When fluid flows through an abrupt expansion as indicated in Fig. P5.97, the loss in ava...

When fluid flows through an abrupt expansion as indicated in Fig. P5.97, the loss in available energy across the expansion, loss_ex, is often expressed as

where A₁ is the cross-sectional area upstream of expansion, A₂ is the cross-sectional area downstream of expansion, and V₁ is the velocity of flow upstream of expansion. Derive this relationship.