Fluid Dynamics
From MyMCAT
Introduction
In the previous sections, Fluids and Solids Introduction and Hydrostatic Pressure, we discussed the concepts of pressure and Pascal's law, however little in the area of flowing liquids was examined. Here we look at the motion of fluids.
Continuity Equation
The first concept we most keep in mind when dealing with moving fluids is the idea that the fluid is incompressible. So if we consider a liquid flowing through a pipe, at any given period of time, the amount of fluid going into the pipe must equal the amount coming out of the pipe. If this were not the case, then the liquid would be some how getting compressed or less dense. Thus, the incoming volume must equal the outgoing volume for incompressible fluids, or mathematically,
After the simplification it is clear we can also say that the cross-sectional area of a pipe and its velocity are proportional for the incoming and outgoing fluid. The larger the cross sectional area of the pipe, the slower the fluid will be flowing at that point, and vice versa.
Bernoulli's Principle
Bernoulli's principle states that an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid's potential energy.
Bernoulli's principle is equivalent to the principle of conservation of energy. This states that in a steady flow the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. This requires that the sum of kinetic energy and potential energy remain constant. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest. The following formula relates these principles,
where the first term, 
, is the dynamic pressure, 
is the static pressure, and 
is the constant pressure of the system (usually atmospheric pressure).
