If I drop a bucket of water from a height, what (if anything) happens to the air pressure on the water?

[DSeid]

My confusion about who was talking to whom! Really need to wait until I drink my coffees. @Machine_Elf’s explanation was very clear to me! I

[Machine_Elf]

@wolfpup

Again, you’re correct, but somewhat obfuscating the point I’m trying to make. A pitot tube is expressly intended to measure dynamic pressure and ignore static pressure. Hook up a pitot tube to a calibrated dial and what you have is an airspeed indicator.

A pitot tube cannot tell you what your airspeed is without measuring stagnation pressure and static pressure. Take a look at the schematic for a pitot tube from the Wikipedia link I posted earlier, and you will see a port on its front for measuring stagnation pressure (static + dynamic), and a port on its side for measuring static pressure.

The equation for airspeed:

u = 2[(p_t - p_s) / rho]^1/2

where:

u = airspeed

p_t = stagnation (total) pressure, measured at the port on the front of the pitot tube

p_s = static pressure, measured at the port on the side of the pitot tube

rho = air density (for low speeds, you can assume this is the same as ambient atmospheric density)

Bottom line, a pitot tube most definitely does not ignore static pressure, at least not one that’s going to be used for measuring airspeed.

@DSeid

One. The air on the sides would be moving quickly, yes? And therefore wouldn’t the pressure be lower there per Bernoulli’s principle?

Assuming the sides of the bucket are exactly parallel to the flow, then the air on the sides shouldn’t be moving much as the bucket slips by. To be clear, the air on the sides may be moving quickly relative to the bucket, but it isn’t moving much relative to the surrounding ambient atmosphere, and so you’d expect its pressure to be quite close to that of the surrounding ambient atmosphere. Some minor perturbations due to turbulent flow roiling off of the bottom of the bucket, but as the static ports on a pitot tube show, you should expect to measure something close to ambient (static) pressure on a flat surface moving parallel to the direction of the slipstream.

@DSeid

Two. Would the average pressure on the object equal the atmospheric pressure at that elevation? I am thinking it would but would appreciate having my understanding confirmed.

It need not be. The low pressure behind a moving object asymptotically approaches zero as the object’s speed increases, but for high enough speeds (i.e. supersonic), the stagnation pressure in front of a moving object can be multiples of ambient pressure, resulting in an average pressure over the surface of the object that’s higher than ambient atmospheric pressure. Example, if an object is moving at something close to the speed of sound, then the pressure on a flat forward-facing surface is roughly double the ambient pressure - and the pressure on a flat rear-facing surface is roughly half ambient, so the average pressure on the object might work out to 1.25 * ambient.