March 2013

Properties of common materials

Material Unit weight
(kN/m3)
Density
(kg/m3)
Specific
Gravity
Aluminum 26.095 2660 2.66
Brass 81.423 8300 8.3
Brick 19.62 2000 2.0
Cast iron 70.632 7200 7.2
Concrete 23.544 2400 2.4
Copper 87.407 8910 8.91
Earth (dry) 12.557 1280 1.28
Earth (wet) 17.266 1760 1.76
Glass 25.408 2590 2.59
Ice 8.829 900 0.9
Lead 111.540 11,370 11.37
Mercury 133.416 13,600 13.6
Oil 8.829 900 0.9
Water (fresh) 9.81 1000 1.0
Water (sea) 10.104 1030 1.03
Wood (hard) 7.848 800 0.8
Wood (soft) 4.709 480 0.48

001 Review Problem - Weight of a brass water pipe

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.
 

002 Review Problem - Great wall of China moved to the equator

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.)
 

003 Review Problem - Sphere melted into cylinder

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.
 

004 Review Problem - Size of a column in Fingal's Cave

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?
 

005 Review Problem - Weight of gravity dam

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.
 

005-gravity-dam.gif

 

006 Review Problem - Area illuminated by light placed in front of the globe

Problem 6
A light is placed 5 ft. from the center of the globe 3 ft. in diameter. Find the area of the illuminated portion.
 

007 Review Problem - Length of wire

Problem 7
If a piece of brass 8 by 6 by 12 in. is drawn out into a wire 1/30 in. in diameter, what will be the length of the wire?
 

008 Review Problem - Pint tin can

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.)
 

009 Review Problem - Volume of anchor ring

Problem 9
An anchor ring is formed by revolving a circle 2 in. in diameter about a line lying in the plane of the circle and at a distance of 7 in. from its center. Find the volume of the solid formed.
 

Solution 9

010 Review Problem - Volume of a stick

Problem 10
How many cubic inches of lumber does a stick contain if it is 4 in. by 4 in. at one end, 2 in. by 2 in. at the other end, and 16 ft. long?
 

011 Review Problem - Cutting the strongest square timber

Problem 11
Find the waste in cutting the strongest square timber from a circular log of uniform diameter 2 ft. and length 8 ft.
 

012 Review Problem - Lake for household water supply

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.)

013 Review Problem - Volume of water inside the Venturi meter

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.
 

013-venturi-meter.gif

 

014 Review Problem - Weight of concrete surge chamber when full of water

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.
 

015 Review Problem - Volume of spherical shell

Problem 15
A spherical shell 2 in. thick has an outer diameter of 12 in. Find the volume of the material of which it is made.