Question

A U-tube is made up of two capillaries of diameters 1.0 mm and 1.5
mm respectively. The U tube is kept vertically and partially filled
with water of surface tension 0.0075kg/m and zero contact angles.
Calculate the difference in the level of the menisci caused by the
capillarity.

Answer 1

Explanation:

T = 0.0075 kg/m = 0.075 N/m

theta = 0°

g = 10 m/s^2

we know that h = T*2cos theta/r*rho*g

for small dia tube

h = 0.075*2/(0.5*10^-3*10^3*10)

= 0.03 m

for large dia tube

h = 0.075*2/(0.75*10^-3*10^3*10)

= 0.02 m

difference between two heights

= 0.03 - 0.02 = 0.01 m

Answer 2

Answer:

The difference in the level caused by the capillarity is 1 m.

Explanation:

We will use the following formula to solve this question,

$\Delta H=\frac{4\sigma cos\theta}{\rho g}(\frac{1}{d_1} -\frac{1}{d_2})$       (1)

Where,

ΔH=difference in the level of menisci caused by the capillarity

θ=contact angle

σ=surface tension

ρ=density of the liquid

g=acceleration due to gravity=10m/s²

d₁,d₂=respective tube diameters

From the question we have,

d₁=1mm=1×10⁻³m

d₂=1.5mm=1.5×10⁻³m

σ=7.5×10⁻³kg/m

The density of water is (ρ)=1000kg/m³

θ=0°

By substituting all the required values in equation (1) we get;

$\Delta H=\frac{4\times 7.5\times 10^-^3\times cos0\textdegree}{1000\times 10}(\frac{1}{1\times 10^-^3} -\frac{1}{1.5\times 10^-^3})$         ($cos0\textdegree=1$)

$\Delta H=30\times 10^-^7(\frac{1.5-1}{1\times 1.5\times 10^-^3} )$

$\Delta H=3\times 10^-^3\times \frac{0.5}{1.5\times 10^-^3}$

$\Delta H=1m$

Hence, the difference in the level of the menisci caused by the capillarity is 1 m.