Would measuring the acid content of the stomach be an activity completed in the study of anatomy or in the study of physiology?
Anatomy, most probably.
Anatomy is the study of the constitution and structure of the human body, while physiology is the function of each part. They interrelate strongly, and most of the time are studied together.
Measuring acid content in the stomach would most likely by an anatomical study, as it is observing structure and constitution, rather than saying how the stomach and acid work. However, the measurements could be a precursor to some physiological work, studying how structure affects function.