As the organism inside the respirometer consumes oxygen what happens to the water

A respirometer is a device that is used to measure the consumption rate of oxygen by any living organism.

So as the oxygen uses by the organism, the pressure of oxygen in the respirometer decreases and as the pressure decrease some amount of water enters the respirometer.  

So according to the consumption of oxygen water will move inside the respirometer due to a reduction in pressure in respirometer. So the rate of respiration can be calculated because the amount of water enters is directly proportional to the amount of oxygen consumed by an organism.