(a) Show that the pressure difference between two points in an incompressible liquid of density \(ho\) in static equilibrium is \(\Delta P=ho g s\), where \(s\) is the vertical separation between the two points and \(g\) is the local gravitational field.

(b) The liquid is caused to flow through a horizontal pipe of varying cross-sectional area, so that its velocity depends upon position. In a particular section of pipe of length \(s\), the pipe is narrowing, so that the fluid's acceleration has the constant value \(a\). Find the pressure difference \(\Delta P\) between one end of the section and the other, in terms of \(ho\) and the change in the velocity squared \(\left(v^{2}ight)\) between the two ends of the section. Is the pressure larger or smaller at the narrower end of the section? (The result is an example of the Bernoulli effect).