5. In lecture, we applied Bernoulli's equation to determine the pressure at exit of an expanding channel at 2 as: v However, this expression of P2 is not accurate as it does not account for head loss. Head loss occurs due to increased pressure in the expansion zone/wall-surface which is denoted as Pwall. If Pwall = P1, then, P₁, A₁, V₁ Pwall P1 P2, A2, V2 a) Show that by applying momentum conversation the force balance over the control volume the pressure at exit P2 is: P₂ = P₁ + pv² (A) (1 − A²) b) Use the exit pressure expression from part a) in Bernoulli's equation to show that the head-loss is H₁ = v - A₁ Az 2

Fig: 1