A horizontal pipe carries an incompressible liquid of density ρf. A stagnation tube placed at the centre of the flow conveys its pressure to limb A of a manometer that contains a liquid of density ρm (ρm>ρf). A wall tapping located 20cm vertically above limb A conveys the static pressure to limb B of the same manometer. Let the observed difference in manometer levels be h. Neglect temperature effects.
(i) Derive an expression for the magnitude of the flow speed v in terms of h, ρf, ρm, g and the vertical separation (20cm) between the tapping points.
(ii) Show explicitly how the elevation difference between the tappings modifies the velocity compared to the case where both tappings are at the same level.