Question

An open glass tube is inserted into a pan of fresh water at 20 °C. What tube diameter is needed to make the height of capillary rise equal to four times the tube diameter? State all assumptions.

Answer 1

Answer:

The tube diameter is 2.71 mm.

Explanation:

Given:

Open glass tube is inserted into a pan of fresh water at 20°C.

Height of capillary raise is four times tube diameter.

h = 4d

Assumption:

Take water as pure water as the water is fresh enough. So, the angle of contact is 0 degree.

Take surface tension of water at 20°C as $72.53\times 10^{-3}$ N/m.

Take density of water as 100 kg/m3.

Calculation:

Step1

Expression for height of capillary rise is gives as follows:

$h=\frac{4\sigma\cos\theta}{dg\rho}$

Step2

Substitute the value of height h, surface tension, density of water, acceleration due to gravity and contact angle in the above equation as follows:

$4d=\frac{4\times72.53\times10^{-3}\cos0^{\circ}}{d\times9.81\times1000}$

$d^{2}=7.39\times10^{-6}$

$d=2.719\times10^{-3}$ m.

Or

$d=(2.719\times10^{-3}m)(\frac{1000mm}{1m})$

d=2.719 mm

Thus, the tube diameter is 2.719 mm.