Question

2.14 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 rate of 1 kg/s. The liquid density is 998 kg/m³.

Answer 1

Answer:

diameter of tube, D = 4 cm

radius of tube, r = 2 cm = 0.02 m

length of the tube, 1 = 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 =

$\pi \: pr ^{4}/8pl$

where, V is the rate of flow, P is the pressuredifference between the ends of the tube, r isthe radius of tube, I is the length of the tubeand n is the coefficient of viscosity.

By substituting the values

1.002 × 10-³ = 3.14 × 2.5 × 10³ × (0.02)⁴/8 × n × 0.2

eta = 0.783 deca poise