### Fluid Mechanics

# Capillary Tube Viscosity Measurements

A capillary tube 0.2 cm in diameter and 10 cm long discharge one liter of a liquid in ten minutes under a pressure difference of 5 cm mercury. Find the viscosity of the liquid using the following data:

Density of oil = 850 kg/m^{3}, Density of mercury = 13600 kg/m^{3}

Data:

Dia of tube(D) = 0.2 cm = 0.002 m

Length of pipe(L) = 10 cm = 0.1 m

Density of mercury = 13600 kg/m^{3}

Density of oil(r) = 850 kg/m^{3}

Pressure drop(Dp) = 5 cm Hg = 0.05 x 13600 x 9.812 N/m^{2} = 6672.16 N/m^{2}

Flow rate(Q) = 1 litre/10 min = 0.001/(10 x 60) = 1.667 x 10^{-6} m^{3}/sec

Formula:

Hagen-Poiseuille law (pressure drop for laminar flow is related to the flow parameters)

Calculations:

In capillary tube viscosity measurements the flow is maintained in laminar conditions.

m =
(p x 6672.16 x 0.002^{4})/(1.667 x
10^{-6} x 128 x 0.1) =
= 0.01572
kg/(m.sec) = **15.72
cP**