# Properties of Fluids Density

Density is the mass per unit volume kg m~3. The density of a fluid depends on temperature and on atmospheric pressure or a static imposed head. At stan­dard conditions 20 °C and 101.325 kPa (atmospheric pressure at sea level)

Pwater = 998.2 kgm’3 Pair = !-2 kg m_J

From these differences it will be seen that water is 832 times as heavy per unit volume as air.

Water at 100 °C at atmospheric pressure has a density of 958 kg m~’. For data at other temperatures and pressures for water and other fluids, full use has to be made of various reference tables.

The relationship that exists between liquid density and temperature is ex­pressed by

Where

Ap = p0 — p &() = 0 — 00

K’here

P is the density at the temperature 6 p0 is the density at the temperature 60 A is a constant, specific to the fluid The relation of liquid density to pressure is

 (4.3) Ap __ Ap Po E ’

Where Ј is the modulus of elasticity.

The density of an ideal gas is dependent on the pressure and temperature as

P = pRT, (4.4)

Where R is the gas constant of the gas in question, J kg-1 K-1. It is calculated by dividing the general gas constant R — 8314.3 J krnoH K-1 by the molecular weight of the gas. If the composition of the ideal gas is unknown, but its pres­sure, temperature, and density are known, the value of the gas constant can be calculated from

R = . /4.5)

Po ‘ 0 (4.6) The equation can also be expressed as P _ PTo Pu Po1" 14.7)

V is the specific volume, v = 1/p,

B is enthalpy,

A and b are constants.

This equation is seldom used, because the tables of the thermodynamic prop­erties of fluids (steam tables) allow the values of the fluid/gas vapor to be ac­curately obtained.

Specific Weight

Specific weight is the weight per unit volume and is equal to p — g, where g is the acceleration due to gravity. In the case of water of density 1000 kg m the specific weight is 9.81 x 103 N nr3.

Specific Gravity

Sometimes called relative density, specific gravity is the ratio of the fluid density with respect to a reference substance at a specified temperature.

Mercury has a density of 13600 kg irr3 and is 13.6 times as heavy as wa­ter, or 11333 times as heavy as the same volume of air.

Water is taken to have a specific gravity of 1.0 at 4 °C, where it has its maximum density, with other liquids having a value either greater or less than this.

In the case of air, the specific gravity is taken as 1.0, with all other gases having specific gravity greater or less than this value.

Plastic Fluids

Various types of fluids, known as plastic fluids, may be encountered, which do not start to flow until a certain minimum shear stress is reached. The relationship between shear stress and the rate of shear strain may or may not take a linear form.

If linear, the plastic is known as a Bingham plastic, a typical case being sewage sludge.

Pseudo-plastic Fluids

With this type of fluid the viscosity decreases as the shear strain increases, typical cases being mud and liquid cement.

Dilatant Fluids

Quicksand is included in this category. The viscosity increases as the rate of shear strain increases.

 V ——- ► Surface Tension

Surface tension is the property of a fluid that produces capillary action, the rise and fall in a tube.

Water in a tube wets the glass, and the liquid rises, producing a cup. In the case of mercury, the glass is not wetted and the liquid falls, producing an inverted cup.

Viscosity

Viscosity is the shear resistance between adjacent fluid layers. Con­sider in Fig. 4.1 the shearing action between two parallel planes, each of area A, separated by a distance Y. The tangential force F for a given area

Required to slide one plate over the other at a velocity (v) parallel to each

Other is

P = fL^A. (4.8)

The proportionality factor ju is the dynamic viscosity of the fluid, its units be­ing force x time/length2 and is expressed as N s irr2 or Pa s.

Examination of the thermodynamic properties of fluid tables shows how the viscosity varies with temperature. In order to obtain a general impression of this, consider the data in the thermal properties of fluid tables and the vari­ous values at different temperatures.

Another viscosity unit is the kinematic viscosity v. This is the ratio of vis­cosity to density. Common units used for this are the stoke (1 cm2 s-1) and the centistoke (1 mm2 s-1).

Because the velocity change in the y direction is linear, Eq. (4.8) can be written as

F = /fyA. (4.91

When the shearing stress r = F/A,

T=fJL(4-10) With most fluids the shearing stress r is linearly proportional to the change of velocity; hence viscosity ju, is not a function of dv/dy. A fluid having these characteristics is called a Newtonian fluid.

 B
 B
 — = exp Mo
 C + T C + Tn
 If the viscosity is a function of dv/dy, the fluid is classed as a non-Newto­nian fluid. Fluids of this type are outside the scope of this chapter. A special case of a Newtonian fluid is that of an ideal fluid, in which the viscosity /x = 0. Ideal fluids do not exist; however, in many noncritical appli­cations, the friction can be ignored to simplify calculations. Thus viscosity is not a function of dw/dy, and it is independent of pres­sure. However, it is a function of the temperature. The viscosity of noncompressible fluids depends on the temperature as Where

 Fji is the viscosity at any temperature T, ju,0 is the viscosity at any temperature T0, B and C are constants, depending on the nature of the fluid. The viscosity of a gas depends on the temperature according to

 IЈ = ^ + Mo S + T
 X VT°, (4.12)

 Where S is a constant specific for the gas. A simplified version sometimes used is

 ( X VT°,

 _M Mo

 (4.13)

 The kinematic viscosity v is the ratio of the dynamic viscosity pi and density p: (4.14)
 V=&. P
 1 cP = 10 ^ g cm! s 1 =10 3 kg m s The non-SI unit of kinematic viscosity is the centistoke: 1 cSt = 10-2 crnV1 = 10~6 m2s_1 .
 -i The kinematic viscosity of a gas is a function of the pressure, and its dimen­sion is the square of length divided by the time, its unit being m2 s-1. In old literature the cgs system is found, in which the dynamic viscosity is measured in centipoise =0.1 poise = 0.001 dyne s cm-2: (4.15) (4.16)