Data Acquisition Systems In The Fluid Mechanics Laboratory: Draining Of A Tank

This paper illustrates one way in which computer data acquisition systems are being utilized in the laboratory. The examples used are from the first course in Fluid Mechanics. We chose experiments related to the draining of a tank to demonstrate the use of data acquisition systems and their impact on assessin, g the validity of the quasi-steady analysis that is commonly used in the theoretical formulation of this problem. We compare the theoretical predictions based upon the quasi-steady theory with experimental results. Introduction Learning from experimentation is an important aspect of engineering education. The time spent in the laboratory can be used to strengthen the connection between the theoretical models presented in lectures and the actual behavior of substances, machines, devices , processes and systems. This connection is accomplished through observation and experimentation with the aid of measuring and recording devices. Naturally, as technology changes, the ways quantities are measured and recorded change as well. Practice in the teaching laboratory must adjust to these changes in order to enhance learning and to keep the subject matter being taught current. We focus on the draining of a tank. We consider the efflux of a liquid of constant density rho through an orifice of cross sectional area A,, located at the bottom of a cylindrical tank ‘of cross section A,, We wish to compare the predictions of Bernoulli’s equation on how the tank drains to experimental results. First, we review the quasi-steady analysis that is commonly used in the theoretical formulation of this problem. Then, we discuss the experimental work done in our laboratory to evaluate the theory. Thirdly, we compare the theoretical predictions based upon quasi-steady theory with experimental results; Finally, we summarize our results and conclusions and assess the impact of the Data Acquisition system used in this project. Theory: Bernoulli’s Equation Applied to the draining of a Cylindrical Tank Draining of a tank appears either as an exercise or as an example somewhere in the text of most introductory textbooks of Fluid Mechanics. 4.2 These books and others are listed in the references shown below to illustrate both the popularity and the importance of this standard problem. Typically, one considers a cylindrical tank of inside cross sectional area At. The tank is oriented such that its axis of symmetry is vertical. The tank contains a fluid of constant mass density P ge 225.1 which can exit the tank through a circular orifice of cross sectional area A, that is axisymmetrically located at the bottom of the tank. If the initial height of the free surface of the fluid is Ho and the instantaneous height is h, one can write Bernoulli’s equation between two points that are assumed to belong to the same streamline. Let point 1 be on the free surface and point 2 at the center of the effluent jet. The resulting Bernoulli’s equation is unsteady and is given by I 2 av v2 p ~~+$+k+~h, =$+-+gh, 1 at (1) P P While the equation of continuity corresponding to it is