hydraulic grade line stays above the pipe.

Orrin Gap Main Profile Poster: Choosing a Vertical Exaggeration — Grade 12 Art & Music
Name: ____________________________ Date: ______________

Student Worksheet

In our scenario, the fictional Stourley Water Authority plans a new 12,000-foot transmission main. It runs from Stourley Reservoir over Orrin Gap, a low ridge, to a storage tank at the edge of town. At a public meeting, the authority will show a poster of the main's profile. You are designing that poster. The profile drawing must fit a panel 48 inches wide, and the band for elevations is 12 inches tall.

Station (feet from the reservoir) 0 3,000 5,000 8,000 12,000
Pipe elevation (feet) 1,000 980 1,040 900 820
Hydraulic grade line elevation (feet) 1,060 1,030 1,010 980 940

The elevations on the poster run from 820 feet up to 1,060 feet, a range of 240 feet. Elevations were surveyed to the nearest 10 feet.

The hydraulic grade line (HGL) shows how high water would rise in a thin open tube tapped into the main at each point. The pressure head at a point is the HGL elevation minus the pipe elevation. Where the pipe rises above the HGL, the pressure head is negative and the pipe runs under suction. Engineers avoid this, because air collects at the high point and any leak can pull groundwater into the pipe. The usual fixes are a booster pump, a lower route, or a larger pipe.

  1. How many feet of pipe does 1 inch of the poster represent horizontally?
  2. If the poster used the same scale vertically, how tall would the 240-foot elevation range be on the poster, in inches?
  3. At a vertical scale of 1 inch = 10 feet, how tall would the 240-foot range be, in inches?
  4. At a vertical scale of 1 inch = 25 feet, how tall would the 240-foot range be, in inches?
  5. Vertical exaggeration equals the horizontal feet per inch divided by the vertical feet per inch. Of the three vertical scales in items 2 through 4, choose the one that fits the 12-inch band and still shows the ridge clearly. What is its vertical exaggeration?
  6. What is the pressure head at station 3,000, in feet?
  7. What is the pressure head at station 5,000, the top of Orrin Gap, in feet?
  8. What is the pressure head at station 12,000, in feet?
  9. Residents know pressure in pounds per square inch from tire gauges. Convert the pressure head at station 3,000 to psi using psi = feet × 0.433. Round to the nearest whole psi for the poster label.
  10. Explain why a whole number is the right precision for the label in item 9.
  11. The poster's main message is that the main, as drawn, cannot carry its design flow over Orrin Gap. Describe how you would make the part of the drawing that shows this problem the first thing a viewer notices.
  12. At a practice run, a resident says Orrin Gap "looks like a cliff." What statement must be printed on the poster so readers can judge how steep the ridge really is?
  13. Describe one small addition to the poster that would show the ridge at its true proportions.
  14. The draft draws the HGL and the pipe as solid lines of the same weight, one blue and one black. Explain why the HGL should also differ from the pipe in dash pattern or line weight.

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: 250 feet.
    The 12,000-foot main is drawn across 48 inches. 12,000 ÷ 48 = 250 feet per inch.
  2. Answer: 0.96 inches.
    At 250 feet per inch, the 240-foot range is 240 ÷ 250 = 0.96 inches tall, which makes the profile an almost flat line.
  3. Answer: 24 inches.
    240 ÷ 10 = 24 inches, which is twice the height of the 12-inch band, so this scale does not fit.
  4. Answer: 9.6 inches.
    240 ÷ 25 = 9.6 inches, which fits inside the 12-inch band and leaves room for labels.
  5. Answer: 10 times
    The 1 inch = 25 feet scale is the only one that fits and still shows the ridge. The exaggeration is 250 ÷ 25 = 10, so slopes on the poster look 10 times steeper than they are.
  6. Answer: 50 feet.
    The HGL is at 1,030 feet and the pipe at 980 feet. 1,030 − 980 = 50 feet.
  7. Answer: -30 feet.
    The HGL is at 1,010 feet and the pipe at 1,040 feet. 1,010 - 1,040 = -30 feet. The pipe sits 30 feet above the HGL, so this stretch runs under suction.
  8. Answer: 120 feet.
    The HGL is at 940 feet and the pipe at 820 feet. 940 − 820 = 120 feet.
  9. Answer: 22 psi.
    50 × 0.433 = 21.65 psi, which rounds to 22 psi.
  10. Answer: The elevations are only known to the nearest 10 feet.
    An error of up to 10 feet in elevation is an error of about 4 psi, so a label such as 21.65 would claim far more accuracy than the survey supports. Residents also need a sense of size rather than a decimal. Accept any answer that ties the rounding to the precision of the input data or to the needs of a public audience.
  11. Answer: Fill the gap where the pipe rises above the HGL near station 5,000 with one strong warm color.
    That crossing is the part of the drawing that shows the problem. Use a single red-orange fill between the two lines there, and keep the rest of the drawing in muted grays and a quiet blue. Add a short direct callout at that spot, such as "The pipe rises above the grade line here, so the main cannot carry its design flow without a pump." Accept any answer that isolates the crossing with a single contrasting color or weight and a direct label.
  12. Answer: "Vertical scale exaggerated 10 times"
    The statement should sit beside the horizontal and vertical scale bars, in type large enough to read at the same distance as the station labels. Accept any wording that names the exaggeration and its factor.
  13. Answer: A thin true-scale strip of the same profile.
    Drawn at 250 feet per inch in both directions, the full profile is under 1 inch tall. Placed under the main drawing and labeled "true proportions," it shows readers how gentle the ridge actually is. Accept an inset of a short section at true scale.
  14. Answer: So the two lines stay distinct without color.
    Posters are photocopied, projectors shift colors, and some readers have color-vision deficiency. A dashed or lighter HGL remains different from a heavy solid pipe line in all of these cases. Labeling each line directly, instead of relying on a legend, also helps.

Differentiation

Support

Give students the scale ratio as a fraction, such as 12,000 feet over 48 inches, and have them simplify it before item 1. Provide a blank profile grid with the station marks already drawn so they can plot the pipe and the HGL for items 6 through 8 and see the crossing at Orrin Gap before answering item 11. Allow calculators throughout.

Extension

Ask students to draw the poster's profile at the scales from item 5 on a 48-inch strip of paper, with both lines, the shaded crossing, the scale bars, the exaggeration statement, and the true-scale strip. Then have them design a second version for the authority's engineers, who read the drawing at a desk, and write two sentences explaining what they changed for that audience and why.

ELL supports

Pre-teach profile, station, elevation, and grade line with a labeled sketch of a pipe crossing a hill. Pair the phrase "pressure head" with a picture of a clear tube rising from a pipe, with the water height marked. Allow items 11 through 14 to be answered with a labeled sketch and a short phrase, and provide the frame "The reader should notice ___ first because ___."

Extensions

Students can redesign the profile for a one-page newsletter column instead of a 48-inch poster. They should recalculate the scales for a drawing area of their choice, decide whether to keep the same exaggeration, and explain in writing how the smaller format changes the line weights, label sizes, and amount of detail that can be shown.