This is the formula used to calculate the heating surface of a power plant boiler:

#### An HRT boiler is 5 ft in diameter and 16 ft long. It contains 60 tubes of 3 inch outside diameter and 2.732 inch inside diameter. Find the boiler-heating surface. Take the inner surface of tubes, half of the shell surface, and two-thirds of the tube plate area, less the area of the tube holes.

Circumference of shell = 5 * 3.14 = 15.700 ft

Half circumference of shell = 15,700 * ½  = 7.850 ft

Area of half of shell = 7.850 * 16 = 125.60 sq. ft

Inner circumference of fire tube = 2.732 * 3.14 = 8.578 in or         8.578 / 12 = 0.7148ft

Surface of one tube = 0.7148 * 16 = 11.437 sq. ft

Surface of 60 tubes = 60 * 11.437 = 686.2 sq. ft

Total area of one tube sheet = 0.785 * 5 * 5 = 19.625

Two-thirds area one tube sheet = 2/3 * 19.625 = 13.083 sq. ft

Area of one tube hole = 0.785 * 3 * 3 = 7.065 sq. in

Area of 60 tube holes = 60 * 7.065 = 423.9 sq. in or 423.9 / 144 = 2.94 sq. ft

Net heating surface of one tube sheet = 13.08 – 2.94 = 10.14 sq. ft

Net surface of two tube sheets = 10.14 * 2 = 20.28 sq. ft

Total net area = 125.60 + 686.2 + 20.28 = 832.08 sq. ft

832 sq. ft