Question

A solution of ethanol 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 pipe is 30 m and contains two elbows with friction equivalent to 20 diameters each. Compute the power requirements of the pump. Solution properties include density of 975 kg/(m^3) and viscosity of 4*10^-4 Pa s. Hint: frictional loss due to elbow is equivalent to having additional length of pipe that is equal to 20 times the diameter of pipe. So you just calculate that additional length and add it to 30 m length of pipe.

Answer 1

Now here will be having two types of head losses  

1) Due to frictional head loss

2) Due to elbows

Hence for elbow we are provided equivalent length hence we don't have to actually calculate each of them separately, rather just use length as sum of actual length + equivalent length

L = 30 + 2* (20*D) = 30 + 2*20*25*10^-3 = 31 m

Step 1: Calculation of Reynolds number

Density = 975 Kg/m³

Viscosity = 4*10^-4 Pa-s

Q = 10 m3/hr =0.00278 m³/s

d = 25 mm

Area = (Pi/d)*d² = 0.00049 m²

Velocity = Q/A = 0.00278/ 0.00049 =5.658 m/s

Step 2: Calculation of friction factor

The basic friction factor equation is given by'

Step 3: Total head loss ( due to friction and elbows)

The general frictional loss equation is given by the fanning friction head loss equation ( You may also use Darcy Weishback equation)

Step 4: Calculation of total head required to pump the liquid to the take

H =Hl + Hstatic = 18 + 25 = 43 m

Step 5: Power requirement calculation

P = Flow rate *density *g* H = 0.0027*975*.81*43 =11.4948 W