The circular hovercraft draws in air through the fan A and discharges it through the bottom B ne

step 1 Pressure in the cushion accelerates air out through the rim gap. Use Bernoulli and continuity. G

The circular hovercraft draws in air through the fan A and...

The circular hovercraft draws in air through the $\operatorname{fan} A$ and discharges it through the bottom $B$ near the ground, where it produces a pressure of $1.50 \mathrm{kPa}$ on the ground. Determine the average velocity of the air entering at $A$ that is needed to lift the hovercraft $100 \mathrm{~mm}$ off the ground. The open area at $A$ is $0.75 \mathrm{~m}^{2}$. Neglect friction losses. Take $\rho_{a}=1.22 \mathrm{~kg} / \mathrm{m}^{3}$.

Key Concepts

Bernoulli's Principle

This principle relates the pressure, velocity, and height in a moving, incompressible, frictionless fluid. It shows that an increase in a fluid's velocity occurs simultaneously with a decrease in static pressure or potential energy, which is key to understanding how dynamic pressure is converted into lift or support forces in many applications.

Continuity Equation

The continuity equation is based on the conservation of mass in fluid dynamics. It states that the mass flow rate must remain constant from one cross-section of a flow to another, meaning that the product of the cross-sectional area and the velocity of the fluid is constant. This concept is critical when linking the flow conditions at different parts of a system.

Dynamic Pressure

Dynamic pressure represents the kinetic energy per unit volume of a flowing fluid and is given by the expression (1/2)?v². It is used to quantify how the speed of a fluid contributes to pressure differences that can generate forces, such as lift or thrust, in various engineering systems.

Pressure and Force Balance

This concept involves equating the pressure-induced force on a surface to the necessary force to achieve a desired mechanical effect, such as lift. In fluid systems, pressure differences over areas create net forces which can be analyzed to ensure equilibrium or motion, making force balance a key tool in design and analysis.

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