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Question

1. Earth = 9.8 meters per second squared [m/s^2]
2. Earth's moon = 1.6 meters per second squared [m/s^2]
3. Mars = 3.7 meters per second squared [m/s^2]

When a liquid is placed in a tube with a small inside diameter, the concept of capillary action will cause the liquid to rise in the tube (see the image below).

 

The height (H) to which it will rise is given by: 

𝐻=(4𝜎)(𝐷𝜌𝑔)H=(4σ)(Dρg)

𝐻=(4𝜎)(𝐷𝜌𝑔)H=(4σ)(Dρg) Here, σ is the surface tension of the fluid, ρ the fluid density, D the tube inner diameter, and g the acceleration due to gravity. 

Assume you are conducting an experiment on the Earth’s moon using mercury. Liquid mercury has a surface tension of 487 millinewton per meter [mN/m] and a specific gravity of 13.6.

How high will the liquid rise in a tube with inside diameter of 0.75 millimeters [mm]? Express your answer in units of inches [in].

Answer 1

We are asked to find the height (inches) of a capillary action on the Earth's moon.

We are given:

Fluid: Mercury

Specific Gravity (SG): 13.6

Surface Tension (σ): 487 mN = 0.487 N

Diameter (D): 0.75 mm = 0.00075 m

Gravity: 1.6 m/s²

Density = SG*1000 = 13.6*1000 = 13600 kg/m³

Using the capillary action equation and evaluating:

h = (4σ)(Dρg) = (4*0.487)/(0.00075*13600*1.6) =0.119m

Convert meters to inches:

0.119m (100cm/m)*(2.54 in./cm) = 30.32 inches.

Final answer: 30.32 inches