Mathematical Modeling of Water Properties

Abstract

Mathematical models describing physical water property data are presented. These models define each of the following water properties as a function of the water temperature. The water property models developed include the specific weight, density, modulus of elasticity, dynamic viscosity, kinematic viscosity, surface tension and vapor pressure. Along with each model, the actual data and calculated values are presented for comparison. The method of least squares fit, which was used to model each set of data, is reviewed. The source of FORTRAN computer program used to generate the equations can be obtained from the Lenox Institute of Water Technology.

7 Appendices

Table 10.18 Physical properties of water (SI units)^a

Table 10.19 Physical properties of water (U.S. customary units)^a

6 Glossary of Water Properties [5–9, 18]

Bulk modulus and fluid elasticity

See modulus of elasticity.

Density

The mass of a substance, such as water, per unit volume.

Dynamic viscosity

It is the property of a fluid whereby it tends to resist relative motion within itself. It is the shear stress, i.e., the tangential force on unit area, between two infinite horizontal planes at unit distance apart, one of which is fixed while the other moves with unit velocity. In other words, it is the shear stress divided by the velocity gradient, i.e., (N/m²)/(m/sec/m) = N-sec/m².

Fluid mechanics

A study of fluids including liquids and gases. It involves various properties of the fluid, such as density , specific weight , modulus of elasticity , dynamic viscosity , kinematic viscosity , surface tension , vapor pressure , velocity, pressure, volume, temperature, etc. as functions of space and time.

Kinematic viscosity

It is the dynamic viscosity of a fluid divided by its density , i.e., (N-sec/m²)/(kg/m³) = m²/sec.

Modulus of elasticity

A material property characterizing the compressibility of a fluid, such as water. The modulus of elasticity can be mathematically modeled as M.E. = − dP/(dV/V) = dD/(dD/D) where

M.E. = modulus of elasticity (psi, lb/in², Pa, kPa, or N/m²);

dP = differential change in pressure on the object (lb/in², or N/m²);

dV = differential change in volume of the object (ft³, or m³);

V = initial volume of the object (ft³, or m³);

dD = differential change in density of the object (slug/ft³, or kg/m³);

D = initial density of the object (slug/ft³, or kg/m³).

Newton (N)

It is the force that, when applied to a body of mass of 1 kg, gives it an acceleration of 1 m/s².

Specific weight

It is defined as weight per unit volume. Weight is a force (N/m³ or lb/ft³.)

Surface tension

The attraction of molecules to each other on a liquid’s surface. Thus, a barrier is created between the air and the liquid.

Vapor pressure

The water vapor pressure is the pressure at which water vapor is in thermodynamic equilibrium with its condensed state. At higher vapor pressures water would condense. The water vapor pressure the partial pressure of water vapor in any gas mixture in equilibrium with solid or liquid water. As for other substances, water vapor pressure is a function of temperature.