What is the equation for velocity of a fluid in a vertical pipe?
The answer is almost the same. In your equation for the horizontal pipe, it probably has a (P_1 – P_0) term, the difference in pressure at the ends of the pipe. To account for gravity, just add rho*g to the pressure term at the top of the pipe, so it becomes (P1 + rho*g – P0), where rho is the density of the fluid and g is the acceleration due to gravity constant. *Note that I am assuming that the velocities at both ends of the pipe remain the same since actual acceleration over distance will be slowed down by friction against the walls. Hope this helps!
