Question

A flow of whole milk at 293 K with a density of 1030 kg / m3 and viscosity of 2.12 cP, passes through a pipe at the speed of 0.605 kg / s through a glass pipe of 63.5mm in diameter.
a) Calculate the Reynolds number. Is the flow turbulent?
b) Calculate the flow velocity in m3
/ s needed for a Reynolds number of 2100 and speed in m / s.

Answer 1

Density of milk = 1030 kg/m3

Viscosity = 2.12 cP x 0.001 Pa-s/cP

= 0.00212 Pa-s = 0.00212 N-s/m2

= 0.00212 kg/m-s

Mass flow rate = 0.605 kg/s = density x area x velocity

0.605 kg/s = 1030 kg/m3 x (3.14/4) x 0.0635*0.0635 m2 x velocity

Velocity = 0.185556 m/s

Diameter = 63.5 mm x 1m/1000mm = 0.0635 m

Part a

Reynolds number = diameter x velocity x density / viscosity

=(0.0635 m x 0.185556 m/s x 1030 kg/m3)/(0.00212 kg/m-s)

= 5724.66

Reynolds number (5724.66) > 4000

The flow is turbulent

Part b

For laminar flow

Reynolds number = 2100

diameter x velocity x density / viscosity = 2100

Velocity = (2100 x viscosity) / (diameter x density)

= (2100 x 0.00212 kg/m-s) / (0.0635 m x 1030 kg/m3)

= 0.068068 m/s

Flow velocity = area x velocity

= (3.14/4) x 0.0635 x 0.0635 m2 x 0.068068 m/s

= 0.0002155 m3/s

= 2.155 x 10^-4 m3/s