Question

Consider a capillary tube as shown in the figure below. Find the diameter of the tube if the contact angle = 20° and the height h 15 mm.Take σ' = 0.073 Nim and y-9789 kN/m' Q3. 2mRe, Liquid 2R 0 3 cm Take i 0025 Ni

Answer 1

Using Jurin's law, we obtain

$\:$

$h=\frac{2\sigma _{s} \cos \phi }{\gamma r}$

$\:$

solving for the radius of the tube r,

$\:$

$r=\frac{2\sigma _{s} \cos \phi }{\gamma h}$

$\Rightarrow \: \: \: r=\frac{2 (0.073\, N/m) \cos (20^{\circ}) }{(9.789\times 10^{3}\, N/m^{3}) (15\times 10^{-3}\, m)}$

$\Rightarrow \: \: \: r=9.34\times 10^{-4}\, m$

$\:$

The diameter of the tube d is related to its radius by the formula

$\:$

$d=2r=2(9.34\times 10^{-4}\, m)$

$\:$

or

$\:$

${\color{Blue} d=1.87\times 10^{-3}\, m=1.87\, mm}$