Maybe I can help out. Hopefully I got it right though.
I had similar results up to this equation and then we diverged:
(1.869e-4)-(7.854e-5)(0.85)sqrt(9.81(H(t)-0.1))=dV/dt
Here's what I did:
dV/dt = v_t*A_t
where v_t is the velocity of decreasing water level in the tank and A_t...