Hydrodynamics, general When an object is immersed in a fluid stream, there is the phenomena of friction and turbulence. when the fluid is air, the study of these phenomena is the aerodynamics. when the fluid is water, the study of these phenomena is the Hydrodynamics . The study of hydrodynamic resistance ( Rh ) does not currently have comprehensive theory which would apply an equation to meet the different cases accurately. We therefore divided the phenomena following parameters: If the object is completely immersed (Drag force)[1] its coefficient will be studied by hydrodynamic cumulation its frictional resistance to its strength of form. The combination of these two-forces is named viscous resistance ( Rv (Newtons) ) or drag force, whose coefficient of viscous resistance ( Cv or Cd if drag has been measured in wind tunnel ) is related to Reynolds number [2]( Re ) and roughness [3] ( K ) on the length of the hull ( L ) Rv= Cv . (Re . K/L) Drag force = Cd .s.(v/2) the Cd is given for Reynolds numbersTotal coefficient of hydrodynamic resistance ( Ch = Rh / Displacement) For an object moving in deep water without surface effect is defined as: Ch =Rv= Cv.(Re.K/L) If the object moving near the surface Hydrodynamics of ships viscous resistance or drag be accompanied by a resistance due to the formation of surface waves, wave resistance ( Rw ), Whose coefficient of resistance to the wave ( Cw) is bound to Froude number [4]( Fr ) Rw= Cw.(Fr) Cw =Rw/(1/2)s.v(Water density, S surface in contact with water, V velocity.Total coefficient of hydrodynamic resistance ( Ch = Rh / Displacement) For an object moving near the surface is defined as: Ch= Cw.(Fr) + Cv.(Re.K/L) If this object is shaped to "Fly" (hydro foils) in water ,the study off drag force and lift force [5] is like Aerodynamics classic. If this object is a type hovercraft forces of hydrodynamic resistance will be significantly diminished .The force and power of the propellers used to create the lift must be evaluate( propeller calculation software ) . Different types of approaches to assess the hydrodynamic coefficient (Ch): Despite advances in computer modeling, testing models are still essential. The effects of friction measured experimentally in basin are themselves subject to problems of scaling resolved through laws of similarity . (see Froude )

scale model tests in basin Another technique for evaluating hydrodynamic behavior is to compare data measured on a series of standard forms and extrapolate the consequences of changing forms. .la srie de Taileur

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The naval hydrodynamics is studying the hydrodynamic resistance force of ships Learn more about naval hydrodynamics The hydrofoils propeller calculation software simple caculation Foils

[1] DRAG FORCEThe drag is the strength (paralell to fluid velocity) of resistance, fluid exerts on an object when the fluid or the object is moving one relative to anotherThe drag force can be calculated from: The coefficient called Cd , ( The Cd is the drag coefficient, is determined experimentally Wind tunnels) The fluid velocity, The fluid density, the surface reference depending on the subject studied: The front surface (projection perpendicular to the flow) if the object is not profiled. The maximum area projected on the ground if the object is shaped with this formula: p is the density fluid Kg/m3 The S surface Reference m v the relative velocity of the fluid * m / s

* whether the fluid, the object or both moving, we take into account the speed of one relative to another . Cd(drag cofficient) and Cl (lift coefficient) are measured experimentally are accessible to all in databases or The value of Cd an cl is always given as a function of Reynolds number which includes the kinematic viscosity of fluid. Methods of mathematical determinations or Cd Cl exist and achieve accuracies interesting . The coefficients of drag and lift are often represented by graphs called Polar The force drag expressed in Newtons is the one that opposes or slows the parachute movement. The Cd allows us to extrapolate resistance to progress to a series of geometrically similar profiles. When the drag is studied in water we talk about viscous resistance Rv and the formula for calculating the drag coefficient is related to Reynolds number Re and take the name of coefficient of viscous resistance Cv Rv = Cv. (Re. K / L) . roughness (K) In hydrodynamics Naval sometimes used a method the method of dual models to determine the viscous resistance.

[2] reynold number

The Reynolds number is a dimensionless number linking viscosity The density , and reference length . The reference length can be : The pipe diameter (ducts) To study the drag of non-geometric body shapes, this reference surface is the width of the front surface (perpendicular to flow) To study the lift and drag of body sections, this reference surface is the maximum projected area, this length is taken along a flow . To study the frictional drag of flat plates, this reference surface is the length of the wetted surface, this length is taken along a flow . Re = V L / u 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 determines the flow regime, Laminar , Transitional or Turbulent and equations to use.

