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

The tube diameter is 2.71 mm.

Step-by-step 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* 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=(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=(4*72.53*10^(-3)\cos0^(\circ))/(d*9.81*1000)`

`d^(2)=7.39*10^(-6)`

`d=2.719*10^(-3)` m.

Or

`d=(2.719*10^(-3)m)((1000mm)/(1m))`

d=2.719 mm

Thus, the tube diameter is 2.719 mm.