Question

A 12-mm-diameter cylindrical jet of water discharges vertically into the ambient air. Due to surface tension the pressure inside the jet will be slightly higher than the surrounding atmospheric pressure. Determine this difference in pressure.

Answer 1

Answer:

Explanation:

Given

Diameter of cylindrical is $d=12\ mm$

There is excess Pressure in the cylindrical jet which can be  calculated by using Equilibrium free body  Diagram of an element of jet

excess Pressure force will balance the Surface tension force of water jet

$\Delta P\times Area=Surface\ tension \times length$

$\Delta P\cdot 2R\delta l=\sigma \times 2\delta l$

where $\sigma =$surface tension of water

$\Delta P=$excess Pressure

R=radius

$\delta l=$length of element

therefore $\Delta P=\frac{\sigma }{R}$

Surface Tension of water is $\sigma =7.34\times 10^{-2}\ N/m$

$\Delta P=\frac{7.34\times 10^{-2}}{6\times 10^{-3}}$

$\Delta P=12.23\ Pa$