Understanding Forces on Fluid Elements in Fluid Mechanics

In the study of fluid mechanics, we analyze the various forces that act upon a small part of the fluid, often referred to as a fluid element. These forces can be broadly classified into two main categories: surface forces and body forces.

What are Body Forces?

Body forces are those forces that act on the entire volume or mass of the fluid element. Unlike surface forces, which act on the boundaries of the fluid element, body forces penetrate the volume. These forces are typically caused by external fields or agencies.

• Examples of body forces include the force of gravity, electric forces (if the fluid is charged or in an electric field), and magnetic forces (if the fluid is electrically conductive or in a magnetic field).
• These forces are proportional to the mass or volume of the fluid element.
• The question specifically mentions forces caused by agencies such as gravity and magnetic fields. These are classic examples of body forces.

What are Surface Forces?

Surface forces are those forces that act on the surface of the fluid element. They are transmitted through direct contact with surrounding fluid or boundaries.

• Examples of surface forces include pressure forces, which are always perpendicular to the surface and act inwards, and viscous forces (shear forces), which are parallel to the surface and arise due to the fluid's viscosity.
• These forces are proportional to the surface area of the fluid element.

Analyzing the Options

Let's look at the given options in the context of forces on fluid elements:

• Pressure: Pressure force is a type of surface force, acting on the boundary of the fluid element. It is caused by the pressure exerted by the surrounding fluid. Therefore, it is not a body force.
• Body: Body forces, as discussed, act on the volume of the fluid element and are caused by external agencies like gravity and magnetic fields. This aligns directly with the description in the question.
• Surface: Surface force is a general term for forces acting on the surface (like pressure and viscous forces). The question asks for the specific type of force caused by gravity and magnetic fields, which act on the volume, not just the surface.
• Velocity: Velocity is a property of the fluid motion (how fast it is moving and in what direction). It is not a force acting on the fluid element itself.

Based on the definitions and examples, the forces on fluid elements caused by agencies such as gravity and magnetic fields are known as body forces because they act throughout the volume of the fluid element.