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 [tex]72.53\times 10^{-3}[/tex] N/m.
Take density of water as 100 kg/m3.
Calculation:
Step1
Expression for height of capillary rise is gives as follows:
[tex]h=\frac{4\sigma\cos\theta}{dg\rho}[/tex]
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:
[tex]4d=\frac{4\times72.53\times10^{-3}\cos0^{\circ}}{d\times9.81\times1000}[/tex]
[tex]d^{2}=7.39\times10^{-6}[/tex]
[tex]d=2.719\times10^{-3}[/tex] m.
Or
[tex]d=(2.719\times10^{-3}m)(\frac{1000mm}{1m})[/tex]
d=2.719 mm
Thus, the tube diameter is 2.719 mm.
