Question

Which of these is a disadvantage of the Navier-Stokes equations?

(a) No independent-equation for pressure

(b) No independent-equation for temperature

(c) No equation to find the density

(d) No equation to find the velocity

This question was posed to me in my homework.

My enquiry is from Incompressible Flows in chapter Incompressible Flows & Compressible Flows of Computational Fluid Dynamics

Answer 1

The disadvantage of the Navier-Stokes equations in the context of fluid dynamics is:

(a) No independent-equation for pressure

The Navier-Stokes equations describe the motion of fluid flow and can be used to compute the velocity field, pressure, and other properties of the flow. However, a disadvantage is that there is no independent equation for pressure; instead, pressure is often solved as part of the pressure-velocity coupling, which involves solving the continuity equation and the momentum equations simultaneously.

Here’s a breakdown of the options:

• (a) No independent-equation for pressure: Correct. Pressure is not explicitly given as an independent equation in the Navier-Stokes framework; it is instead coupled with the velocity field and is found through a pressure-velocity coupling.
• (b) No independent-equation for temperature: The Navier-Stokes equations are typically not formulated to include temperature as a variable; however, the energy equation is often used in conjunction with them to solve for temperature in thermal flows.
• (c) No equation to find the density: The density is typically assumed constant in incompressible flows (which simplifies the equations), but in compressible flows, density is solved using the continuity equation.
• (d) No equation to find the velocity: This is incorrect because the Navier-Stokes equations themselves are used to calculate the velocity field of the fluid.

Correct Answer: (a) No independent-equation for pressure