Question

A capillary-tube viscometer is being selected to measure viscosity of a liquid food. The maximum viscosity to be measured will be 230 cP, and the maximum flow rate that can be measured accurately is 0.015 kg/min. If the tube length is 10 cm and a maximum pressure of 25 Pa can be measured, determine the tube diameter to be used. The density of the product is 1000 kg/m3.

Answer 1

Answer:

The diameter to be used is 0.98 cm

Explanation:

The Poiseuille´s law is equal to:

$Q=\frac{\pi Pr^{4} }{8\eta L}$

Where

Q = flow rate = 0.015 kg/min = 2.5x10⁻⁷m³/s

P = pressure difference = 25 Pa

r = radius

η = viscosity = 230 cP = 0.23 Pa s

L = length of the tube = 10 cm = 0.1 m

Clearing r:

$r=\sqrt[4]{\frac{8\eta LQ}{\pi P} } =\sqrt[4]{\frac{8*0.23*0.1*2.5x10^{-7} }{\pi *25} } =0.0049m$

The diameter is:

$d=2r=2*0.0049=0.0098m=0.98cm$