Final answer:
Wind pressure on vertical surfaces is directly proportional to the square of wind velocity, with the relationship given by P psf = .00256 v² mph. This dynamic pressure can be used to approximate forces on structures like roofs using Bernoulli's principle, but turbulence can affect accuracy. The drag force on an object in air also follows a similar quadratic relationship with speed.
Step-by-step explanation:
The direct wind pressure on a vertical surface, often referred to as dynamic pressure, is directly proportional to the square of the wind velocity. The pressure (P psf) related to the basic wind velocity (v) can be expressed by the equation P psf = .00256 v² mph. This relationship means that as wind velocity doubles, the wind pressure increases by a factor of four (since 2² = 4), illustrating a quadratic relationship between wind velocity and pressure.
When determining the force due to the Bernoulli effect on surfaces such as sails or roof areas in high wind conditions, the quantification of the force can be quite complicated due to variables such as air density, atmospheric pressure, and turbulence. For example, the Bernoulli principle, assuming laminar flow, can be used to approximate the force on a roof having an area, but due to turbulence in real-world conditions, the results are only an approximation. The drag force (FD) experienced by an object moving through air is also proportional to the square of the object's speed.