Physics:Momentum theory
In fluid dynamics, momentum theory or disk actuator theory is a theory describing a mathematical model of an ideal actuator disk, such as a propeller or helicopter rotor, by W.J.M. Rankine (1865),[1] Alfred George Greenhill (1888) and Robert Edmund Froude (1889).[2]
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 and induced velocity. Friction 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:
- [math]\displaystyle{ P = \sqrt{\frac{T^3}{2 \rho A}} }[/math]
where:
- T is the thrust
- [math]\displaystyle{ \rho }[/math] is the density of air (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 propellers, windmills, helicopter rotors, centrifugal pumps, wind turbines, turbochargers and chemical agitators.
See also
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References
- ↑ Rankine, W.J. Macquorn (6 April 1865). "On the Mechanical Principals of the Action of Propellers". Transactions of the Royal Institution of Naval Architects 6: 13. https://hdl.handle.net/2027/mdp.39015022700325?urlappend=%3Bseq=47%3Bownerid=13510798885881399-61.
- ↑ Froude, Robert (12 April 1889). "On the Part Played in Propulsion by Differences in Fluid Pressure". Transactions of the Royal Institution of Naval Architects 30: 390. https://babel.hathitrust.org/cgi/pt?id=hvd.hnhtv1&seq=424.
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