# 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

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
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Jazlene Dickson
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,
$\rho \frac{D\stackrel{\to }{V}}{Dt}=-\stackrel{\to }{▽}P+\rho g+\mu {▽}^{2}\stackrel{\to }{V}$
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, $\stackrel{\to }{▽}P$ is the pressure gradient which indicates the pressure force, $\stackrel{\to }{V}$ is the velocity vector field of the flow, $\mu$ is the dynamic viscosity. Here, $\mu {▽}^{2}\stackrel{\to }{V}$ is the viscous force on the fluid, and $\frac{D\stackrel{\to }{V}}{Dt}$ is the total derivative of the velocity vector i.e. the acceleration vector for the flow. Hence, $\rho \frac{D\stackrel{\to }{V}}{Dt}$ 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.