I don't think that there is a 'formula'; instead,I think you need to look at solving the St Venant or related equations, as the upstream and downstream conditions will affect the water height.

Most people look to using packaged solutions - you could look through the SWMM5 code for inspiration.

thanks Dr.Dudley for your answer...

try the following:

http://arxiv.org/pdf/1402.4254.pdf

http://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/181516/1/a56b0p55.pdf

http://www.nws.noaa.gov/oh/hrl/hsmb/docs/hydraulics/papers_before_2009/hl_226.pdf

http://web.extension.illinois.edu/iwrc/pdf/149.pdf

Good luck!

thanks a lot Dear Dr.Dudley