a circular cross section when it is filled with waterunder pressure. The outward push of the wateris equal in every direction.So far we have explained the effects ofatmospheric pressure on liquids and how externalforces are distributed through liquids. Let us nowfocus our attention on forces generated by theweight of liquids themselves. To do this, we mustfirst discuss density, specific gravity, and Pascal’slaw.Density and Specific GravityThe density of a substance is its weight per unitvolume. The unit volume in the English systemof measurement is 1 cubic foot. In the metricsystem it is the cubic centimeter; therefore, densityis expressed in pounds per cubic foot or in gramsper cubic centimeter.To find the density of a substance, you mustknow its weight and volume. You then divide itsweight by its volume to find the weight per unitvolume. In equation form, this is written asEquation 2-4.EXAMPLE: The liquid that fills a certaincontainer weighs 1,497.6 pounds. Thecontainer is 4 feet long, 3 feet wide, and2 feet deep. Its volume is 24 cubic feet(4 ft x 3 ft x 2 ft). If 24 cubic feet of thisliquid weighs 1,497.6 pounds, then 1 cubicfoot weighsor 62.4 pounds. Therefore, the density ofthe liquid is 62.4 pounds per cubic foot.This is the density of water at 4°C and isusually used as the standard for comparingdensities of other substances. The temperature of4°C was selected because water has its maximumdensity at this temperature. In the metric system,the density of water is 1 gram per cubiccentimeter. The standard temperature of 4°C isused whenever the density of liquids and solidsis measured. Changes in temperature will notchange the weight of a substance but will changethe volume of the substance by expansion orcontraction, thus changing the weight per unitvolume.In physics, the word specific implies a ratio.Weight is the measure of the earth’s attraction fora body. The earth’s attraction for a body is calledgravity. Thus, the ratio of the weight of a unitvolume of some substance to the weight of anequal volume of a standard substance, measuredunder standard pressure and temperature con-ditions, is called specific gravity. The termsspecific weight and specific density are sometimesused to express this ratio.The following formulas are used to find thespecific gravity (sp gr) of solids and liquids, withwater used as the standard substance.or,The same formulas are used to find the specificgravity of gases by substituting air, oxygen, orhydrogen for water.If a cubic foot of a certain liquid weighs 68.64pounds, then its specific gravity is 1.1,Thus, the specific gravity of the liquid is theratio of its density to the density of water. If thespecific gravity of a liquid or solid is known, thedensity of the liquid or solid maybe obtained bymultiplying its specific gravity by the density ofwater. For example, if a certain hydraulic liquidhas a specific gravity of 0.8, 1 cubic foot of theliquid weighs 0.8 times as much as a cubic footof water—0.8 times 62.4, or 49.92 pounds. In themetric system, 1 cubic centimeter of a substancewith a specific gravity of 0.8 weighs 1 times 0.8,or 0.8 grams. (Note that in the metric system thespecific gravity of a liquid or solid has the samenumerical value as its density, because waterweighs 1 gram per cubic centimeter.)Specific gravity and density are independentof the size of the sample under consideration anddepend only on the substance of which it is made.A device called a hydrometer is used formeasuring the specific gravity of liquids.2-4
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