Gravitational head against an adverse pressure drop
Currently I have a system where I have a high pressure at the lowest point of a vertical pipe and a low pressure at the highest point of the pipe. I want the flow to travel down the pipe vertically under gravity but I am unsure of how gravitational head works in the mechanical energy balance equation. My pressure difference between the top and bottom of the pipe is 27kPa and the pipe is 12 metres in length. If my gravitational head (rho*g*h) exceeds my head due to the current pressure drop will the fluid flow down the pipe under gravity un-aided by a pump?
Thanks for your responses