Relationship Between Wind and Pressure

[Mykhalo P]

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.

 

[A.T.]

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'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.

 

[zanick]

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.

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.
KE = 1/2mv^2. the rate of doing work of moving the air molecules out of the way, goes up with the square of speed. and another mind bogler, is that say you are in a car and have reached the top speed of the car at 100mph and it has 100hp. to go 200mph will take the cube of the speed difference, so it will take 8 tiimes the HP to go 200mph. why? because aero resistance goes up with the square of speed and HP is force times speed. walla... 8x the power for 2x the speed

 

[jbriggs444]

[...]will take the cube of the speed difference

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

 

[A.T.]

the rate of doing work of moving the air molecules out of the way, goes up with the square of speed.

With the cube of speed: F ~ v² so F * v = P ~ v³

 

[lychette]

pressure is due to FORCE on the wall, force is equal to rate of change of momentum, momentum = mass x velocity,
If you double the velocity you double the mass hittting the wall per second and therefore, with double the velocity the force is 4 x bigger.
force is proportional to v²

 

[zanick]

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

sorry, meant "cube of the speed change" not difference. it changes by factor of 2, power changes by 2^3 or 8 times)

 

[SteamKing]

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.

As this article shows:

https://en.wikipedia.org/wiki/Stagnation_pressure

the stagnation pressure resulting from wind blowing perpendicular to a flat surface can be derived using a simplified form of teh Bernoulli equation for incompressible flow. Bernoulli gives stagnation pressures, which vary as wind speed squared, and the resulting force is F = Pstag * A.

As others have pointed out, the kinetic energy in the wind flow has been converted to pressure energy as the wind velocity goes to zero, or stagnates, against the surface it is striking.