The lower end of a capillary tube of diameter 2.0 mm is dipped 8.00cm below the surface of water in a beaker. What is the pressure required in the tube in order to blow a hemispherical bubble at its end in water? The surface tension of water at temperature of the experiments is `7.30 xx 10^(-2) Nm^(-1)`. 1 atmospheric pressure =` 1.01 xx 10^(5) Pa`, density of water `= 1000 kg//m^(3), g=9.80 ms^(-2)`. also calculate the excess pressure.

Explanation

To solve the problem, we need to find the pressure required to blow a hemispherical bubble at the end of a capillary tube submerged in water. We will use the following parameters:

- Diameter of the capillary tube, \(d = 2.0 \, \text{mm} = 2.0 \times 10^{-3} \, \text{m}\)
- Radius of the capillary tube, \(r = \frac{d}{2} = 1.0 \, \text{mm} = 1.0 \times 10^{-3} \, \text{m}\)
- Depth of the tube in water, \(h = 8.00 \, \text{cm} = 0.08 \, \text{m}\)
- Surface tension of water, \(S = 7.30 \times 10^{-2} \, \text{N/m}\)
- Density of water, \(\rho = 1000 \, \text{kg/m}^3\)
- Acceleration due to gravity, \(g = 9.80 \, \text{m/s}^2\)
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