Computing pressure at rho points

[flq321]

I am trying to compute pressure at rho-locations ('zrho') from ROMS history files. I am attaching a short write-up showing how I am calculating it. Does that look correct? I ask because I am using the pressure values in an EKE budget analysis and the pressure-work term is looking weird. [The 'xi' variable in the write-up is 'zeta' in ROMS output.]
Thanks for any help.