CONTINUITY EQUATION
Fluid Flow
Even though a detailed analysis of fluid flow can be extremely difficult, the basic concepts
involved in fluid flow problems are fairly straightforward. These basic concepts can be applied
in solving fluid flow problems through the use of simplifying assumptions and average values,
where appropriate. Even though this type of analysis would not be sufficient in the engineering
design of systems, it is very useful in understanding the operation of systems and predicting the
approximate response of fluid systems to changes in operating parameters.
The basic principles of fluid flow include three concepts or principles; the first two of which the
student has been exposed to in previous manuals. The first is the principle of momentum
(leading to equations of fluid forces) which was covered in the manual on Classical Physics. The
second is the conservation of energy (leading to the First Law of Thermodynamics) which was
studied in thermodynamics. The third is the conservation of mass (leading to the continuity
equation) which will be explained in this module.
Properties of Fluids
A fluid is any substance which flows because its particles are not rigidly attached to one another.
This includes liquids, gases and even some materials which are normally considered solids, such
as glass. Essentially, fluids are materials which have no repeating crystalline structure.
Several properties of fluids were discussed in the Thermodynamics section of this text. These
included temperature, pressure, mass, specific volume and density. Temperature was defined as
the relative measure of how hot or cold a material is. It can be used to predict the direction that
heat will be transferred. Pressure was defined as the force per unit area. Common units for
pressure are pounds force per square inch (psi). Mass was defined as the quantity of matter
contained in a body and is to be distinguished from weight, which is measured by the pull of
gravity on a body. The specific volume of a substance is the volume per unit mass of the
substance. Typical units are ft3/lbm. Density, on the other hand, is the mass of a substance per
unit volume. Typical units are lbm/ft3. Density and specific volume are the inverse of one
another. Both density and specific volume are dependant on the temperature and somewhat on
the pressure of the fluid. As the temperature of the fluid increases, the density decreases and the
specific volume increases. Since liquids are considered incompressible, an increase in pressure
will result in no change in density or specific volume of the liquid. In actuality, liquids can be
slightly compressed at high pressures, resulting in a slight increase in density and a slight
decrease in specific volume of the liquid.
Buoyancy
Buoyancy is defined as the tendency of a body to float or rise when submerged in a fluid. We
all have had numerous opportunities of observing the buoyant effects of a liquid. When we go
swimming, our bodies are held up almost entirely by the water. Wood, ice, and cork float on
water. When we lift a rock from a stream bed, it suddenly seems heavier on emerging from the
water. Boats rely on this buoyant force to stay afloat. The amount of this buoyant effect was
first computed and stated by the Greek philosopher Archimedes. When a body is placed in a
fluid, it is buoyed up by a force equal to the weight of the water that it displaces.
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