Mass Conservation and Flow Rate Measurements

Source: Ricardo Mejia-Alvarez and Hussam Hikmat Jabbar, Department of Mechanical Engineering, Michigan State University, East Lansing, MI

The purpose of this experiment is to demonstrate the calibration of a flow passage as a flowmeter using a control volume (CV) formulation [1, 2]. The CV analysis focuses on the macroscopic effect of flow on engineering systems, rather than the detailed description that could be achieved with a detailed differential analysis. These two techniques should be considered complementary approaches, as the CV analysis will give the engineer an initial basis on which route to pursue when designing a flow system. Broadly speaking, a CV analysis will give the engineer an idea of the dominant mass exchange in a system, and should ideally be the initial step to take before pursuing any detailed design or analysis via differential formulation.

The main principle behind the CV formulation for mass conservation is to replace the details of a flow system by a simplified volume enclosed in what is known as the control surface (CS). This concept is imaginary and can be defined freely to cleverly simplify the analysis. For instance, the CS should 'cut' inlet and outlet ports in a direction perpendicular to the dominant velocity. Then, the analysis would consist of finding the balance between the net mass flux through the CS and the rate of change of mass inside the CV. This technique will be demonstrated with the calibration of a smooth contraction as a flowmeter.