Buoyancy and Drag on Immersed Bodies

Source: Alexander S Rattner and Sanjay Adhikari; Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, PA

Objects, vehicles, and organisms immersed in fluid mediums experience forces from the surrounding fluid in the form of buoyancy- a vertical upward force due to fluid weight, drag- a resistive force opposite the direction of motion, and lift- a force perpendicular to the direction of motion. Prediction and characterization of these forces is critical to engineering vehicles and understanding the motion of swimming and flying organisms.

In this experiment, the balance of buoyancy, weight, and drag forces on submerged bodies will be investigated by tracking the rise velocity of air bubbles and oil droplets in a glycerin medium. The resulting drag coefficients at terminal rise velocities will be compared with theoretical values.

1. Fabrication of gas injection test section (see schematic and photograph, Fig. 2)

Drill a hole in the bottom of a tall, flat walled plastic container. Install a through-wall bulkhead fitting through this hole. Install a reducing fitting to a ~3.2 mm tube compression connection in the bulkhead fitting outlet. This will be the bubble/droplet injection port.
Insert a short length (~1 cm) of 3.2 mm diameter soft rubber cord in the compression connection, and tighten the fitting nut. Using a sewing pin

A series of rising air bubbles and oil droplets of varying diameters are presented in Fig. 3. The small bubbles and droplets rise at lower velocities due to relatively stronger drag forces. At these low velocity and length scales, strong surface tension forces result in nearly spherical bubbles and droplets. The largest bubbles approach Re ~ 2, resulting in somewhat flattened tails in the wake region. The largest oil droplets only approach Re ~ 0.2 due to thei

This experiment demonstrated the measurement of drag coefficient for rising bubbles and droplets in a fluid medium. Drag coefficients were determined by accounting for weight, buoyancy, and drag forces. Results were compared with a theoretical model for bubble/droplet C_D at low Reynolds numbers.These results could be directly applicable to the design of industrial heat and mass exchangers, such as steam generators in power plants. In steam generators, vapor bubbles must be removed from the heated area

J.S. Hadamard, Motion of liquid drops (viscous), Comp. Rend. Acad. Sci. Paris. 154 (1911) 1735-1755.
W. Rybczynski, On the translatory motion of a fluid sphere in a viscous medium, Bull. Acad. Sci., Cracow, Ser. A. (1911) 40.

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