Question

A capillary tube is being used to measure the viscosity of a Newtonian liquid. The tube has a 4-cm diameter and a length of 20 cm. Estimate the viscosity coefficient for the liquid if a pressure of 2.5 kPa is required to maintain a flow 3 rate of 1 kg/s. The liquid density is 998 kg/m .

Answer 1

Answer:

η = 0.783 deca poise

Explanation:

diameter of tube, D = 4 cm

radius of tube , r = 2 cm = 0.02 m

length of the tube, l = 20 cm = 0.2 m

Pressure, P = 2.5 kPa = 2.5 x 1000 Pa

Rate of flow of mass = 1 kg/s

density of liquid, d = 998 kg/m³

Rate of flow of volume, V = mass pr unit time / density

V = 1 / 998 = 1.002 x 10^-3 m³/s

By use of Poiseulli's formula

$V = \frac{\pi P r^{4}}{8\eta l}$

where, V is the rate of flow, P is the pressure difference between the ends of the tube, r is the radius of tube, l is the length of the tube and η is the coefficient of viscosity.

By substituting the values

$1.002\times 10^{-3} = \frac{3.14\times 2.5\times 10^{3}\times (0.02)^{4}}{8\times \eta \times 0.2}$

η = 0.783 deca poise