Pressure gain from water dropped from a height

[nfneilfrancis]

if an unlimited source of water was dropped twenty meters directly downwards into a meter cubed steel box through a hose, would there be the same psi in the box as there would be twenty meters under the sea?

 

[russ_watters]

Welcome to PF.

The question doesn't make all that much sense - the box is a cube, not a square, right? So what is the depth? 1m?

Anyway...the pressure at the bottom (directly under) of a column of water is equal to the pressure due to the height. This is a manifestation of pressure conversion in Bernoulli's equation: potential energy due to height converted to velocity, then velocity pressure converted to static pressure on impact.

But that means if you pour water from a garden hose into a 1 meter cubed container 20m below, the pressure will not be the same as 20m under the ocean because the garden hose is much smaller than 1 square meter in cross sectional area (and the water column, much smaller than that).

 

[nfneilfrancis]

thanks very much for the help, but it is difficult to describe my question without a diagram... if for example a water-tank containing 50 square meters of water was suspended 20m vertically over a one cubed meter box and they were connected by an airtight hose... would the box have the same psi as there would be 20m under the sea, or would the pressure depend on the water in the water-tank?

 

[russ_watters]

In your second case, the pressure would be equal to being 20m under the ocean.

 

[nfneilfrancis]

thanks very much!