Question

A liquid food(viscosty: 0.003 Pa S; density:1033 kg/m^3) is being pumped at a rate of 3 m^3/h from a tank A, where the absolute pressure is 12,350 Pa, to a tank B, where the absolute pressure is 101,325 Pa, through a sanitary with 3.8 cm diameter and 4.6x10^-5 m surface roughness. The pump is 1 m below the liquid level in tank A and the discharge in tank B is 3.3 m above the pump. If the length of the pipe in the suction line is 2 m, the dischargeline 10 m, and there are one 90 degree anlge flanged elbow in the suction line, two 90 degree angle thread elbowsin the discharge line, and one globe valve in the discharge line. Calculate he pump power required for finishing this job, assuming the efficeincy of the pump is 65%.

Answer 1

Flow diagram

Mass flow rate of food inlet m

The nominal dia for the given inside pipe(3.8 cm)

D = 3.561 cm = 0.03561 m

Area A = (3.14/4)*0.03561*0.03561 = 9m959 x 10^-4 m2

Mean velocity

Reynolds number

Friction factor for the rough pipe

= surface roughness/D

= 4.6x10^-5 m/0.03561 m

= 0.0013

From moody chart

f = 0.008

Equivalent length for three 90° elbow

Le = 3*32D = 3*32*0.03561 = 3.42 m

Equivalent length for globe valve

Le = 300D = 300*0.03561 = 10.68 m

Frictional loss

Frictional loss due to sudden contraction

Total frictional loss = 8.42 + 0.19 = 8.61 J/kg

Apply the mechanical energy balance

pump power required

efficeincy of the pump = 65%

Actual power required = 101.33/0.65 = 155.9 W