1 The Joukowsky equation for fluids and solids

This report provides an extension to a previous paper (Tijsseling and Anderson, 2004) in which we showed that Johannes von Kries (1883) was the first to derive and validate the "Joukowsky equation " for waterhammer. Since there is a strong analogy between pressure waves in fluids and stress waves in solids, and waterhammer relates to impact mechanics, it is likely that the "Joukowsky equation " for solids already existed before 1883. Also, 19th century's scientists must have been aware of the fluids/solids analogy. In this historical study we try to answer the question of who was the first to derive the Joukowsky equation in either fluids or solids