_To find the water pressure_ on steam pipes leading from boiler to steam gauge, divide the difference in height between the highest point of pipe and the center of steam gauge by 2³/₁₀; the result will be the pressure exerted by the water in the pipe in pounds upon the gauge.
_Area of a Circle._—To find the area of a circle when the diameter is given, multiply the diameter by itself, or in other words square the diameter and multiply the result by .7854.
Ex. Diameter 5 inches, 5 × 5 = 25 × .7854 = 29.635 area.
_Circumference of a Circle._—To find the circumference of a circle when the diameter is given, multiply the diameter by 3.1416.
Ex. Diameter is 5 inches. 5 × 3.1416 = 15.708 inches circumference.
_Diameter of a Circle._—To find the diameter of a circle when the circumference is given, multiply the circumference by .31831.
Ex. Circumference 20 inches. 20 × .31831 = 6.362 diameter.
_To find the pressure_ of pounds per square inch of a column of water, multiply the height of the column in feet by .434. Approximately, we generally call every foot elevation equal to one-half pound pressure per inch, this allows for ordinary friction.
_To find the diameter_ of a pump cylinder to move a given quantity of water per minute (100 feet of piston being the standard of speed), divide the number of gallons by 4, then extract the square root and the product will be the diameter in inches.
_To find the horse-power_ necessary to elevate water to a given height, multiply the total weight of water in pounds by the height in feet and divide the product by 33000 (an allowance of 25% should be added for friction, etc.).
_The area of the steam piston_ multiplied by the steam pressure, gives the total amount of pressure that can be exerted. The area of the water piston multiplied by the pressure of water per square inch gives the resistance. A margin must be made between the power and the resistance to move the piston at the required speed—say 50%.
_To find the capacity_ of a cylinder in gallons, multiply the area in inches by the height of stroke in inches, which gives the total number of cubic inches; divide this amount by 231 (which is the cubic contents of a gallon in inches), the product is the capacity in gallons.