The device in the figure is called venturi meter, which consists of a converging and diverging

conical section of a pipe arranged to give an increase in velocity as the pipe converges,

causing a measurable drop in pressure. The diverging section is used to reconvert the

increased kinetic energy of the fluid stream into pressure energy at the outlet with minimum

losses. Show for this meter with no losses

that $Q=A_1\sqrt[\phantom{2}]{\frac{2gh}{(\frac{A_1}{A_2}{)}^2-1}}$