Why is water pressure increased in a plastic bag in a bucket?

[sophiecentaur]

The vertical pressure gradient in the medium surrounding the bag, is greater in D than in B.

The medium surrounding the bag is the same for both (water columns). The pressure gradients will both be the same. It's the pressure in the bag that counts and the value will depend on the nature of the bag material but the bag will deform in shape. Assume no stretching of the membrane. It will depend on the pressure on its outside but that air pressure will be the same throughout. The bag will deform to balance the outside pressure of the water which will correspond to the normal pressure gradient. The bag will be squeezed in at the bottom of the air space (even wrinkling) and up at the top and the air pressure will be higher than ambient by an 'unspecifed' amount - somewhere corresponding to the head of water in D but the membrane will modify (support) that to some degree, everywhere.

I imagine that any resulting air pressure at the surface could be achieved just by tightening the neck of the bag and doing away with the bucket.

 

[A.T.]

The vertical pressure gradient in the medium surrounding the bag, is greater in D than in B.

The medium surrounding the bag is the same for both (water columns).

Look at the diagram again.

 

[Herman Trivilino]

It's fascinating to me that even with that 1' there's a gradient and that such a small amount could still be enough.

It's smaller than that!

We don't have 1 ft of pressure gradient. The 1 ft is the amount of pressure, but the height of the bag, just a few inches, is the amount of pressure gradient.