Name: Fluids in Motion
Uploaded: 2019-07-19
Duration: 9 min 47 s
Description: In this video, let us explore fluid motion and how pressure in different places changes its flow. Jump into this video to learn more! Have fun learning.

Question

Derive an expression of excess pressure inside a liquid drop.

Accepted Answer

Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. It also helps in minimising the energy required to maintain the shape.

On a liquid drop, there exists two different forces, one upward force due to the air pressure and one downward force due to the surface tension of the liquid material.

Let us consider a liquid drop of spherical shape with radius $r$ , the initial pressure is $P_{i}$ , the final pressure is $P_{f}$ and the surface tension of the fluid is $T$ .

The formula to calculate the upward force $(F_{u})$ on the liquid drop is given by

$F_{u} = π r^{2} (P_{f} - P_{i}) . . . . . . . . . . . . . . . . . . . . . . . . . . . (1)$

The formula to calculate the downward force $(F_{d})$ on the drop is given by

$F_{d} = 2 π r T . . . . . . . . . . . . . . . . . . . . . . . . . . (2)$

In balanced condition, equate both the equations and simplify to obtain the required excess pressure inside the drop.

$\begin{array}{rcl} π r^{2} (P_{f} - P_{i}) & = & 2 π r T \\ P_{f} - P_{i} & = & \frac{2 T}{r} \end{array}$

Derive an expression of excess pressure inside a liquid drop.

Important Questions on Mechanical Properties of Fluids

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