I am trying to calculate the pumping pressure needed to backfill a borehole with geothermal grout. The hose is pulled up at the same rate as the borehole fills, so pumping pressure will get lower as the hole is filled. The borehole is initially filled with water and is filled bottom to top.
The way I am calculating it now is like this:
Pb: pressure at B (start of the hose going into the borehole).
i: Percentage of the borehole filled with grout).
g: acceleration due to gravity.
y: depth of the borehole.
τw: friction loss from hosewall.
D: diameter of the hose.
f: Friction coefficient.
vg: velocity of the grout in the hose.
Problem is: I don't know if this is correct. Can somebody validate this or come with the right way to calculate this?