Gravitational head against an adverse pressure drop

[Fishinev]

Hey,

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

 

[Navin A S]

. Yes, the fluid will flow down the pipe under gravity un-aided by a pump. The equation you are looking at is the Bernoulli's equation. This equation states that the total energy of a fluid in a steady state flow is constant and it includes the pressure, velocity and height difference of the fluid. So, in your case, the pressure difference between the top and bottom of the pipe is 27kPa, the height difference is 12 metres and the gravitational head is equal to the density of the fluid times the acceleration due to gravity times the height difference (rho*g*h). If the gravitational head is greater than the pressure difference, then the fluid will flow down the pipe without the need for a pump.