fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) a ...

, momentum theory or disk actuator theory is a theory describing a

mathematical model A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...

of an ideal actuator disk, such as a

propeller A propeller (colloquially often called a screw if on a ship or an airscrew if on an aircraft) is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral which, when rotated, exerts linear thrust upon ...

helicopter rotor A helicopter main rotor or rotor system is the combination of several rotary wings (rotor blades) with a control system, that generates the aerodynamic lift force that supports the weight of the helicopter, and the thrust that counteracts aero ...

, by W.J.M. Rankine (1865),

Alfred George Greenhill Sir Alfred George Greenhill, FRS FRAeS (29 November 1847 in London – 10 February 1927 in London), was a British mathematician. George Greenhill was educated at Christ's Hospital School and from there he went to St John's College, Cambridge ...

(1888) and (1889). The rotor is modeled as an infinitely thin disc, inducing a constant velocity along the axis of rotation. The basic state of a helicopter is hovering. This disc creates a flow around the rotor. Under certain mathematical premises of the fluid, there can be extracted a mathematical connection between power, radius of the rotor,

torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...

and induced velocity.

Friction Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction: *Dry friction is a force that opposes the relative lateral motion of ...

is not included. For a stationary open rotor with no outer duct, such as a helicopter in hover, the power required to produce a given thrust is: :

P = \sqrt

where: * T is the

thrust Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction to be applied to that ...

\rho

is the

density of air The density of air or atmospheric density, denoted '' ρ'', is the mass per unit volume of Earth's atmosphere. Air density, like air pressure, decreases with increasing altitude. It also changes with variation in atmospheric pressure, temperature a ...

(or other medium) * A is the area of the rotor disc * P is power A device which converts the translational energy of the fluid into rotational energy of the axis or vice versa is called a Rankine disk actuator. The real life implementations of such devices include marine and aviation

windmill A windmill is a structure that converts wind power into rotational energy using vanes called sails or blades, specifically to mill grain (gristmills), but the term is also extended to windpumps, wind turbines, and other applications, in some ...

centrifugal pump Centrifugal pumps are used to transport fluids by the conversion of rotational kinetic energy to the hydrodynamic energy of the fluid flow. The rotational energy typically comes from an engine or electric motor. They are a sub-class of dynamic ...

wind turbine A wind turbine is a device that converts the kinetic energy of wind into electrical energy. Hundreds of thousands of large turbines, in installations known as wind farms, now generate over 650 gigawatts of power, with 60 GW added each year. ...

turbocharger In an internal combustion engine, a turbocharger (often called a turbo) is a forced induction device that is powered by the flow of exhaust gases. It uses this energy to compress the intake gas, forcing more air into the engine in order to pro ...

s and chemical agitators.

External links

{{dead link, date=October 2020 Momentum theory (Froude)
Fluid dynamics Propellers Momentum

See also

External links