Uh, sorry but again, 中 is chu
u[ちゅう]/ju
u[じゅう], not chu[ちゅ]/ju[じゅ].
e.g.
重: じゅう(not じゅ) - 重要[じゅうよう]
需: じゅ(not じゅう) - 需要[じゅよう]
じゅうよう "important" is not same to じゅよう "demand." It's important to remember the readings correctly.
In additon to Glenn-san's examples, ちゅう can be used for both meanings "in motion/ongoing" and "in/inside," whereas なか can't be used with suru-verb nouns/verb-origin nouns as the meaning "in motion/ongoing."
in motion/ongoing: 考え中 お試し中 お取り込み中 勉強中 思考中 試用中 (all 中 are read as ちゅう)...
in/inside: 大気中[たいきちゅう] 水中[すいちゅう] 車中[しゃちゅう] 町中[まちなか] 山中[やまなか/さんちゅう]...
まちなか/やまなか is a bit old expression. 町の中/山の中 is more commonly used. In conclusion, "noun + 中" is rarely read as なか.
A bit off topic. When 町中 is read as まちじゅう, the meaning is changed. Please refer to the thread below.
かと思うと | Japan Forum
(Sorry, Glenn-san. I didn't read the final post in this thread until now.

)
Let's say I was describing an economic crisis such a the great depression of 1930s. Would I use naka?
Depending on the expression.
世界恐慌中[せかいきょうこうちゅう] can mean "in the great depression," but when used with の, it would be more natural to use 間[あいだ] as "term/span" instead of 中, like 世界恐慌の間.
Another is asking someone what my drink is made up of. (in this drink is...).
このドリンクの中[なか]には何が入っていますか?
このドリンク中[ちゅう]には何が入っていますか?
Both are acceptable. The former would be more common, though.