# 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 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 modelling 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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