A fluid of density '$$\rho$$' is flowing through a uniform tube of diameter '$$d$$'. The coefficient of viscosity of the fluid is '$$\eta$$', then critical velocity of the fluid is

What should be the diameter of a soap bubble, in order that the excess pressure inside it is $$25.6 \mathrm{~Nm}^{-2}$$ ? [surface tension of soap solution $$\left.=3 \cdot 2 \times 10^{-2} \mathrm{~Nm}^{-2}\right]$$

Two capillary tubes of the same diameter are kept vertically in two different liquids whose densities are in the ratio $$4: 3$$. The rise of liquid in two capillaries is '$$h_1$$' and '$$h_2$$' respectively. If the surface tensions of liquids are in the ratio $$6: 5$$, the ratio of heights $$\left(\frac{h_1}{h_2}\right)$$ is

(Assume that their angles of contact are same)

A spherical liquid drop of radius $$\mathrm{R}$$ is divided into 8 equal droplets. If surface tension is $$\mathrm{S}$$, then the work done in this process will be