Pressure Gradient Force

From Wind wiki

Pressure gradient is the difference in pressure between high and low pressure areas. Wind speed is directly proportional to the pressure gradient. The pressure gradient force is a force that tries to equalize pressure differences and dictates the initial wind direction and speed. This is the force that causes high pressure to push air toward low pressure. Thus air would always flow from high to low pressure if the pressure gradient force was the only force acting on it. The pressure gradient force refers to the horizontal movement of air according to the equations:

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The term F / m is equal to the acceleration dv / dt because this is an expression of Newton's law F = ma. dp / dx (the spatial derivative of the air’s momentum) is the component of the pressure gradient along the x-axis. ρ is the mass density and (1 / ρ) shows that as the mass density increases, the acceleration due to the pressure gradient becomes smaller. It was said earlier that the wind speed is directly proportional to the the pressure gradient. If there is a large difference between two pressure centers across a given distance, air will move faster than if the pressure differences were smaller. Likewise, if the pressure difference is the same across two pairs of points but the distance between one pair of points is less than the distance between the first pair of points, we would say that the pressure gradient is greater. If there is no difference in pressure across a distance, the air will not move.