An incompressible fluid of density and viscosity flows through a curved duct that turns the

Question:

An incompressible fluid of density ρ and viscosity μ flows through a curved duct that turns the flow 180?. The duct cross-sectional area remains constant. The average velocity, momentum flux correction factor, and gage pressure are known at the inlet (1) and outlet (2), as in Fig. P13??44.?

(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, μ = 1.003 × 10^-3 kg/m ? s, A₁ = A₂ = 0.025 m², β₁ = 1.01, β₂ = 1.03, V₁ = 10 m/s, P_1,gage = 78.47 kPa, and P_2,gage = 65.23 kPa.