[3] roughnessof ducts and pipes The roughness is a parameter essential in fluid mechanics. It gives information on the surface of the walls in contact with the fluid. The Roughness ducts is a factor in the selection of pipe materials when studying a hydraulic system or air handling Tthe unit varies depending on the application: for the study of pressure losses in pipes and flat plates we use the average depth of roughness mm ( R ) . This is the average distance projection-hollow surface defect consisting of striations, grooves, slots or tearing. Les formules d'valuation du rgime d'coulement (voir Colebrook)utilisent un rapport de la rugosit moyenne(R) sur le diamtre(D) des conduits appel rugosit relative(D et R dans la mme unit):R/D On utilise parfois un rapport de rugosit constitu de grains de sables dont le diamtre est compar l'paisseur de la couche laminaire d'coulement sur une plaque plane. Il est constat que lorsque ce rapport dpasse 0.5 la rugosit commence jouer un rle dterminant dans la rsistance de frottement sur plaque plane En hydrodynamique navale on utilise aussi une rugosit moyenne de carne, utilisant la rugosit de grains de sables quivalents(K), divis par la longueur de carne(L):K/L(K et L dans la mme unit) La rugosit des conduits d'une matire donne volue dans le temps suivant le fluide transport(agressif, oxydant, acide, charg de matire abrasives..) et les conditions d'exploitation(constamment en eau ou avec des temps d'exposition a l'air oxydant..)Une conduite peut devenir ainsi d'une rugosit couteuse en nergie d'exploitation et voir son prix rel dcupler au cours du temps. Le temps d'exploitation est donc appliquer l'volution de la rugosit lors de l'tude du prix d'achat. l'diteur de rugosit: The pressure loss formulas (see Colebrook )are using a ratio of the average roughness (R) / diameter ( D ) :relative roughness ( D and R in the same unit): R / D Sometimes used a ratio of roughness consisting of sand grains whose diameter is compared to the thickness of the laminar flow on a flat plate . It is found that when this ratio exceeds 0.5 the roughness begins to play a role in the resistance of friction flat plate In naval hydrodynamics it also uses an average hull roughness using the roughness of grains of sand equivalent ( K ) Divided by the length of keel ( L ): K / L ( K and L in the same unit) The roughness of the material given to the purchase evolves in time according to the transported fluid (aggressive, oxidizing, acidic, charged with abrasive material ..) and operating conditions (constant water or with exposure time seems oxidative ..) The roughness of pipes and ducts is costly in energy use. the real operating price can increase tenfold over time. The operating lifetime and the evolution of roughness(operating cost) during this time , must be compared with the purchase price.Mecaflux Editor roughness :

Choice of roughness following material and condition of water pipes or air flow in the software MECAFLUX Examples of roughness of pipe or water pipe networks: ( + 140 roughness data can cover all cases encountered in the study network of air or water in the software MECAFLUX) steel welded New 0.04

Welded Steel Pipes New, coated with bitumen 0.05

Welded Steel Pipes For a long time in service, bitumen partially disappeared, corroded s 0.1

Welded Steel Pipes For a long time in service, uniform corrosion 0.15

Welded Steel Pipes Without significant inequalities joints; internally coated (thick ur layer about 10 mm); ill 0.3 to 0.4

Welded Steel Pipes Mains gas, after many years of achievement ation 0.5

Welded Steel Pipes With riveting transverse single or double; coated internally Or without coating, but not corroded 0.6 to 0.7

Welded Steel Pipes Coated internally, but not free of oxidation was fouled uring service with water, but not corroded 0.95 to 1

Welded Steel Pipes Mains gas, after 20 years of service, stratified deposits s 1.1

Welded Steel Pipes With double riveted cross, not corroded, clogged during service with water 1.2 to 1.5

Welded Steel Pipes Deposits low 1.5

Table of roughness of a few led by their state or number of years of service [4] Froude number

William Froude ( 1810 - 1878 ) English Engineer and naval architectcreator of the first basin for testing models

Featured in studying hydrodynamics, Froude number ( F r ) Is a dimensionless number linking gravity (g) , velocity (v) and length (L) of vessel: Fr = V / v (g.L)

