Question
Asked Sep 3, 2019
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Fluid Mechanics

A drop of water at 20oC is forming under a solid surface. The configuration just before separating and falling as a drop is shown in the picture. Assume the forming drop has a volume of a hemisphere and the force holding the drop to the surface is the surface tension. What is the diameter of the hemisphere just before separating? 

D
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Expert Answer

Step 1

Assume:

The surface tension of the water (σ) at 20ºC is 0.073 N/m.

The value of acceleration due to gravity (g) is 9.8 m/s2.

The density of water (ρ) is 1000 kg/m3.

The volume and diameter of the water drop is denoted by V and D.

Step 2

The separation of the droplet happens only when the weight of the drop W exceeds the surface tension F.

The weight o...

W F
ρVg-σ(Penimeter )
2D=TD)
24
2TD9.8- 0.073(TD)
24
D?0.073 x24
(19.6)x p
0.073 x 24
D =
(19.6)x1,000
1000mm
D 9.45x103mx
1m
D 9.45 mm
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W F ρVg-σ(Penimeter ) 2D=TD) 24 2TD9.8- 0.073(TD) 24 D?0.073 x24 (19.6)x p 0.073 x 24 D = (19.6)x1,000 1000mm D 9.45x103mx 1m D 9.45 mm

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