Holding force on a contracting nozzle ($F=\rho Q^2(A_0/A_1-1{)}^2/(2A_0)$)

For steady ideal flow through a horizontal contracting nozzle, Bernoulli equation gives inlet gauge pressure $p_0=\rho Q^2(A_1^{-2}-A_0^{-2})/2$. The integral momentum equation gives the fluid's force on the nozzle as $p_0{A}_0-\rho Q^2(A_1^{-1}-A_0^{-1})$ in the outlet direction. Simplification yields the displayed nonnegative magnitude. The external holding force has equal magnitude and the opposite direction.