Mechanical Properties Of Fluid

From the definition of surface tension , the surface tension of a liquid is equal to the work (W) required to increase the surface area of the liquid film by unity at constant temperature.

Since, surface area of a sphere is and there are two free surfaces, we have
...(i)
and volume of sphere
i.e,
...(ii)
From Eqs. (i) and (ii), we get


and

For a drop of radius and terminal velocity ,
the viscous force is given by
where is coefficient of viscosity.
Putting the numerical values from the question, we have
poise

The excess pressure inside the soap bubble is inversely proportional to radius of soap bubble
i.e. being the radius of hubble. It follows that pressure inside a smaller bubble is greater than that inside a bigger bubble. Thus, if these two bubbles are connected by a tube, air will flow from smaller bubble to bigger bubble and the bigger bubble grows at the expense of the smaller one

Key Idea : At the same level in the two limbs of a U-tube, pressure is same.
On pouring water on left side, mercury rises (say) from its previous level in the right limb of -tube creating a difference of levels of mercury by . Equating pressures at and , we get

Bernoullis equation for flowing liquid be written as
constant ...(i)
Here, pressure energy per unit volume of liquid
density of liquid (water)
height of liquid column
velocity of liquid and
acceleration due to gravity
Dividing the E (i) by , we have
constant
In this expression, is velocity head and is pressure head.
It is given that,
Velocity head pressure head
ie,
or
or

At bottom of tank

Pressure due to liquid column

Velocity of water