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Question
Calculate the rise of water inside a clean glass capillary tube of radius 0.1 mm, when immersed in water of surface tension 7 × 10-2 N/m. The angle of contact between water and glass is zero, the density of water = 1000 kg/m3, g = 9.8 m/s2.
Solution 1
Given :
▪ Radius of capillary tube = 0.1 mm
▪ Surface tension of water = 7×10-2 N/m
▪ Angle of contact = 0°
▪ Density of water = 1000 kg/m
▪ Acceleration due to gravity = 9.8 m/s
To find:
▪ Height of water column inside the capillary tube.
Formula:
When a capillary tube of radius 'r' is dipped in a liquid of density ρ and surface tension T, the liquid rises or falls through a distance,
H = `(2"T" "cos" theta)/(rho "gr")`
H = `(2 xx 7 xx 10^-2 xx "cos" theta)/(1000 xx 9.8 xx 0.1 xx 10^-3)`
H = 0.142 m
Solution 2
Given:
r = 0.1 mm = 10−4 m,
T = 7 × 10−2 N/m,
θ = 0°,
ρ = 1000 kg/m3, g = 9.8 m/s2
To find: Height of capillary rise (h)
Formula: h = `(2Tcosθ)/(rρg)`
Calculation: From formula,
h = `(2 xx (7 xx 10^-2) xx cos0^circ)/(10^-4 xx 10^3 xx 9.8)`
= `(14 xx 10^-1)/(9.8)`
= `1/7`
= 0.1429 m
The rise of water inside the glass capillary is 0.1429 m.
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