I learned that when drinking wine you should drink the cup in two gulps in order not look like a glutton or arrogant person, does this apply to water also?
It applies to other drinks as well. However, it does not apply to water and the like, which you drink to quench your thirst.
קיצור שו”ע מב, ב. שלחן הטהור סי’ קע סי”א.