Consider a small-diameter open-ended tube inserted at the interface between two immiscible fluids of different densities. Derive an expression for the height difference \(\Delta h\) between the interface level inside and outside the tube in terms of tube diameter \(D\), the two fluid densities \(ho_{1}\) and \(ho_{2}\), and the surface tension \(\sigma\) and angle \(\theta\) for the two fluids' interface. If the two fluids are water and mercury, find the height difference if the tube diameter is 40 mils ( \(1 \mathrm{mil}=0.001 \mathrm{in}\).).