The fluid forces considered in the Navier-Stokes equation are

Explanation:

Navier-Stokes Equation:

• The Navier-Stokes equation is a set of partial differential equations that describe the motion of fluid substances. These equations are fundamental in fluid dynamics and are used to analyze the behavior of fluids under various forces and conditions. The forces considered in the Navier-Stokes equation govern the dynamics of fluid flow and are integral to understanding fluid behavior in engineering and natural systems.

1. Gravity Forces: Gravity is a body force acting on the fluid due to the weight of the fluid particles. It is represented as a gravitational acceleration term multiplied by the fluid density. Gravity plays a significant role in fluid flow, especially in natural systems like rivers, oceans, and the atmosphere. In the Navier-Stokes equation, the gravity force is accounted for by the body force term, which contributes to the overall momentum balance.

2. Pressure Forces: Pressure forces arise due to the variation in pressure within the fluid. These forces act perpendicular to the surface of a fluid element and are responsible for driving fluid motion in many situations, such as in pipelines, pumps, and atmospheric flows. The pressure gradient term in the Navier-Stokes equation captures the effect of pressure forces on fluid motion.

3. Viscous Forces: Viscous forces are internal frictional forces within a fluid that resist relative motion between adjacent fluid layers. These forces are a result of the fluid's viscosity and play a crucial role in determining the flow characteristics, such as laminar or turbulent flow. The viscous forces are represented by the viscous stress tensor in the Navier-Stokes equation, which accounts for the shear stresses due to velocity gradients within the fluid.

Navier-Stokes Equation:

The Navier-Stokes equation can be expressed in its general form as:

ρ (∂v/∂t + v · ∇v) = -∇p + μ∇²v + ρg

Where:

• ρ = Fluid density
• v = Velocity vector
• t = Time
• p = Pressure
• μ = Dynamic viscosity
• g = Gravitational acceleration
• ∇ = Gradient operator