Question

The Navier-Stokes equation is based on:

• A. Conservation of mass only
• B. Newton's second law for fluids
• C. Bernoulli's principle
• D. Pascal's law

Hint:

The Navier-Stokes equation is essential for analyzing fluid flow in various practical applications, from predicting weather patterns to designing aircraft and engines. Its complexity means that numerical methods are often used to approximate solutions for real-world problems.

Answer 1

The Correct Option is B

The Navier-Stokes equation is a fundamental equation in fluid mechanics. It describes the motion of viscous fluids. It is derived directly from Newton's second law of motion and applies it to fluid flow. In this context, Newton's second law, which states that the sum of forces acting on a body equals its mass times acceleration, is applied to a small fluid element. This law accounts for forces such as pressure, viscous forces, and external forces. The Navier-Stokes equation is a partial differential equation that describes how the velocity field of a fluid evolves over time.
This equation is crucial for understanding the behavior of real-world fluids, especially in complex situations like turbulent flow, where the fluid is not easily modeled by simpler equations. It is applicable in a wide range of engineering disciplines, including aerodynamics, hydraulics, and weather modeling.
The equation considers several variables like velocity, pressure, density, and viscosity, making it highly complex and sometimes challenging to solve directly for practical problems. Despite this, it is the cornerstone of fluid dynamics analysis and computational fluid dynamics (CFD).