No the size or the volume of the barrel is not part of the column. The barrel could also be a lake, or any container. The only consideration is the height difference between the top water level and the pump. The height refers only to the water column which is a 1 square inch imaginary column to the top of the water level at the top barrel, or the top of the lake, or wherever the top end of the hose ends up.
Let's say the hose goes from the pump, up 40 feet to the top of the barrel. Then the water pressure would be 40 x 0.43 psi = 17.2 psi. Now if the hose makes a 180 degree turn at the top and goes down into the barrel 3 feet, then after you pump the initial water to the top of the hose, the 3 feet of siphon action of the water in the hose will cause the pressure to be 37 x
0.43 = 15.91 psi.If the water level in the top barrel rises above the end of the hose (which is at 37 feet) the pressure will increase according to the top of the water level. Same formula: about 0.43 psi for every foot of height.
Another way to visualize water pressure: A diver at 100 feet deep in the ocean experiences the exact same water pressure as a diver 100 feet deep in a small swimming pool (if there were such a thing.) The volume of water does not matter. The only thing that matters is the height of the imaginary 1 square inch water column.
Tom