Similarity - Velocity

Water at 20oC (viscosity = 1 cp) flows through a smooth straight pipe A of inside diameter 4 cm at an average velocity of 50 cm/sec. Oil flows through another pipe B of inside diameter 10 cm. Assuming similarities, calculate the velocity of oil through pipe B. Specific gravity of oil is 0.8 and its viscosity is 2 cp.

Data:

A:

Dia of A = 4 cm

Velocity of fluid in A = 50 cm/sec

Density of fluid in A = 1 g/cc

Viscosity of fluid in A = 1 cp

B:

Dia of B = 10 cm

Density of fluid in B = 0.8 g/cc

Viscosity of fluid in A = 2 cp

Formulae:

For dynamic similarity, ratio of forces to be equal

Inertial forceA / Inertial forceB = Viscous forceA / Viscous forceB

i.e. NReA = NReB

Calculations:

NReA = NReB

Therefore,

4 x 50 x 1 / 1 = 10 x VB x 0.8 / 2

200 = 4 VB

VB = 200/4 = 50 cm/sec

Velocity of oil through B = 50 cm/sec