The relationship between wind velocity and pressure is defined by the principle that pressure increases with the square of the wind velocity, as established through empirical observation and mathematical derivation. The kinetic energy (KE) of wind, expressed as KE = 1/2mv^2, illustrates that as wind speed doubles, the momentum change quadruples, leading to a fourfold increase in pressure. This relationship is further supported by the Bernoulli equation, which indicates that stagnation pressure varies with the square of wind speed, confirming that force exerted on a surface is proportional to the square of the wind velocity.
PREREQUISITESEngineers, physicists, and students studying fluid dynamics or aerodynamics will benefit from this discussion, particularly those interested in the effects of wind on structures and vehicles.
It's empirically derived, for a certain range of speeds. Conceptually in a simplified model: Twice the speed means twice the number of particles loose twice the momentum in the same time, so four times the momentum change in the same time.Mykhalo P said:I read in a book that the pressure caused by a wind blowing against a structure increases as the square of the wind velocity. I cannnot logically understand how that makes sense, and I can't think of any equation to support it. Can somebody please shed light, conceptually or mathematically, as to why this statement holds true? I appreciate any and all help.
it also has to do with KE . KE will go up with the square of speed. those molecules of air at higher speed have a squared weight attached to them.A.T. said:It's empirically derived, for a certain range of speeds. Conceptually in a simplified model: Twice the speed means twice the number of particles loose twice the momentum in the same time, so four times the momentum change in the same time.
Cube of the speed, not the speed difference. The incremental power requirement for, say, a 1 mph speed difference goes as the square of the current speed.zanick said:[...]will take the cube of the speed difference
With the cube of speed: F ~ v2 so F * v = P ~ v3zanick said:the rate of doing work of moving the air molecules out of the way, goes up with the square of speed.
sorry, meant "cube of the speed change" not difference. it changes by factor of 2, power changes by 2^3 or 8 times)jbriggs444 said:Cube of the speed, not the speed difference. The incremental power requirement for, say, a 1 mph speed difference goes as the square of the current speed.
1013 - 1003 ~= 30,000
2013 - 2003 ~= 120,000
As this article shows:Mykhalo P said:I read in a book that the pressure caused by a wind blowing against a structure increases as the square of the wind velocity. I cannnot logically understand how that makes sense, and I can't think of any equation to support it. Can somebody please shed light, conceptually or mathematically, as to why this statement holds true? I appreciate any and all help.