a solution o ehtanol is pumped to a vessel 25 m above a refe

a solution o ehtanol is pumped to a vessel 25 m above a reference level through a 25-mm-inside-diameter steel pipe at a rate of 10 m^3/h. The length of pipeis 30 m and contains two elbows with friction equivalent to 20 diameters each. Compute the power requirenments of the pump. Solution propterites include density of 975 kg/m^3 and viscosity of 4x10^-4 Pa s. Show ALL work please

Solution

volume flow rate is,

Q = AV

Thus the velocity is,

V = Q/A = 10/(60*60*3.14*12.5^2*10^-6)

= 5.67 m/s

friction loss = f*density*(velocity)^2/2

= 2*20*975*5.67^2/2

= 627 kW

heat loss = density*gh

= 975*9.81*25

= 240 kW

therefore, the total required power is

P = 627+240 = 867 kW