Q. Calculate the capillary rise þin a glass tube 2.5 mm diameter when immersed vertically in (a) water and (b) mercury. Take surface tensions o = 0.0725 N/m for water and sigma = 0.52N / m for mercury in contact with air. The specific gravity for mercury is given as 13.6 and angle of contact = 130°.
SOLUTION:
Given:
Dia. of tube d = 2.5mm = 2.5 * 10 ^ – 3 m Surface tension, σ for water = 0.0725 N/m
σ for mercury = 0.52N / m
Sp. gr of mercury = 13.6
Density = 13.6 * 1000kg / (m ^ 3)
(a) Capillary rise for water (θ = 0)
Using equation, we get
h = (4σ)/(p×g×d)
= 4*0.0725 /1000 * 9.81 * 2.5*10-³
= 0.0118m = 1.18cm Ans.
(b) For mercury
Angle of constant between mercury and glass tube, θ = 130°
Using equation, we get
h = (4σ cos θ)/(p×g×d)
= (4 * 0.52cos 130°)/(13.6 * 1000 * 9.81 * 2.5 * 10-³)
= – 0.004m = – 0.4cm Ans.
The negative sign indicates the capillary depression
Q. Calculate the capillary effect in millimeters in a glass tube of 4 mm diameter, when immersed in (i) water, and (ii) mercury. Take surface of liquid is 20° C and the values of the surface tension of water and mercury at 20º C in contact with air are 0.073575 N/m and 0.51 N/m respectively. The angle of contact for water is zero that for mercury 1.30°. Take density of water at 20°C as equal to 998 kg/m³.
SOLUTION:
Given:
Dia. of tube, d = 4mm = 4 * 10-³m
The capillary effect (i.e., capillary rise or depression) is given by equation.
h = (4σ * cos θ)/(p×g×d)
σ = Surface tension in kgf/m
θ= Angle of contact, and
p = Density
(i) Capillary effect for water
σ = 0.073535N / m
θ = 0°
rho (p) = 998kg / (m ^ 3) at 20° C
h = (4 * 0.073575×cos 0°)/(998 * 9.81 * 4 * 10-³) = 7.51 * 10-³ m = 7.51mm Ans.
(ii) Capillary effect for mercury
σ = 0.51N / m
θ = 130°
ρ= Sp. Gravity × 1000
= 13.6 * 1000 = 13600kg / (m³)
h = 4×0.51×cos130°/13600×9.81×4×10-³
= -2. 46×10³ = -2. 46mm
The negative sign indicates the capillary depression
