Math for the Workplace 12
Plumbing Information Sheet
Number Sense
Plumbers work with integers, decimals, fractions, ratios, proportions, and percentages. As well, they work with monetary values. When working with elevations, plumbers work with feet and decimal feet. Dimensions could be given in feet, inches and fractions.
Plumbers usually round to two numbers after the decimal point.
Operation Sense
Calculations performed by plumbers include, but are not limited to, calculating the amount of materials being used, such as, pipe, connectors, and fixtures. They must also calculate the cost price and in turn the retail price charged to the consumer to obtain a profit. The business calculation of Profit = Retail Price – Cost Price is critical to the viability of a plumber’s business.
A well developed sense of estimation is also important. Estimating the materials for a job or the length of time to complete a job are both important to being a successful plumber.
They must be very comfortable using technology such as calculators. Plumbers also need well developed problem solving skills. Problem solving through obstacles such as design changes or availability of resources all require problem solving skills.
Measurement
Measurement for reading blueprints and using scales requires proportional thinking. Plumbers use scales both in imperial measurements, such as and in metric measurements, such as 1:50 or 1:100. Plumbers must measure lengths of pipes. They must also be able to measure the angles. It is essential that all of these measurements be done with both precision and accuracy.
Plumbers must also be very comfortable doing conversions. Common conversions for plumbers include:
BTU = KW
1” = 25 mm
1 psi = 7 kPa
1 imp gal = 4.5 l
Geometry
Understanding angles and geometric properties cannot be understated. Degrees are important for calculating offsets. Plumbers also use right angle properties and Pythagorean Theorem for calculating the hypotenuse.
Examples of Math in Plumbing
Conversions: fractions to decimals, inches to feet, feet and decimal feet
Fixture spread for single bathroom group: equal spacing between fixtures
Angle parts: squares, rectangles, circles, triangles
Circle parts
Measurements: centre, face, back, end and throat
Fitting allowances
Offsets 45 degrees: 1.414, .707
Metric and Imperial systems of measurement
- Areas: squares, rectangles, circles and triangles
- Volumes: gallons, weight of water, 6.25 gallons per cubic foot
- Length
- Mass: weight of liter
- Pressure
- Temperature
Conversions in back of plumbing code
Grading with a level: 1/4“ per ft., 2% and 1:50
Fixture spread, battery of fixtures
Drop, rise and run (Grading)
Elevations (Horizontal drains)
Head pressures: 0.434 psi / 0.0361 psi, 27.7” / 2.31’ 1 kPa = 1 dm
1 gal = 277” cu., 6.25 gal./1ft.cu., 1 gal. = 10 lb.
1 dm cu. =1 litre=1 kg.
US to Imperial gal. 5/6 or 6/5
1 IMP Gal. = 4.54 litres
1 US Gal. = 3.78 litres
Parallel offsets using 45 ( 1 and 2 X factors )
Offset factors from IPT book
D² over d²
Linear expansion (coefficients)
Rolling offsets with 45
Elevations (Horizontal and vertical) - Transits
Absolute pressure and temperature
Water columns
Psi to ounces
PPM, mg/l, grains /gal
Head pressure
Head of Hg
Jumper Offsets using 2 - 45 and 1 – 90
Jumper Offsets using 4 – 45
Plumbing Worksheet #1
IMPERIAL CYLINDER TANK CAPACITIES
Where “D” is the diameter in inches, where “r” is the radius, or half the diameter in inches and where “L” is the length or height in inches:
Volume in Gallons = π r ² H = cubic inches divided by 277 = IMP. Gallons
**** Note: 1 gallon contains 277 cu. inches ****
If “D”, “r” and “L” are measured in feet:
Volume in Gallons = π r ² H = cubic feet multiply by 6.25 = IMP. Gallons
****Note:1 cu. ft. contains 6.25 gallons:****
SAMPLE PROBLEM SAMPLE PROBLEM
D equal 24” D equal 2 ft.
r equal 12” r equal 1 ft
L equal 48” L equal 4 ft.
Cubic inches______Cubic feet______
Gallons______Gallons______
****NOTE : 1 Imperial Gallon = 10 pounds****
Plumbing Worksheet #2
Plumbing Worksheet #3
ROLLING OFFSET # 3
Calculate the following:
A ______B ______C ______D ______
Plumbing Worksheet #4
JUMPER OFFSET
2 - 45 and 1 - 90
1.K = Half the diameter plus the space times two
K = 7” + 2” = 9” X 2 = 18”
Note:
The 45 degree elbow is above the centre of the cylinder.
K = 18” – (2” X 1.414)
K = 18” – 2.83” = 15.17”
k = 15.17”
2.L = Half the diameter plus the space times two
L = 7” + 2” = 9” X 2 = 18”
Note:
The 45 degree elbow is below the centre of the cylinder.
L = 18” + (2” X 1.414)
L = 18” + 2.83” = 20.83”
L = 20.83”
- J = the overall measurement minus Half the diameter, plus the space, times two, times .707 minus the distance above the centre line.
J = 21” – (7 + 2) X 2 X .707 – 2”
J = 21” – (9 X 2) X .707 – 2”
J = 21” – (18 X .707) – 2”
J = 21” – (12.73 – 2”)
J = 21” – 10.73 = 10.27”
J = 10.27”
- M = the overall measurement minus Half the diameter, plus the space, times two, times .707 plus the distance below centre line.
M = 26” – (7 + 2) X 2 X .707 + 2”
M = 26” – (9 X 2) X .707 +2”
M = 26” – (18 X .707) + 2”
M = 26” – (12.73 +2”)
M = 26” – 14.73”
M = 11.27”
Math For The Workplace 12: Plumbing Information Sheet August 2008