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Using a Homemade Low Speed Wind Tunnel to Illustrate the Continuity Equation Robert Edwards Penn State Erie, The Behrend College

Abstract:

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.

I. Introduction:

The continuity equation states that for steady state operation, the mass flow rate at any cross- section in a duct is a constant. In an introductory course in fluid mechanics it is common practice to use average flow rate values across a cross-section when doing continuity equation calculations. It is very helpful to the students, however, to recognize that the continuity equation holds for velocity profiles other than uniform velocity. This concept can be presented in a lecture, and calculations can be performed to demonstrate the theory. Equation 1 gives the general equation for the mass flow rate at any cross-section.

m = ∫ ρV dA (Equation 1) & A

Where: ρ is density V is velocity A is area.

If the density is assumed to be constant, which is the case for most problems encountered in a first course in fluid mechanics then it can be brought outside the integral giving equation 2.

m = ρ ∫ V dA (Equation 2) & A

If the function for the velocity profile V as a function of position is known, then it can be evaluated at each cross-section.

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Edwards, R. (2007, June), Using A Homemade Low Speed Wind Tunnel To Illustrate The Continuity Equation Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--2042