A pump is lifting water (density equal to 62.4 lb/ft^3) by 50 ft and increasing the pressure of the water by 30 psig. The water flows through a 3-inch inside diameter tube at 40 lb/second. Starting with the general energy balance. Determine the power that is required by the pump in hp?
We have to use Bernoulli's:theorem here
Let A = Area ρ=density; v = velocity of flow; g =acceleration due to gravity
Z =Δheight; p = pressure; P = power and Q =f low rate
Q = mass/ density = (40lb/s) / 62.4 lb/ft³ = 0.641 ft³/s
Considering density and flow rate to be based on lbm,
Q=A·v = m / ρ ==> v = m / (Aρ) = (40lb/s) /(¼π·¼² · 62.4 lb/ft³) = 13.06 ft/s
P = [(½v² + gz)·ρ + p]·Q
Considering that ρ = 62.4/32.2
P = [(½{13.06}² + 32.2·50ft)·62.4/32.2 + 30*144]·[0.641] ft³/s
P = [1695.267 · 62.4/32.2 + 30*144]·[0.641] ft³/s
P = [3285.24 + 4320]·0.641 ft³/s = 4875.2 ft·lb/sec
Power of the pump = 8.86 HP ( since HP/(550 ft·lb/sec)
