Problem 1
Find the weight of a brass water pipe 20 ft. long whose inside diameter is 1.5 in. and whose thickness is 1/4 in., if brass weighs 520 lb. per cu. ft.
Problem 2
The great Chinese wall is said to be 1500 miles long, 20 ft. high, 15 ft wide at the top, and 25 ft. wide at the bottom. If it were possible to build with this material a wall around the earth at the equator, of a uniform thickness of 4 ft., how high could it be made? (The equator is approximately 24,900 miles long.)
Problem 3
Two spheres of lead, of radii 2 and 3 in., respectively, are melted into a cylinder of revolution of radius 1 in. Find the altitude of the cylinder.
Problem 4
In Fingal’s Cave, on the Island of Staffa (Hebrides, Scotland), the walls are formed by basaltic prismatic columns varying in height from 18 to 36 ft. These columns, mostly hexagonal, are so perfect as to suggest the hand of man. One of the vertical columns is 29.3 ft. in height and has a base of 4.7 sq. ft. What is its volume?
Problem 5
If the gravity whose cross section is shown in the figure weighs 150 lb. per cu. ft., find the total weight of a section of a dam 50 ft. long.
Problem 8
Find the diameter of the base of the pint tin can whose height is 4 in. (231 cu. in. = 1 gal.); also, find the number of square feet of tin required to manufacture 10,000 such cans with tops. (Neglect the waste due to seams, etc.)
Problem 12
The water supply of a district consists of a lake whose surface area is 1000 acres. The number of household supplied with water is 60,000. Supposing each household to use 25 gal. per day, calculate how many days’ supply (to the nearest day below the exact number) is represented by a depth of 1 ft. of water in the lake. (1 acre equals 43,560 sq. ft.)
Problem 13
The accompanying figure represents the longitudinal view of a Venturi meter, a device designed to measure the flow of water in pipes. If the throat of the of the meter is 6 in. long and has an inside diameter of 4 in., find the volume of water in the meter which is used in 12-in. pipe line if the altitudes of the tapering parts are in the ratio 1:3 and the smaller altitude measures 12 in.
Problem 14
A concrete surge chamber with circular cross section and vertical inner walls has an inside diameter of 100 ft. The outer walls taper uniformly. The outer walls taper uniformly ¼ in. to 1 ft. of rise, and at the base the thickness is 5 ft. The height of the surge chamber is 150 ft. above the pressure tunnel, and the material used in its construction weighs 150 lb. per cu. ft. Find the total weight of the chamber when full of water.