## Related questions with answers

Two small liquid-propellant rocket motors are mounted at the tips of a helicopter rotor to augment power under emergency conditions. The diameter of the helicopter rotor is $7 \mathrm{~m}$, and it rotates at $1 \mathrm{rev} / \mathrm{s}$. The air enters at the tip speed of the rotor, and exhaust gases exit at $500 \mathrm{~m} / \mathrm{s}$ with respect to the rocket motor. The intake area of each motor is $20 \mathrm{~cm}^2$, and the air density is $1.2 \mathrm{~kg} / \mathrm{m}^3$. Estimate the power provided by the rocket motors. Ignore the mass rate of flow of fuel in this calculation.

Solutions

Verified**Given**:

Fluid Density, $\rho = 1.2 ~ \mathrm{\frac{kg}{m^3}}$

Diameter of Helicopter Rotor, $D = 7 ~ \mathrm{m}$

Angular Velocity of Helicopter Rotor, $\omega = 1 ~ \mathrm{\frac{rev}{s}}$

Exit Velocity of Air from Rotor, $V_o = 500 ~ \mathrm{\frac{m}{s}}$

Intake Area of Rotor, $A = 20 ~ \mathrm{cm^2}$

**Required**:

Power to Provided by the Helicopter Rotor, $P$

**Given:**

- Diameter of the rotor 1: $D=7\hspace{0.1cm} \text{m}$
- Intake area: $A=0.002\hspace{0.1cm} \text{m}^2$
- Rotor speed: $n=1\hspace{0.1cm} \frac{\text{rev}}{\text{s}}$
- Exaust gasses velocity: $V_{2}=500\hspace{0.1cm} \frac{\text{m}}{\text{s}}$
- The density of the fluid: $\rho=1.2\hspace{0.1cm} \frac{\text{kg}}{\text{m}^3}$

**Find:**
The power of the motors $P$.

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