Fluid dynamicists and other engineers who deal with fluid flow have three equations that describe all the aspects of a flow mathematically. The first and simplest of these is the continuity equation, which deals with mass flow. The equation comes from the principle of "conservation of mass." This principle states that whatever mass enters a system must either come out of the system or be stored in the system. For pipe flow, this means the mass flow entering the pipe must be equal to the mass flow leaving the pipe.
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Determine if your flow meets the necessary requirements to use the simple form of the continuity equation. First, the flow must be "steady-state," which means the flow has no points of acceleration. Another name for this is "fully developed" flow. Second, the flow should be "incompressible," which means density remains constant. This only applies to the area of the flow you are examining. If the density changes outside that region, you can still use the incompressible assumption. Finally, you must be able to assume that gravity has little or no effect on the flow. In other words, the flow is independent of body forces, such as weight. This holds true for most flows, but if your fluid is very dense, very slow or highly viscous, body forces may enter into the equations.
Determine the cross-sectional area where the flow enters the area you are examining. For a pipe, calculate the area based on the inner diameter (ID).
Example: ID = 2 cm A = (pi)r^2 r = ID/2 r = 1 A = 3.14159 * (1)^2 = 3.14159 cm^2
Determine the density of the fluid you are examining. Most of the time, you will be able to look this value up in one of many engineering references. If not, you will need to determine it through direct measurement. You may also calculate it through a number of engineering equations, such as the perfect gas equation or Bernoulli's equation, depending on the fluid you are using and the measurements you have available. Convert either the density or the area so that the units are compatible.
Example: Water = 0.998 g/cm^3 Area = 3.14159 in^2 = 20.268 cm^2
Determine the velocity of the flow. This must be done by direct measurement or through calculation. Just as for density, a number of equations are available depending on the fluid you are using and the values you already have available. Convert the value to be compatible with the rest of the values, if necessary. If the flow is viscous, calculate the average velocity. For a round pipe, for example, average velocity equals one-half maximum velocity.
Example: Velocity = 10 m/s = 1000 cm/s
Multiply the density, the area and the velocity to determine the mass flow rate.
Example: (rho)AV = 0.998 * 20.268 * 1000 = 20227.464 g/s = 20.227 kg/s
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