principales équations et formules utilisées dans mecaflux standard. principales équations et formules utilisées dans mecaflux standard. .

main equations and formulas mecaflux standard.

EQUATIONS MECAFLUX standard

main equations and formulas mecaflux standard.

Mass flow = volume flow x density

volume flow(m3/second) = section (m²) x average speed (m/second)

For conversions or Nm3 Nm3 m3 / h m3 / h

P1V1/T1 = P2V2/T2

p1 and T1 are the normal temperatures and pressures v1 is the normal volume (relaxed), P2 and T2 being the temperature and pressure of gas V2 is the volume of the compressed gas
with:
P = Absolute pressure (gauge pressure + atmospheric pressure)
V = volume
T = temperature Kelvin

 

Average speed

In a pipe, friction along the walls slows the fluid, so that the fluid center is at its maximum speed .. The maximum speed is generally evaluated as twice the average speed

We actually find different rates for the same pipe section. To simplify the calculations we use the average speed.

average speed

The average speed is based on the ratio :

volume flow (m3 / s) / section area (m²) = average velocity (m / s)

The average speed in the case of a constant flow leads to the continuity equation

Reynolds number Re=V.L/u

Reynolds number is a dimensionless number linking viscosity, density, and a reference length, to the speed.

Re = ((average speed) x (reference length)) / (kinematic viscosity of the fluid)

or

Re = ((density) x (average speed) x (reference length)) / (dynamic viscosity of the fluid)

The Reynolds number is used to determine the flow regime, Laminar, Transitional and Turbulent and equations to use.

 

The reference length can be :

The pipe diameter (for conduits)

For the Study drag unshaped geometric body, this length reference is the width of the end face (perpendicular to flow)

For the study of the lift and drag of profiled bodies, the reference surface is the maximum projected area, this length is measured parallel to the flow.

For the study of friction drag of flat plates, the reference surface is the length of the wetted surface, this length is measured parallel to the flow.

The flow continuity equation :

 Section A x Speed ​​A = Section B x Speed ​​B = constant volume flow

 Speed ​​B = Section A / Section B x Speed ​​A

la section diminue,le fluide accelere,la pression diminue, le débit reste constant

Bernoulli Théorèm          

The sum of the pressures and mechanical energy per unit volume, is constant along the flow tube.

or: FORMULA Bernoulli:

bernoulli

Pressure Kinetics + Pressure of weight + Pressure energy  = constant

r is the density in Kg/m3.

V is fluid velocity in m/s.

g is the gravity 9.81 m/s².

Z is the vertical drop of the pipe in meters.

P is the static pressure in pascals.

Drag is the resistance force that exerts a fluid to an object while the fluid or object are moving relative to each other. This force is opposite to and parallel to the fluid path.

The drag force is calculated from:

with the formula:trainée et Cx

p is the density of the fluid KG/m3

S the reference surface en  m²

v the relative velocity of the fluid m/s

The frictional drag and boundary layer:

The Reynolds number L (or x) distance reference

where ρ = fluid density, μ = dynamic viscosity of fluid ν = kinematic viscosity of fluid, U= flow velocity characteristic, x = characteristic dimension of flow..

The transition from laminar to turbulent is usually expressed by a Reynolds number, local critical

In the case of boundary layer flow over a flat plate, it can vary between the following limits:

For incompressible flows on a flat plate, the critical number corresponding to xcr is::

So for x <xcr the flow is laminar and turbulent if x> xcr.

The boundary layer flow over a flat plate, is a laminar flow for x <xcr, and turbulent flow for x> xcr,

Mecaflux calculating the thickness limit and Cd layer using appropriate expressions for these two flow patterns:

 

With drag coefficient Cd and Fd drag in Newtons

The lift is calculated as follows: :

CL or lift coefficient is measured in the wind tunnel and there are databases available for many profiles of speed and different impacts the lift is needed to fly the wing with its load force, it is related to the drag, which will be compensated by a thrust at least equal to take off

Lift in Newtons 

p is the density KG/m3

S is the wing area (chord*Length) m²

v relative speed of fluid m/s

 

The major head loss represent energy losses due to friction of the fluid in a conduit of constant section. they are expressed in fluid heights (in meters) and in pascals.

DH is the pressure drop in fluid meter column

ll is the major head loss coefficient

major head losses formula

V  is the average flow velocity
D is the diameter of the duct
L is the length of the duct

The minor head loss  represent energy losses in the fittings or various element of the fluid network. they are expressed in fluid heights (in meters) and in pascals..

DH   is the pressure drop in fluid meter column

l is the minor head loss coefficient

minor head losse formula

V  is the average flow velocity

 

Colebrook-White formula  is operable to evaluate the coefficient of major head loss in the conduits for all values ​​of the Reynolds number

 

coefficient pertes de charges  

MECAFLUX using this equation for Re > 105

Blasius

This formula is used to evaluate the coefficient of losses in turbulent flow moderate: (2000 < Re < 105)

l is the major head loss coefficient ,

Re is the number of Reynolds

 

 

coefficient perte de charge 

Poiseuille:

This formula is used to evaluate the coefficient of losses in laminar flow: (Re < 2000)

l is the major head loss coefficient ,

coefficients perte de charge

 

charge hydrostatique derive aerodynamique hydrodynamique construire aile foil construire eolienne dimensionner conduits fumée carene dirigeable construire helice propulsion derive aerodynamique hydrodynamique frottement sur une surface de coque trainée resistance au vent trainée resistance au vent construire eolienne trainée resistance au vent conception helice bateaux derive aerodynamique hydrodynamique carene dirigeable frottement sur une surface de coque construire aile foil construire aile foil conception hydrolienne calcul voile frottement sur une surface de coque trainée resistance au vent calcul voile construire aile foil construire eolienne construire helice propulsion aeraulique aspiration air systemes ventilation aeration pertes charges vannes debit et pression conduits pompes et ventilateurs vidange reservoir construire aile foil Logiciels de la suite Mecaflux Forces sur des objets géometriques dans un courant de fluide ramification et boucles réseaux dimensionner conduits fumée calcul systemes réseaux fluides gaz liquides helice a vitesse nulle sustentation resistance aerodynamique vehicules calcul debit rivierre helice de captage turbine Kaplan hydroelectrique charge hydrostatique carene dirigeable construire helice propulsion derive aerodynamique hydrodynamique