(a) Newton’s first law

(b) Newton’s second law

(c) Newton’s third law

(d ) Continuity equation

(e) Energy equation

Hayley Bernard
2022-07-18
Answered

The Navier–Stokes equation is also known as:

(a) Newton’s first law

(b) Newton’s second law

(c) Newton’s third law

(d ) Continuity equation

(e) Energy equation

(a) Newton’s first law

(b) Newton’s second law

(c) Newton’s third law

(d ) Continuity equation

(e) Energy equation

You can still ask an expert for help

Jazlene Dickson

Answered 2022-07-19
Author has **15** answers

Navier-Stokes equation is a partial differential equation that is a fundamental equation for describing the motion of fluids. The most common form of the Navier-Stokes equation is the conservation of momentum equation.

The general form of the Navier-Stokes equation for an incompressible flow is,

$\rho \frac{D\overrightarrow{V}}{Dt}=-\overrightarrow{\u25bd}P+\rho g+\mu {\u25bd}^{2}\overrightarrow{V}$

Here, $\rho $ is the density of the fluid, g is the acceleration due to gravity, $\rho g$ represents the body force or the weight of the fluid element, $\overrightarrow{\u25bd}P$ is the pressure gradient which indicates the pressure force, $\overrightarrow{V}$ is the velocity vector field of the flow, $\mu $ is the dynamic viscosity. Here, $\mu {\u25bd}^{2}\overrightarrow{V}$ is the viscous force on the fluid, and $\frac{D\overrightarrow{V}}{Dt}$ is the total derivative of the velocity vector i.e. the acceleration vector for the flow. Hence, $\rho \frac{D\overrightarrow{V}}{Dt}$ is the net force on the fluid element.

Since the Navier-Stokes equation is similar to the conservation of momentum equation, this is also known as Newton's second law for fluids. Hence, the correct option is (b) Newton's second law.

Answer: The correct option is (b) Newton's second law.

The general form of the Navier-Stokes equation for an incompressible flow is,

$\rho \frac{D\overrightarrow{V}}{Dt}=-\overrightarrow{\u25bd}P+\rho g+\mu {\u25bd}^{2}\overrightarrow{V}$

Here, $\rho $ is the density of the fluid, g is the acceleration due to gravity, $\rho g$ represents the body force or the weight of the fluid element, $\overrightarrow{\u25bd}P$ is the pressure gradient which indicates the pressure force, $\overrightarrow{V}$ is the velocity vector field of the flow, $\mu $ is the dynamic viscosity. Here, $\mu {\u25bd}^{2}\overrightarrow{V}$ is the viscous force on the fluid, and $\frac{D\overrightarrow{V}}{Dt}$ is the total derivative of the velocity vector i.e. the acceleration vector for the flow. Hence, $\rho \frac{D\overrightarrow{V}}{Dt}$ is the net force on the fluid element.

Since the Navier-Stokes equation is similar to the conservation of momentum equation, this is also known as Newton's second law for fluids. Hence, the correct option is (b) Newton's second law.

Answer: The correct option is (b) Newton's second law.

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On earth, the acceleration due to gravity is an average of $9.80$$m/{s}^{2}$. The mass of the earth is approximately $5.972\times {10}^{24}kg$. The acceleration due to gravity on the surface of the sun is $273.7$$m/{s}^{2}$ and its mass is about $1.989\times {10}^{30}$

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I've been having some trouble in understanding acceleration due to gravity.

On earth, the acceleration due to gravity is an average of $9.80$$m/{s}^{2}$. The mass of the earth is approximately $5.972\times {10}^{24}kg$. The acceleration due to gravity on the surface of the sun is $273.7$$m/{s}^{2}$ and its mass is about $1.989\times {10}^{30}$

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Why don't the above numbers equal each other? Is it because I am doing mass divided by acceleration?

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