Using A Homemade Low Speed Wind Tunnel To Illustrate The Continuity Equation

The continuity equation is one of the most basic formulas used in fluid dynamics. The conservation of mass principle is crucial to most fluid flow problems, and it is that principle that is represented by the continuity equation. In a first course in fluid mechanics the continuity equation is usually applied by using average values for the velocity across any cross-section in the duct. However, it is important for the students to recognize that the equation applies for non-uniform velocity profiles also. This paper describes a lab experiment that can be used to illustrate the application of the continuity equation to a duct with a non-uniform velocity profile. The students take a grid of velocity data across two different cross-sections within the duct, calculate the total mass flow rate at each cross-section, and compare the two results.