浮力和拖曳在浸没的身体

Archimedes' Principle states that the buoyant force on a fully immersed object equals the weight of the fluid displaced by that object. Mathematically, buoyant force equals fluid density times object volume times gravitational acceleration. This principle determines whether an object floats, sinks, or remains neutrally buoyant depending on whether its average density is less than, greater than, or equal to the surrounding fluid density.

The Reynolds Number captures the relative magnitude of inertial and viscous fluid forces acting on an object. The drag coefficient depends on Reynolds Number, which is calculated using relative velocity, characteristic length scale, fluid density, and viscosity. For low Reynolds Number conditions, the drag coefficient follows the relationship of 16 divided by the Reynolds Number, allowing predictable drag behavior in viscous-dominated flows.

Terminal velocity is the constant speed at which an object moves through a fluid when all forces reach equilibrium. At this point, the buoyant force and drag force together balance the gravitational force, resulting in zero net acceleration. Terminal velocity depends on object density, size, shape, and fluid properties. Measuring terminal velocity allows calculation of the drag coefficient for the object.

Drag force is modeled as one-half the product of fluid density, projected body area, drag coefficient, and relative velocity squared. The drag coefficient captures the effect of object shape and depends on Reynolds Number, requiring empirical or numerical determination since no simple equation exists. This formula enables prediction of resistive forces opposing motion in applications ranging from vehicle design to organism locomotion.

Smaller bubbles and droplets experience relatively stronger drag forces compared to their buoyant forces due to their reduced size and lower velocity. Surface tension effects keep both bubbles and droplets nearly spherical at low Reynolds Numbers. The drag force increases with velocity squared, causing smaller particles to reach lower terminal velocities where drag balances buoyancy and weight more quickly than larger particles.

Terminal velocity is measured by tracking an object's vertical position and time as it rises through a fluid using video analysis. The scaling factor from a calibration ruler converts pixel measurements to meters. Terminal velocity equals the change in vertical distance divided by the time interval. Using measured terminal velocity, object diameter, fluid properties, and the drag force equation, the drag coefficient can be calculated and compared to theoretical predictions.

In boiling water reactors, buoyancy and drag determine whether gas bubbles are removed quickly enough from fuel rod surfaces; insufficient removal risks surface drying and overheating. In vehicles, drag forces at highway speeds require significant power to overcome aerodynamic resistance. Careful design of vehicle shape and airflow pathways reduces drag, improving fuel efficiency. Understanding these forces is critical for safe reactor operation and efficient vehicle design.