The air-cushion vehicle in Fig. P3.123 brings in sea-level...

The air-cushion vehicle in Fig. P3.123 brings in sea-level standard air through a fan and discharges it at high velocity through an annular skirt of $3-\mathrm{cm}$ clearance. If the vehicle weighs $50 \mathrm{kN}$, estimate (a) the required airflow rate and $(b)$ the fan power in $\mathrm{kW}$.

Key Concepts

Fan Power and Energy Considerations

Fan power is calculated based on the work done to accelerate the air and overcome losses, including converting electrical energy into kinetic energy of the airflow. This involves determining the energy input required to achieve the necessary pressure difference and flow speed, expressed by a relationship involving the mass flow rate and the velocity squared. This concept is key for designing a system that can generate sufficient lift while being energy efficient.

Air Cushion Mechanism

This concept involves the idea of supporting the weight of a vehicle by creating a cushion of pressurized air beneath it. The pressurized air, properly contained by skirts or seals, generates an upward force that counterbalances gravity. Understanding this mechanism is crucial when estimating the airflow needed to sustain the vehicle's weight.

Continuity Equation and Mass Flow Rate

The continuity equation in fluid dynamics states that the mass flow rate of a fluid must remain constant across any cross-section of a flow channel, assuming incompressible steady flow. This concept is used to relate the speed of the air, the cross-sectional area of the gap through which it flows (in this case, an annular skirt), and the density of the air, thereby allowing the determination of the required airflow rate to support the vehicle.

Bernoulli’s Principle

Bernoulli’s principle explains the relationship between the velocity of a fluid and its pressure. In the context of the air cushion system, this principle is used to understand how the fast-moving air through the clearance gap produces a dynamic pressure that contributes to supporting the vehicle’s weight. It provides insight into the trade-offs between flow speed, pressure distribution, and energy requirements.

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