How can I derive the equation for calculating pump horsepower?

[mhzq007]

hi everyone can anyone please give me a clue of how to derive this equation

Hp= Q(gpm)* Δp(psi)/1714

Q is volumetric flow rate
Δp is pressure

 

[SteamKing]

hi everyone can anyone please give me a clue of how to derive this equation

Hp= Q(gpm)* Δp(psi)/1714

Q is volumetric flow rate
Δp is pressure

1 HP = 33000 ft-lb/min.

1 gal. water = 8.33 lbs

for water, Δp = H * 144 in$^{2}$/ft$^{2}$ / 62.4 lbs / ft,
where H is the pump head in feet of water

So

HP = Q*H / 33000 = [Q gal/min * 8.33 lbs / gal * H feet of water * Δp * (144/62.4 lbs / ft$^{2}$)] / 33000

HP = [Q * Δp * 8.33 * (62.4/144)] / 33000 = Q * Δp / 1714