Consider the curved duct of Prob. 13–44, except allow the cross-sectional area to vary along the duct (A₁ ≠ A₂).

(a) Write an expression for the horizontal force F_x of the fluid on the walls of the duct in terms of the given variables.

(b) Verify your expression by plugging in the following values: ρ = 998.2 kg/m³, A₁ = 0.025 m², A₂ = 0.015 m², β₁ = 1.02, β₂ = 1.04, V₁ = 20 m/s, P_1,gage = 88.34 kPa, and P_2,gage = 67.48 kPa.