Hydrodynamics : studies the dynamics of incompressible fluids.
Summary
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- 1 Definition
- 2 Features
- 3 Mathematical Expressions
- 4 Source
Definition
Etymologically, hydrodynamics is the dynamics of water , since the Greek prefix “hydro-” means “water”. Even so, it also includes the study of the dynamics of other liquids . For this, the speed, pressure, flow and flow of the fluid are considered, among other things.
characteristics
For the study of hydrodynamics, normally three important approaches are considered:
- That the fluid is an incompressible liquid, that is, that its density does not vary with the change in pressure, unlike what happens with gases .
- The loss of energy due to the viscosity is considered negligible , since it is assumed that a liquid is optimal to flow and this loss is much less compared to the inertia of its movement.
- The flux of the liquids is assumed to be in a stable or stationary regime, that is, the velocity of the liquid at a point is independent of time.
Hydrodynamics has numerous industrial applications, such as canal design, port and dam construction, ship manufacturing, turbines, etc.
Mathematical expressions
The expense or flow is one of the main variables in the study of hydrodynamics. It is defined as the volume of liquid ΔV flowing per unit time Δt. Its units in the International System are m3 / s and its mathematical expression:
G = \ frac {\ Delta {V}} {\ Delta {t}}
This formula allows us to know the amount of liquid that passes through a conduit in a certain time interval or to determine the time it will take for a certain amount of liquid to pass.
The principle of Bernoulli is a consequence of the conservation of energy in moving liquids. It establishes that in an incompressible and non-viscous liquid, the sum of the hydrostatic pressure , the kinetic energy per unit volume and the gravitational potential energy per unit volume, is constant throughout the entire circuit. That is, this magnitude takes the same value at any pair of points in the circuit. Its mathematical expression is:
P_1 + \ rho g h_1 + \ frac {1} {2} \ rho v_1 ^ 2 = P_2 + \ rho g h_2 + \ frac {1} {2} \ rho v_2 ^ 2
where P is the hydrostatic pressure , ρ the density , g the acceleration due to gravity , h the height of the point and v the speed of the fluid at that point. Subscripts 1 and 2 refer to the two points of the circuit.
The other equation that non-compressible fluids meet is the continuity equation, which establishes that the flow is constant throughout the entire hydraulic circuit :
G = A1v1 = A2v2
where A is the area of the section of the duct through which the fluid circulates and v its average speed.
In the case of compressible fluids, where the Bernouilli equation is not valid, it is necessary to use the most complete formulation of Navier and Stokes . These equations are the mathematical expression of conservation of mass and momentum. For compressible but non-viscous fluids, also called colloidal fluids, they come down to the Euler equations.
Daniel Bernoulli was a mathematician who studied dynamics.
Hydrodynamics or moving fluids have several characteristics that can be described by very simple mathematical equations.
Torricelli’s Law : if a fluid is found in a container that is not covered and a hole is opened in the container, the speed with which that fluid will fall will be:
v = \ sqrt {2 g H}
The other mathematical equation that describes fluids in motion is the Reynolds number :
N = dVD / n
where d is the density v the speed D is the diameter of the cylinder and n is the dynamic viscosity.
