Question

For a small droplet of water show that surface tension y =Pd/4
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Answer 1

Step-by-step explanation:

Surface tension is the force acting per unit length on the boundary between two immiscible fluids or a fluid and a solid surface.

For a small droplet of water, the surface tension is the force acting along the circumference of the droplet, which is balanced by the pressure difference across the droplet.

The pressure difference across the droplet is given by the Laplace's law, which states that the pressure difference, P, across a curved surface is proportional to the surface tension, y, and the curvature, d.

Mathematically, it is expressed as:

P = yd

For a small droplet of water, we can assume that the curvature is constant and equal to the radius of the droplet, r. Therefore, the pressure difference across the droplet can be expressed as:

P = 2y/r

Since the droplet is assumed to be spherical, the circumference of the droplet is given by 2πr. Therefore, the force acting along the circumference of the droplet can be expressed as:

F = P × Circumference/2 = Pπr

Substituting the value of P from the Laplace's law equation, we get:

F = yπr^2

The force acting along the circumference of the droplet is also equal to the weight of the water droplet. Therefore, we can express the weight of the droplet as:

W = πr^2d

Equating the force and weight, we get:

yπr^2 = πr

Simplifying, we get:

y = Pd/4

Hence, we have shown that for a small droplet of water, the surface tension y = Pd/4.

Answer 2

Surface tension is defined as the force acting per unit length perpendicular to an imaginary line drawn on the surface of a liquid. The force acting on a small droplet of water is given by the formula F = Pd^2/4, where P is the pressure acting on the surface of the droplet and d is the diameter of the droplet.

If we express the force F in terms of surface tension y, we get:

F = yL, where L is the length of the imaginary line on the surface of the droplet.

Equating the two expressions for F, we get:

yL = Pd^2/4

Solving for y, we get:

y = Pd/4