Computing Pipe
Offsets
The illustration in Figure 4-9 presents a
typical pipe offset problem. Two parallel pipes
must be joined by a short length of pipe
running at a 45° angle. Determining the length
of the short piece of pipe can be difficult unless
the right mathematical formulas are used. Two
different techniques for finding the length of
the diagonal pipe will be discussed.
Computing Pipe Offset
Using Pythagorean
Theorem
In the first method, a formula is used for
finding the length of one side of a right-angle
triangle. Known as the Pythagorean theorem,
this formula states that the square of the
hypotenuse (side opposite the 90° angle) of
a right-angle triangle is equal to the sum of
the squares of the other two sides. Look at
Figure 4-10. Note that the vertical distance
between the parallel pipes is 10″. Since 45°
elbows are being used, the distance is also
equal to 10″. To compute the theoretical length
of the diagonal pipe, the Pythagorean theorem
Chapter 4 Mathematics for Plumbers
91
Figure 4-7. When subtracting dimensions given in fractions of an inch, you can borrow from the whole number.
1
1 2 3
31∕8″ – 15∕16″ = ______
15∕16″
31∕8″
Converting the fractions to equal fractions with
common denominators makes it possible to write
the problem as:
32∕16″ – 15∕16″ = ______
Since 5∕16″ is greater than 2∕16″ it is not possible to
subtract. By borrowing one from the whole
number 3 and changing the 1 to its fractional
equivalent in sixteenths, the problem can be
written as:
2 + (16∕16 + 2∕16)″ – 15∕16″ = ______
Simplified, the problem becomes:
218∕16″ – 15∕16″ = ______
Subtracting the fractions gives:
218∕16″ – 15∕16″ = ______″16∕13
Subtracting the whole numbers completes the
problem:
218∕16″ – 15∕16″ = 113∕16″
Figure 4-8. Method of converting inch dimensions to
feet.
52 Inches = _______ Feet
Since 12″ equals 1′, 12 is divided into 52:
4
12 52
48
4
The answer is written:
4′-4″
Pythagorean theorem: Formula that states that the
square of the hypotenuse (side opposite the 90° angle)
of a right-angle triangle is equal to the sum of the
squares of the other two sides.
Figure 4-9. Typical pipe offset problem. Find the
length of the diagonal pipe.
10″
?
45° elbows