2.1-Properties Involving Mass a...pdf

Properties Involving Mass and Weight

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2.1 Properties Involving Mass and Weight

Mass and weight properties are needed for most problems in fluid mechanics, including the flow of ground

water in aquifers and the pressure acting on a scuba diver or an underwater structure.

Mass Density ρ

Mass density is defined as the ratio of mass to volume at a point, given by

(2.1)

Review the continuum assumption developed in Section 1.2 for the meaning of approaching zero. Mass

density has units of kilograms per cubic meter (kg/m 3 ) or poundsmass per cubic foot (lbm/ft 3 ). The mass

density of water at 4°C is 1000 kg/m 3 (62.4 lbm/ft 3 ), and it decreases slightly with increasing temperature, as

shown in Table A.5. The mass density of air at 20°C and standard atmospheric pressure is 1.2 kg/m 3

(0.075 lbm/ft 3 ), and it changes significantly with temperature and pressure. Mass density, often simply called

density, is represented by the Greek symbol ρ (rho). The densities of common fluids are given in Tables A.2 to

A.5.

Specific Weight, γ

The gravitational force per unit volume of fluid, or simply the weight per unit volume, is defined as specific

weight . It is given the Greek symbol γ (gamma). Water at 20°C has a specific weight of 9790 N/m 3 (or

62.4 lbf/ft 3 at 50°F). In contrast, the specific weight of air at 20°C and standard atmospheric pressure is

11.8 N/m 3 . Specific weight and density are related by

(2.2)

Specific weights of common liquids are given in Table A.4.

Variation in Liquid Density

In practice, engineers need to decide whether or not to model a fluid as constant density or variable density.

Usually, a liquid such as water requires a large change in pressure in order to change the density. Thus, for most

applications, liquids can be considered incompressible and can be assumed to have constant density. An

exception to this occurs when different solutions, such as saline and fresh water, are mixed. A mixture of salt in

water changes the density of the water without changing its volume. Therefore in some flows, such as in

estuaries, density variations may occur within the flow field even though the fluid is essentially incompressible.

A fluid wherein density varies spatially is described as nonhomogeneous. This text emphasizes the flow of

homogeneous fluids, so the term incompressible, used throughout the text, implies constant density.

Specific Gravity, S

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Properties Involving Mass and Weight

http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...

The ratio of the specific weight of a given fluid to the specific weight of water at the standard reference

temperature 4°C is defined as specific gravity, S:

(2.3)

The specific weight of water at atmospheric pressure is 9790 N/m 3 . The specific gravity of mercury at 20°C is

Because specific gravity is a ratio of specific weights, it is dimensionless and therefore independent of the system

of units used.

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