A common trend I see is for the global search bar to be at the top right corner, take Stack Exchange for example.
Though normally I would say group common functionality, since both the local and global search do the same thing essentially but with differing scopes, grouping them can cause some confusion. So my suggestion would be to have the global search bar at the top right, and the local placed centered or to the left of the page. This distancing of space helps separate them, and help establish their presumed functionality.
Labeling is your best friend here. The placeholder text can help the user better identify the scope in which the search is being applied. So instead of just saying "Search...", say "Find Customer", or "Search Q&A".