Viskositets indflydelse på dynamikken af en væskefyldt cylinder

Casper Weile, Christian Kjeldbjerg Kristensen, Jesper Olsen, Kim Bonde Jensen, Mikkel Sakse Bennetsen & Nanna Kerlauge

Studenteropgave: Semesterprojekt

Abstrakt

The influence of the viscosity of respectively water and glycerol is analyzed with respect to the motion of a cylinder rolling down an inclined plane wit- hout slipping. An experimental set-up is build for this purpose utilizing a Go!Motion detector and a set of photocells connected to a timer. Viscosity is defined in terms of shearing forces, laying a foundation for descri- bing this property of the liquids inside the cylinder. Reynolds numbers for the two liquids are calculated in order to account for the flow of the liquids inside the rotating cylinder. Moment of inertia and torque is calculated in terms of the set-up and used in calculations of the kinetic energies, and a model for the influence of the viscosity is presented to account for the apparent gain of mechanical energy. The Navier-Stokes equation is solved for the special case of stationary flow, to help produce this model to describe the motion of the liquid as a function of radius. We conclude that the less viscous the liquid inside the cylinder is, the less it behaves like a rigid body thus allowing the cylinder to obtain greater velocity.

UddannelserBasis - Naturvidenskabelig Bacheloruddannelse, (Bachelor uddannelse) Basis
SprogDansk
Udgivelsesdato25 jun. 2015

Emneord

  • Viscosity
  • Fluid Dynamics
  • Classical Mechanics