4. Properties of liquids

In this course of hydraulics we shall be concerned mainly with liquids, therefore we shall begin with an examination of their basic physical properties.

We shall accept the following definitions and symbols. The spe­cific weight of a liquid is its weight per unit volume:

(1.4)

where G = weight of the liquid

W = volume of the liquid

Specific weight, thus, has dimension and its value depends on the units employed. The specific

weight of water at 4°C, for ex­ample, is

The density of a liquid is its mass per unit volume:

(1.5)

where M = mass of the given volume W of the liquid.

Specific weight and density are related as follows (remembering that G = (gM):

For a nonhomogeneous liquid, formulas (1.4) and (1.5) give the average specific weight and density, respectively. To determine the absolute values of у and q at any point, the volume must be regarded as tending to zero and the limit of the corresponding ratio calculated.

The specific gravity δ of a liquid is the ratio of its specific weight to that of water at 4°C:

We shall discuss briefly the following physical properties of liquids: compressibility, thermal expansion, tensile strength, vis­cosity and evaporability. _

1. Compressibility characterises the ability of a fluid to change its volume under pressure. The relative change of volume per unit pressure is given by the coefficient of compressibility:

The minus sign is due to the fact that a positive pressure incre­ment results in a negative volume increment, i. e., an increase in pressure causes a decrease in volume.

The reciprocal of the coefficient of compressibility is called the volume, or bulk, modulus of elasticity. Expressing volume in terms of density, we obtain instead of Eq. (1.8)

The volume modulus of liquids increases somewhat with tempera» ture and pressure. Thus, for water it rises from К = 18,900 kg/cm², at t=0°C and p=5 kg/cm², to K=22,170 kg/cm², at t=20°C and p=5 kg/cm², the mean value being K=20,000 kg/cm². Con­sequently, when the pressure is increased by 1 kg/cm², the volume of water decreases by only 1/20,000 th. The volume modulus of other liquids is of the same order, and in the overwhelming majority of cases liquids are treated as practically incompressible and their specific weight у as being independent of pressure.

2. Thermal expansion is characterised by the relative change in volume when the temperature increases by 1°C:

For water p, increases with pressure and temperature from 14x10^-6, at 0°C and 1 kg/cm², to 700 x 10^-6, at 100°C and 100 kg/cm².

For oil products p_t may be from half again as much to twice that of water.

3. The tensile strength of liquids is negligible. Thus, the required stress for water rupture is 0.00036 kg/cm², and even this grows small­er with the temperature increasing. If a tensile load is of very short duration the resistance may be greater, but for practical purposes liquids are assumed to be incapable of resisting any direct tensile stress.

Liquid surfaces are subjected to surface tension, which tends to collect a liquid volume into a sphere and which accounts for a cer­tain additional pressure in liquids. This pressure, however, is mani­fest only when the working dimensions are small. In narrow tubes it causes_a liquid to rise above (or drop below) the surface level, producing the so-called capillary or meniscus effect. Capillary rise (or depression) in a glass tube of diameter d is determined by the equation

where the value of k, in sq mm, is + 30 for water, — 14 for mercury and + 12 for alcohol.

The three properties of real liquids considered above are of small importance in hydraulics as they are usually manifest to a very small degree. The reverse is true of the following property of liquids, viscosity.

4. Viscosity is the property of a fluid to resist the shearing or slid­ing of its layers. This displays itself in the appearance, under cer­tain conditions, 5f shearing stresses. Viscosity is the reciprocal of fluidity; viscous liquids, such as glycerine and lubricants, are less fluid, and vice versa.

When a viscous liquid flows along a solid boundary, there takes place a> change in the velocity across the flow due to viscosity (Fig. 2). The velocity v of the moving layers is the lower the closer they are to the solid boundary; at у = 0, v= 0. Thus, the different lay­ers are moving with respect to each other and shear, or friction, forces appear.

According to the hypothesis first formulated by Isaac Newton in 1686, and proved experimentally by Prof. N. P. Petrov in 1883, shear strain depends on the fluid and the type of flow; in laminar flow it is directly proportional to the so-called velocity gradient at right angles to the flow:

where μ = absolute, or dynamic, viscosity of the fluid;

dv = velocity increment corresponding to the increment dy (see Fig. 2).

The velocity gradient dvldy characterises the change of velocity per unit length in the у direction and, consequently, the intensity of shear in the liquid at the given point.

