Is the word água the same in Brazilian and European Portuguese?

Yes

The spelling, meaning, and grammatical gender of "água" are identical in both Brazilian and European Portuguese. The only difference lies in pronunciation. Brazilian Portuguese tends to have more open vowels and a more melodic, rhythmic cadence, making the "á" sound bright and clear. European Portuguese often features more closed vowels and a more "clipped" or consonant-heavy rhythm, where vowels can sometimes be more reduced or swallowed.

Brazilian Portuguese Examples:

1. Eu bebo muita água todos os dias. (I drink a lot of water every day.)
2. Você pode me dar um copo de água, por favor? (Can you give me a glass of water, please?)
3. A água da piscina está muito gelada. (The pool water is very cold.)
4. Eu preciso comprar uma garrafa de água. (I need to buy a bottle of water.)
5. A água está correndo na torneira. (The water is running in the tap.)

European Portuguese Examples:

1. Eu bebo muita água todos os dias. (I drink a lot of water every day.)
2. Podes dar-me um copo de água, por favor? (Can you give me a glass of water, please?)
3. A água da piscina está muito fria. (The pool water is very cold.)
4. Tenho de comprar uma garrafa de água. (I have to buy a bottle of water.)
5. A água está a correr na torneira. (The water is running in the tap.)