Theorie de Froude relative aux on propeller propulsion or traction

- To understand Theory Froude, the notion of momentum must be mastered, because it is on the balance of momentum that the Froude theory is based ..

- are not taken into account the rotation of the flow.
- we consider a fluid stream out of which the flow is not disturbed
- The pressure at infinity upstream and downstream is equal to the static pressure of undisturbed flow
- The air disturbance are sufficiently small that it is assumed that the fluid density is constant.

fig. 1

lthe continuity equation allows us to calculate the volume added to the control zone per second (volume flow Q in m3/sec),: Q is the volumetric flow discharged from the volume control. From the theorem of momentum, the thrust, T of the propeller is obtained, that is to say the variation of the amount of movement between the sections 2 and O, whose projection on the horizontal axis indicates thrust : The derivative of the momentum versus time : Momentum out "M_2" volume control in Section 2 = Total amount of movement "M_1" within the volume control = Momentum in the volume entry - momentum laterally inserted= Therefore, the axial force of the fluid on the rotor becomes(T=M_2-M_1): One can also express the axial force of the fluid on the rotor T, according the result of the static pressure which is exerted on the surface of dis: where A is the surface of the disc swept by the propeller and Dp, the pressure difference across the disc. Using Bernoulli's equation, we obtain pressure difference O to 1 upstream, and: pressure difference 2 to 1 downstream.The static pressure difference between the upstream and downstream sides of the disk of the propeller as the expression: From the continuity equation:

**can be derived: and consider the speed of the flow through the disk as an arithmetic average of the velocities upstream and downstream of the propeller:**

*,*Is called induced velocity w, increasing speed at the propeller disk: where "a" represents the axial interference factor.

Now, if we consider the expression:,the axial force exerted on the disc of the impeller is:

From this expression we can identify push the notion of mass flow: The mass of fluid passing through the propeller per second :

- (kg/sec) m = r.p.r².V2

- It is important to note that create thrust, therefore, is to increased the speed of a mass flow of fuide. This highlights the levers available to us to generate the propulsive force: The choice to act on the mass or speed variation is crucial for the propulsive efficiency

**Bibliographic references propeller**