Question

Determine the minimum size of glass tubing that can be used to measure water level. If the capillary rise in the tube does not exceed 0.25mm. Take surface tension of water in contact. With air as 0.0735N/m

Answer 1

Step-by-step explanation:

The formula to determine the size of a capillary tube is

h = 2•T•Cos θ / r•ρ•g

Where

h = height of liquid level

T = surface tension

r = radius of capillary tube

ρ = density of liquid

θ = angle of contact = 0°

g =acceleration due to gravity=9.81m/s²

The liquid is water then,

ρ = 1000 kg / m³

Given that,

T = 0.0735 N/m

h = 0.25mm = 0.25 × 10^-3m

Then,

r = 2•T•Cos θ / h•ρ•g

r = 2 × 0.0735 × Cos0 / 2.5 × 10^-3 × 1000 × 9.81

r = 5.99 × 10^-3m

Then, r ≈ 6mm

The radius of the capillary tube is 6mm

So, the minimum size is

Volume = πr²h

Volume = π × 6² × 0.25

V = 2.83 mm³

The minimum size of the capillary tube is 2.83mm³