SlowMoCapture 2

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SIMIODE

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486

Published on February 26, 2016 11:42:28 AM ● Video Link: https://www.youtube.com/watch?v=s9CZ-yR-j2Q

Duration: 0:41

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This is a video which can be used to collect data on the height of a column of water (with blue food dye for visual ease) in a right circular cone as it falls due to a hole in the bottom of the cone. The dimensions of the inner cone of this glass funnel used in this experiment are 4.95 cm for the radius of the top cross section of the cone with a height of 9 cm (roughly from visual inspection) from the top cross section to the “point” at the base of the inverted cone. The radius of the hole at the bottom of the cone is 0.4 cm. One can stop and start the video to collect data on the height of liquid as a function of time and build a mathematical model for this process. In this model (using Torricelli’s Law as the guiding principle) one can then estimate the main parameter, namely the effective area (as a percent of the cross sectional area of the hole through which the water exits at the bottom of the cone) for fluid flow. That percent or fraction is called the discharge or contraction coefficient.

This video was taken on 4 February 2016 in Cornwall NY USA using the camera in an iPad 5 and then converted using an app called SloMo so that the user could more readily collect data.

Visit www.simiode.org to learn more about this community of teachers and students committed to modeling first teaching of differential equations in SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations.