Question

The pressure required in the tube in order to blow a hemispherical bubble at its end in water is $1.01146\times {10}^x$.Find the value of x.

Answer 1

Applying Pascal's Law

The pressure in an incompressible liquid at the same horizontal level is the same.

Therefore, the pressure outside the bubble formed should be the same as that exerted by the fluid at that depth.

Since, the capillary tube is dipped 10 cm = 0.1 m below the water surface.

Pressure at this depth, P = $P_o+\rho gh$

P = ${10}^5+{10}^3\times 10\times 0.1$

P = $1.01\times {10}^5$

Now, the pressure inside the bubble is more than that outside the bubble.

And the two are related as

$P_{outside}-P_{inside}=-\frac{4T}{r}$

$P_{inside}=1.01\times {10}^5+\frac{4\times 7.3\times {10}^3}{0.002}$

or $P=1.01146\times {10}^5$