Wind engineering basics: If P is the wind pressure (kg/cm²) and v is the wind speed (km/h), which proportional relationship correctly expresses the dependence of pressure on velocity, using a constant of proportionality K?

Introduction / Context:
Wind load calculations start from the fundamental idea that dynamic pressure exerted by wind increases with the square of the wind speed. This principle underlies building codes and structural wind design for cladding, frames, towers, and roofs.

Given Data / Assumptions:

• P is wind pressure in kg/cm² (any consistent pressure unit works).
• v is wind speed in km/h (or any consistent speed unit).
• K is a lumped constant accounting for air density and unit conversions.

Concept / Approach:

Dynamic pressure q is proportional to 0.5 * rho_air * V^2. When expressed in practical units, constants and conversion factors are absorbed into K. Thus, pressure varies as the square of speed: P ∝ v^2. This is why doubling wind speed roughly quadruples the pressure, a key design insight for extreme wind events.

Step-by-Step Solution:

Verification / Alternative check:

Checking dimensions confirms a constant K must convert velocity-squared into pressure. Empirical code equations are consistent with this quadratic dependence.

Why Other Options Are Wrong:

• P = K/v^2 or P = K v: contradicted by fluid dynamics; do not reflect energy considerations.
• v = K/P^2, P = K √v: mathematically inconsistent with dynamic pressure theory.

Common Pitfalls:

• Using linear relationships that underestimate loads at high wind speeds.
• Mixing units without adjusting K appropriately.

Final Answer:

P = K v^2.