### Fluid Mechanics

# Similarity - Velocity

Water at 20^{o}C (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 force_{A} / Inertial force_{B} = Viscous force_{A} / Viscous force_{B}

i.e. NRe_{A} = NRe_{B}

Calculations:

NRe_{A} = NRe_{B}

Therefore,

4 x 50 x 1 / 1 = 10 x V_{B} x 0.8 / 2

200 = 4 V_{B}

V_{B} = 200/4 = 50 cm/sec

Velocity of oil through B = **50 cm/sec**