Forces on Submerged Planes An submerged plane in a fluid is subject to various forces that determine its motion and equilibrium in the fluid. These forces ca...
An submerged plane in a fluid is subject to various forces that determine its motion and equilibrium in the fluid. These forces can be categorized into two types: pressure forces and hydrodynamic forces.
Pressure forces arise from the fluid's inherent tendency to maintain a constant pressure. When a plane is placed partially or fully submerged in a fluid, the fluid exerts pressure on the plane's front surface, pushing it upwards. This creates an upward force (upthrust) on the plane, similar to how a balloon rising into a wind is pushed upwards.
Hydrodynamic forces arise from the interaction between the fluid and the submerged plane. When a plane is placed in the fluid, it experiences a resistance to its motion caused by the fluid's viscosity and the pressure exerted by the surrounding fluid. This resistance creates a drag force (downforce) on the plane, pushing it downwards. Additionally, when the plane moves through the fluid, it creates a shear stress on its surface, causing a pressure difference that generates an additional lift force.
Equilibrium is the overall balance between the upward pressure forces and the downward hydrodynamic forces. When the magnitude of the pressure forces is greater than the magnitude of the hydrodynamic forces, the plane will float upright in the fluid. Conversely, if the hydrodynamic forces are greater, the plane will sink.
Examples:
A boat floating in water experiences an upward buoyant force due to the pressure exerted by the surrounding water.
A submarine cruising underwater experiences a downward hydrodynamic force due to the resistance to its motion caused by the water's viscosity.
A floating disk placed on the surface of a fluid will experience a net upward force due to the combined action of pressure and hydrodynamic forces