The experimental ground-effect machine has a total weight of...

The experimental ground-effect machine has a total weight of 4200 lb. It hovers 1 or $2 \mathrm{ft}$ off the ground by pumping air at atmospheric pressure through the circular intake duct at $B$ and discharging it horizontally under the periphery of the skirt $C$. For an intake velocity $v$ of $150 \mathrm{ft} / \mathrm{sec},$ calculate the aver age air pressure $p$ under the 18 -ft-diameter machine at ground level. The specific weight of the air is $0.076 \mathrm{lb} / \mathrm{ft}^{3}$.

Key Concepts

Area and Distributed Load

The integration of pressure over a specific area produces a total force, which must match the weight of the object in equilibrium. Dividing the total weight by the area over which the pressure acts provides the average pressure required to sustain hover, highlighting the interplay between fluid pressure and mechanical stability.

Bernoulli's Principle

Bernoulli's principle states that for an incompressible, frictionless fluid, an increase in the fluid's velocity occurs simultaneously with a drop in pressure. This relationship is used to relate the speed of the air being pumped to the lower pressure zones created, which in turn contribute to the lift of a hovering machine.

Air Pressure and Force

In fluid mechanics, pressure represents the force exerted per unit area by a fluid. When a machine hovers, the air pressure acting underneath it must counterbalance its weight. Understanding how distributed pressure results in an upward force is key to analyzing lift and hovering phenomena.

Ground Effect

The ground effect refers to the increased lift or reduced aerodynamic drag experienced by a body as it moves close to a fixed surface. In hovercraft or similar devices, the interaction of the air flow with the ground creates higher pressure zones that aid in supporting the weight of the machine.

Dynamic Pressure

Dynamic pressure is the pressure associated with the motion of a fluid and is given by the expression ½?v², where ? is the fluid density and v is its velocity. This concept is essential in understanding how the velocity of air through an intake or duct modifies the pressure distribution and influences lift.

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