Is there any pressure inside the free falling fluid?

[sbu]

Imagine a high cylindrical vessel (like a vertical pipe with bottom installed) of an OD = 10 inches and fluid inside that vessel (e.g. water). If we install pressure sensor on the wall of the vessel (inside the the vessel) near the bottom, it will read hydro-static pressure of the fluid column inside the vessel.

Now imagine that we will take the bottom of the vessel away, so that fluid will fall off freely, but we will keep filling the top of the vessel with fluid so that it will be constantly kept full, even though the fluid is just leaking out at the bottom. What will the pressure sensor read?

The versions that were brought up during discussion with my colleagues are:
- sensor will read zero pressure because the fluid is in free fall and hence it is a condition similar to the absence of gravity (so falling fluid will have no weight and hence no hydro-static pressure will be exerted on the sensor)
- sensor will read hydro-static pressure minus friction pressure loss between the fluid and the walls of a vessel

It will be interesting to hear your thoughts on this :)

 

[Noctisdark]

This seems interesting and I've been thinking of it for a while, but I think I have convinced myself, the fundamental principle of hydrostatics states that the change in pressure ΔP = pgΔh, for a free falling object (assuming negligeable tidal forces), the object is "weightless", it will seem at it is in outer space [this is Einstein's equivalence principle], so g = 0 and ΔP = 0, but there must be some constant pressure out there, it might due to friction, one thing for sure that the sensor will read a constant pressure that isn't issued from the fluid itself, but transmitted by the fluid [Pascal's theorem], if the sensor read only relative pressure, the result will be zero (+ some errors due the bumbing with air outside at it's pressure get's higher), I'd like to hear some thoughts too !,

 

[Chestermiller]

There is a simple way of reasoning out the answer to this question. Here are two questions to stimulate your thinking:

1. What is the pressure in the air in the region immediately surrounding the fluid exiting from the bottom of the pipe?

2. Is pressure continuous at the interface between the fluid and the air?

Chet