While the architects of the time agreed to say that only the real experimentation results could provide applicable, and considered experiments on the models as "nice little fun experiences," William Froude was developing laws similarity and practiced the work on friction. William Froude to put forth the basic assumption which states that resistance to the progress of vessels is the sum of: resistance mainly due to direct wave This resistance is a function of Froude number frictional resistance This resistance is a function of Reynolds number and roughness coefficient of buoyancy Although this resistance separation into distinct parts , is theoretically questionable, thus separating the two components and by assuming independent, it is possible to identify rules similarity between displacement resistance of scale models and prototypes of actual size.

similarity Predictions he made on models, verified by the towing of an offshore ship, (Greyhound) were successful in providing resistance to movement of the ship with only 10% below actual observations. The method models now entering the era of practical applications.

Sketch of W. Froude representing the train of waves due to the bow Despite advances in theory and methods of computer calculation method remains valid and is practiced today for the design of modern ships [5] lift force coefficient of lift The lift is a force perpendicular to the displacement of fluid. It is created by aspiration in a low pressure area formed on top of profile designed for this purpose. It depends on the mass of fluid displaced. The lift is calculated versus: coefficient measured in wind tunnel known as Cl or lift coefficient the projected wing area on the ground speed the fluid density . The Cl or lift coefficient, is measured in wind tunnels and there are databases available for many profiles , velocity and different incidences lift force is usually the strength necessary to fly.The ratio lift/ drag is the efficiency of the wingIn the case of Profiles measured in wind tunnel, the lift is calculated by the the projected surface ground .

Lift force in Newtons The Cz(or cl) is the coefficient of lift, it is determined experimentally in wind tunnels or basin.Note tha the wind tunnels test are available for hydrodynamics because de Cl(Cz) value is versus the Reynolds number.p is the fluid density Kg/m3 S projected wing area on the ground m v the velocity of the fluid m / s

Ship or naval hydrodynamicsThe ship Hydrodynamics is studying the hydrodynamic resistance force on ships. This resistance is composed of forces from several phenomena that are distinguished in the study but whose interactions are intimately intertwined. The results of calculations or measurements are most often given as hydrodynamic coefficients Ch, by relating the hydrodynamic resistance Rh, the weight and volume of water displaced (Ch = Rh / displacement) * the displacement of a vessel is the weight of water it displaces, so the immersed volume X density of water. .We assume that the environment is calm (no waves or current or wind) and we limit our discussion by neglecting the resistance of superstructure (about 3% of Rh). The resistance of ship is study into two parts: resistance viscous and resistance to the wave. (see Froude) viscous resistance (Rv), the viscous resistance coefficient (Cv) is related to Reynolds number (Re) and roughness (K) on the hull length (L) Rv= Cv . (Re . K/L)If the object is near the surface, the viscous resistance or drag is accompanied by a resistance due to the formation of surface waves: the wave resistance (Rw), whose coefficient of resistance to the wave (Cw) is related to Froude number (Fr) There are different types and causes of waves ( resistance of waves more..) Rw= Cw.(Fr) Cw =Rw/(1/2)s.v(density, S surface in contact with water, V velocity.

Total coefficient of hydrodynamic resistance (Ch=Rh/Displacement) for a ship hull moving near the surface is defined as: Rv= Cv . (Re . K/L) Rw= Cw.(Fr) Ch= Cw.(Fr) + Cv.(Re.K/L) Different types of approaches to assess the hydrodynamic coefficient (Ch):

Method of testing models in basin :Despite advances in computer modeling, testing models are still essential. The effects of friction measured experimentally in basin are themselves subject to problems of scaling resolved through laws of similarity . (see Froude )

Method of testing models in basin Method series: Another technique for evaluating hydrodynamic behavior is to compare data measured on a series of standard forms and extrapolate the consequences of changing forms. The specific hydrodynamic resistance (Rh / Move *) is given as a function of Froude number in series:srieTaileur

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the series of tailor, by Admiral Taylor Model Basin Experimental in Ashington

The series of tailor is still required for the most comprehensive research in the effects on power efficient. In naval hydrodynamics, to evaluate independently the viscous resistance of the surface resistance , the method of dual models is sometimes used . It involves deep immersion in tow a geometric shape composed of model hull of a ship and its symmetry to the waterline . The measured drag force is then divided by two . The experiment at sea is costly and complex , so it is achieved in wind tunnel. The profiles that drag (Cd) is already set in Mecaflux thus serve to evaluate the hydrodynamic viscous resistance.

