Propeller Theory

Prove that ideal propulsive efficiency of the propulsion system $\eta_i = \frac{V}{\frac{1}{2}(V_s + V)}$. The symbols have usual meaning.

An aircraft is propelled by a 4.472 m diameter propeller, which produces 35.6 kN thrust. The aircraft is flying at an altitude where the atmospheric conditions are such that the density of air is 1.03 kg/m$^3$. Using momentum theory, determine: (i) the induced velocity, and (ii) the final velocity of the flow in the far wake. Assume the efficiency of the propeller is 90%.

What is drag polar? Write down the drag polar of complete airplane and explain each term.

Using the momentum theory of propeller, show that
$$\eta = \frac{V}{V_a}$$
where the symbols have their usual meaning.

A propeller with a diameter of $3 \text{ m}$ produces a positive thrust of $4450 \text{ N}$ at $45 \text{ m/s}$ under standard sea level conditions ($\rho = 1.226 \text{ kg/m}^3$). Determine:
(i) the maximum efficiency
(ii) The pressure difference between atmospheric pressure and pressure immediately in front of the propeller

Prove that idea propulsive efficiency of the propulsion system (Fig. 5(a))
$\eta_i = \frac{V}{\frac{1}{2}(V_s + V)}$