2013 Problem 12: Helmholtz Carousel

Abstract

In our solution, we try to investigate the origin of the force that propels the Helmholtz Carousel. We build a theoretical model from the fundamental hydrodynamics. As the propelling force is in fact a nonlinear effect, we examine the nonlinear terms with care. The nonlinear terms in our equation corresponding to two origins of the force: one origins from the nonlinearity of the impedance, the other origins from nonlinear "restoring force". We will prove that the true origin of the force effect is the nonlinear impedance, which resembles the recoil force of a balloon that breathes air in and out unsymmetrically in a period of motion. Modification to linear impedance is also made which is important in giving a correct resonant frequency. Finally, we optimize the Helmholtz carousel according to the predictions of our model. Among the parameters we investigated, specific frequency, neck length, neck radius values exist to optimize the Helmholtz carousel, while larger resonator volume produces larger driving force. Predictions based on our model are supported by experimental results. 157 International Young Physicists' Tournament Downloaded from www.worldscientific.com by UNIVERSITY OF BIRMINGHAM LIBRARY -INFORMATION SERVICES on 03/20/15. For personal use only.