In the case when the shear stress is uniform over an area 5, the total shearing strain (the frictional force) acting over that area is

The dimension of absolute viscosity is obtained by solving Eq. (1.11) with respect to μ:

In the CGS system the unit of viscosity is the poise:

As 1 kg (force) = 981,000 dynes, and 1 sq m =10 sq cm,

Another characteristic of the viscosity of a fluid is its so-called kinematic viscosity:

The name "kinematic" viscosity was suggested by the absence of a force dimension (kg) in it. The unit of kinematic viscosity is the stoke:

1 stoke =1 cm2/sec.

The viscosity of liquids depends to a great extent on temperature, decreasing when the latter increases (Fig, 3). In gases the reverse is true, and viscosity increases with temperature. This is explained by the different nature of viscosity in liquids and gases.

In liquids, the molecules are much more tightly packed than in gases, and viscosity is due to molecular cohesion. The cohesive forces between molecules decrease with the temperature increasing, and viscosity decreases accordingly.

In gases, viscosity is due to the disorderly heat motion of mole­cules, the intensity of which increases with temperature. Therefore, the viscosity of gases increases with temperature.

The change in the dynamic viscosity \i of both liquids and gases caused by pressure is so small that it is usually neglected. It is tak­en into account only when extremely high pressures are involved.

Hence, the shea stress in a fluid may also be regarded as being in­dependent of absolute pressure.:

It follows from Eq. (1.11) that shear stresses can appear only in a moving fluid, i. e., that the viscosity of a fluid is manifest only when it flows. In a fluid at rest there are no shear stresses.

The above considerations lead to the conclusion that the laws of friction in fluids due to viscosity are of an entirely different nature \ than the laws of friction of solid bodies.

5. Evaporability is characteristic of all liquids. Intensity of eva­poration varies for different liquids and depends on specific conditions.

One of the indices characterising evaporation is the boiling tem­perature of a liquid at normal atmospheric pressure. The higher the boiling temperature, the less the rate of evaporation. In aircraft f hydraulic systems one frequently has to deal with cases of evapora­tion and even boiling of liquids in closed circuits at different temratures afid pressures. Accordingly, a more general characteris­tic of vaporisation is used: the saturation vapour pressure p_t as a function of temperature. The higher the saturation pressure of a liquid at a given temperature, the higher the rate of evaporation.

R

The saturation pressure of different liquids increases with temperature to a different extent.

For simple liquids the relationship p_t = f(t) has a definite ex­pression. For compound liquids, such as gasoline, the saturation pressure p_t depends not only on physico-chemical properties and temperature but also on the relative volumes of the liquid and va­pour phases. The vapour pressure increases when the portion occu­pied by the liquid phase increases. Fig. 4 shows the dependency of the vapour pressure of gasoline on the liquid-to-vapour ratio for three temperature levels.

Table 1 on the next page presents the physical properties of £ some liquids employed in aircraft and rocket systems.

Basic Physical Properties of Some Liquids Employed in Aircraft and Rocket System

Table 1.

Liquid	Spesific gravity	Kinematic viscosity ν at temperature t, centistokes						Vapour pressure Pt, mm Hg			Volume modulas K, kg/cm2
		+70C	+50C	+20C	0C	-20C	-50C	+60C	+40C	+20C
Aviation gasoline Б95/130	0.750	—	0.54	0.73	0.93	1.26	2.60	—	195	90	13.300
Kerosene T-1	0.800-0.850	1.2	1.5	2.5	4.0	8.0	25	59	27	11.5	13.000
Kerosene T-2	0.775	—	—	1.05	2.0	—	5.5	—	100	—	13.000
Lubricating oil MC-20	0.895	65	155	1.100	10.10	congeals
Lubricating oil MK-8	0.885	—	8.3	30	—	498	—
Hydraulic fluid AMГ-10	0.850	7.5	10	16	42	130	1.250				13.300
Nitric acid (98%)	1.510	0.30	0.38	0.58	0.70	0.83	1.72	355	156	60
Ethyl alcohol	0.790	—	—	1.52	—	—	6.5	352	135	44
Hydrogen peroxide (80%)	1.34	—	—	0.95	1.42	—	—	61.4	56.7	46.4
Liqiud oxygen	1.15 1.25	t	-175C	-184C	-190C	-200C	-204C	t	-140C	-160C	-190C	-200C
		Ν cst	0.125	0.170	0.193	0.257	0.297	Pt atm	21	7	0.45	0.11