The settling of particles in a square contained medium

Author

Richard S. Matyas, New Jersey Institute of Technology

Document Type

Thesis

Date of Award

6-30-1977

Degree Name

Master of Science in Chemical Engineering - (M.S.)

Department

Chemical Engineering and Chemistry

First Advisor

Ernest N. Bart

Second Advisor

John E. McCormick

Third Advisor

Hung T. Chen

Abstract

Stokes' Law, has been standardly utilized to calculate the terminal velocity of falling particles. However, the limitation of Stokes' Law is that it does not take into account the container walls and their resulting drag forces. Extensive work with additional drag due to cylindrical container walls has been examined by many investigators. The classical and earliest is the well know Ladenburg Correction which cannot be utilized with non-cylindrical containers. This experimental thesis examines the analog of the Ladenburg relationship for a square container. This experimental thesis was undertaken to experimentally determine the value of the constant K₁ for a square contained medium. The theoretical relationships that were previously done utilized a calculated theoretical value of the constant K₁ in the formula y=~K (1 - K₁ x).

In this series of experiments, measurements were taken on the weight, diameter and density of the spheres utilized. Temperature dependent properties of viscosity and density of the fluid medium were measured and plotted. Actual settling velocities of the spheres were measured along with fluid medium temperatures. Because of the differences in the sphere densities and temperature differences of the fluid medium each data point was considered independently. Each data point had its unique Stokes' settling velocity and this was taken into account during the calculations. The data points were plotted and computer analyzed for the constant value K₁.

This series of experiments has experimentally determined the value of the constant K₁ to be 1.8932. This differs from the theoretically calculated K₁ value of 1.903 by 0.51%.

The plotted data points indicate increased scattering as the spheres become smaller. This appears to be directly related to the convection currents in the fluid medium.

Recommended Citation

Matyas, Richard S., "The settling of particles in a square contained medium" (1977). Theses. 2106.
https://digitalcommons.njit.edu/theses/2106