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16.2: Density

Last updated

Aug 8, 2022
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- 16.1: Introduction to Hydrostatics
- 16.3: Pressure

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There is little to be said about density other than to define it as mass per unit volume. However, this expression does not literally mean the mass of a cubic metre, for after all a cubic metre is a large volume, and the density may well vary from point to point throughout the volume. Density is an intensive quantity in the thermodynamical sense, and is defined at every point. A more exact definition of density, for which I shall usually use the symbol $\rho$ , is

$\rho=\lim_{\delta V\rightarrow 0}\frac{\delta m}{\delta V}. \label{16.2.1}$

The awful term “specific gravity” was formerly used, and is still regrettably often heard, as either a synonym for density, or the dimensionless ratio of the density of a substance to the density of water. It should be avoided. The only concession I shall make is that I shall use the symbol s to mean the ratio of the density of a body to the density of a fluid in which it may be immersed or on which it may be floating,

The density of water varies with temperature, but at 4 ºC is 1 g cm^-3 or 1000 kg m^-3, or 10 lb gal^-1. The original gallon was the volume of 10 pounds (lb) of water. These are Imperial (UK) gallons, and avoirdupois pounds - not the gallons (wet or dry) used in the U.S., and not the pounds (troy) used in the jewellery trade.

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