This resistance is composed of viscous frictional resistance and resistance form. The frictional resistance can be calculated with the detailed study of flat plate in Mecaflux

Wave resistance (Rw), whose coefficient of resistance to the wave (Cw) is linked to the Froude number (Fr) Rw= Cw.(Fr) Cw =Rw/(1/2)s.v(density, S surface in contact with water, V velocity.

A body that moves on the calm surface of water produces a wave systm. This system is produced by the pressure field around the body and wave energy is given by the body . This transfer of energy from the body to the surrounding system, product our wave resistance . ( the boat made pretty waves for water skiing but it cost him in energy and that's why water skiing is expensive ...)

There are two types of wave systems produced by the hull: a system of diverging waves inclined from the axis of the boat a system of transverse waves perpendicular to the axis of the boat . This system of waves, divergent and transverse, is produced by the stern (stern) and stem (bow). The interference between these systems of waves, and generates peak along the wall of the hull. . Simplifying, one can say that resistance of the wave is generated by the difference between the pressure on the bow and stern , if the surface of bow generating low pressure decreases because of the bottoming , resistance to the wave decreases ... In this curve wave resistance based on speed and length of the hull ( Froude) shows that the wave resistance evolves by highlighting the peak or trough at the stern .

Graphs of the evolution of resistance coefficient Cw wave, depending on the ratio Speed / length In total, the coefficient of hydrodynamic resistance (Ch) is defined as :Ch= Cw.(Fr) + Cv.(Re.K/L) (Ch=Rh/Displacement)

Acceleration unit Acceleration meters per seconds per second (m / s ) For an stoped object a increase of speed (acceleration) of 1 meter seconds per second means that after 2 seconds, object will have a speed of (1m/s x 2) = 2 m / s Acceleration calculation the Newton's second law: Force = mass x acceleration A force (F) in Newtons applied to an object of mass (m) in Kg causes an acceleration "a" m/s of this object as F / m = a This equation is implemented with some representative examples of acceleration and deceleration (accident, elevator ..) tab mass and acceleration converter included in MECAFLUX . Acceleration gravity g According to the hypothesis: "Any force acting alone is proportional to acceleration" and considering that "the weight of an object (the force applied to it) is that force is determined as the gravity acceleration the mass of an object that gives the weight of the object. on Earth this acceleration is 9.81m / s at the poles and 9.78m / s at the equator (the effect of centrifugal force) on the moon this acceleration is de1.62m / s Representative examples of the effects of gravity (accident, elevator ..) tab mass and acceleration of converter included in MECAFLUX. Acceleration centripetal Consider an object whose trajectory is a curve the force as to be away from the center is the centrifugal force (memotechnique: center-flee) the force holding the object close to the center are the centripetal force (memotechnique: near center) These two forces are equal and opposite because they are action and reaction. One can not exist without the other with m = mass of the object, R = radius of the circular path of the object, a = centripetal acceleration, and V = velocity of the object was: m V / R = Strength a = V / R Acceleration fluid In a tube tapering l 'Acceleration fluid is related to a loss of pressure. It is effect Venturi or effect Bernoulli If the tube is narrowed between point A and point B is to: The equation of continuity gives us a speed increase due to shrinkage as Section: (In Section A) x (speed in A) = (in Section B) x (Speed B) = volume flow rate constant we deduce the speed at point B (Speed B) = (in Section A) / (in Section B) x (speed in A)

Bernoulli equation links the pressure to speed:. (pressure at point A) + (1/2 density) x (velocity at point A) = (pressure at point B) + (1/2 density) x (speed B) replacing (speed B) by [(in Section A) / (in Section B) x (Speed A)] we have: (pressure A) + (1/2 density) x (speed A) = (pressure B) + (1/2 ) x ([(Section A) / (Section B) x (speed A)]) if we know the pressure drop and sections of the tubes we can deduce the velocity in A: = pressure drop (pressure A) - (pressure B) = x 1/2masse volume (speed) x [(Section A ) / (Section B ) -1] By knowing the speed at A we can infer the speed at B by the continuity equation already cited. if we know the speed and sections of the tubes we can deduce the pressure drop. Applications of these equations: flow venturi water pump systems, vacuum using compressed air stream, spray ...

copyright MECAFLUX mis jour le 10 /2009

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