As Drew pointed out HEC-RAS is the program typically used. If you have never modelled open channels, I recommend that you contract with a engineer that has experience with these.
You could do it in Excel via Direct Step method pretty easily if you knew the math. A senior level undergrad class or masters level class in open channels should cover Direct Step method, which isn't too hard if you understand what you're doing. If you want software, then yes HEC-RAS will do it (Standard Step method, not Direct Step) and produce similar results for simplified systems.
If you're outsourcing a pro familiar with open channel hydraulics to do the analysis for you, including stamping a letter or report summarizing the findings of the analysis, expect to pay a thousand to a few thousand bucks depending on how complicated the system is and how much information (e.g. hydrology) they have to dig up on their own.
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