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

Prove that equivalent S.I unit of surface tenison is

J / m^{2}

Accepted Answer

Surface tension of a fluid is an important property which determines the shape of the surface of the fluid and ensures the minimum energy to main the shape.

Surface tension of a fluid arises because of intermolecular forces, which are of two types-adhesive force and cohesive force.

Surface tension $(T)$ is measured as the ratio of the tangential force $(F)$ acting per unit length $(L)$ on both sides of an imaginary line drawn on the free surface of liquid. Mathematically, it can be written that

$T = \frac{F}{L} . . . . . . . . . . . . . . . . . . . . . . (1)$

Multiply both the numerator and the denominator of the right-hand side of equation (1) by $L$ ,

$\begin{array}{rcl} T & = & \frac{F \cdot L}{L^{2}} \\ = & \frac{W}{L^{2}} . . . . . . . . . . . . . . . . . . . . . . . . . . (2) \end{array}$

where, $W$ indicates the work done or equivalently the energy.

Substituting the appropriate energy for energy and square of the length from equation (2), it can be wriiten that the equivalent S.I. unit of surface tension is $J / m^{2}$ .

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