A parachute has a drag coefficient of CD=1.36 . Determine...

A parachute has a drag coefficient of $C_{D}=1.36 .$ Determine the open diameter of the parachute if the terminal velocity as the man parachutes downward at the air temperature of $20^{\circ} \mathrm{C}$ is $12 \mathrm{~m} / \mathrm{s}$. The total mass of the parachute and man is $100 \mathrm{~kg}$. Neglect the drag on the man.

Key Concepts

Terminal Velocity

Terminal velocity is reached when the downward gravitational force on an object equals the upward drag force from the fluid it moves through, resulting in zero net acceleration. This balance is fundamental in analyzing free-fall motion in fluids and is critical for determining conditions like safe descent speeds in parachute systems.

Drag Force

Drag force is the resistive force exerted by a fluid on an object moving through it, and it is typically modeled by the equation D = 0.5 * ? * v² * C_D * A. This concept is essential for understanding how objects slow down in a fluid and is used to relate the properties of the fluid and the object's geometry to the force experienced by the object.

Drag Coefficient

The drag coefficient is a dimensionless parameter that quantifies the drag per unit area of an object, capturing the effects of shape and flow conditions. It is crucial in aerodynamics because it allows engineers and scientists to predict the drag force on various bodies when they move through a fluid.

Air Density

Air density, which is the mass per unit volume of air, plays a significant role in determining the magnitude of the drag force. Variations in air density due to temperature, pressure, and altitude impact the performance of aerodynamic systems such as parachutes, making it an important factor in their design.

Parachute Geometry

Parachute geometry involves the relationship between the physical dimensions of a parachute, such as its open diameter and effective area, and its aerodynamic performance. By linking the parachute’s area to its diameter (using the area formula for a circle), one can calculate the necessary dimensions to achieve a specific balance of forces at terminal velocity.

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