Constant head is important in simplifying constraint when measuring the movement of water in soil.  Several measurement techniques employ the Mariottes bottle to provide constant head. The Guelph Permeameter measures unsaturated hydraulic conductivity in the field and uses this principle to create a constant head.  Single and double ring infiltrometers can also use the Marriottes bottle.
Another application is a similar arrangement in some fuel tanks used in control line model airplanes, where it is called a "uniflow" tank, where the tank venting tubing goes to the end of the prismatic tank, close to the fuel pick-up tube that feeds the engine; thus, when fuel is consumed, the uniflow tank supplies approximately the same pressure, regardless of the quantity of fuel that remains in the tank for the rest of the flight, which keeps the same carburetor calibration and air-fuel ratio.