 # Fluid Dynamics

## What is Fluid Dynamics?

Fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow in motion. There are many branches in fluid dynamics, aerodynamics and hydrodynamics few among the popularly known fluid mechanics.
It involves in a wide range of applications such as calculating force & moments, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modeling fission weapon detonation. ### What is computational fluid dynamics?

Computational fluid dynamics is a branch of fluid mechanics that uses numerical analysis and algorithms to solve and analyze problems that involve fluid flows. High-speed supercomputers are used to perform the calculation that is required to simulate the interaction of liquids and gases.

### Applications of fluid dynamics

Fluid Dynamics can be applied in the following ways:

• Fluid dynamics is used to calculate the forces acting upon the aeroplane.
• It is used to find the flow rates of material such as petroleum from pipelines.
• It can also be used in traffic engineering (traffic treated as continuous liquid flow).

### Equations in Fluid Dynamics: Bernoulli’s Equation

$\large \frac{P}{\rho }+g\;z+\frac{v^{2}}{2}=k$

$\large \frac{P}{\rho g}+z+\frac{v^{2}}{2g}=k$

$\large \frac{P}{\rho g}+\frac{v^{2}}{2g}+z=k$

Here,

$\frac{P}{\rho g}$ is the pressure head or pressure energy per unit weight fluid

$\frac{v^{2}}{2g}$ is the kinetic head or kinetic energy per unit weight

z is the potential head or potential energy per unit weight

P is the Pressure

ρ is the Density

K is the Constant

The Bernoulli equation is different for isothermal  as well as adiabatic processes.

$\large \frac{dP}{\rho } + V \; dV + g \; dZ = 0$

$\large \int \left ( \frac{dP}{\rho }+ V\; dV + g\; dZ \right )=K$

$\large \int \frac{dP}{\rho}+\frac{V^{2}}{2}+g\;Z=K$

Where,

Z is the elevation point

ρ is the density of fluid

The equation can also be written as,

$\large q + P = P_{o}$

Where,

q is the dynamic pressure

PO is the total pressure

P is the static pressure

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