An incompressible fluid of density rho and viscosity mu flows through a curved d

Question

An incompressible fluid of density rho and viscosity mu flows through a curved duct that turns the flow 180degree. 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. P6-40. (a) Write an expression for the horizontal force Fx 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: rho = 998.2 kg/m3, mu = 1.003 times 10-3 kg/m s, A1 = A2 = 0.025 m2, beta1 = 1.01, beta2 = 1.03, V1 = 10 m/s, P1,gage = 78.47 kPa, and P2,gaga = 65.23 kPa. Answer: (b) Fx = 8680 N to the right FIGURE P6-40

Explanation / Answer

Momentum equation in x-direction
Fx = p1A1+p2A2 +1A1V12+2A2V22

plugging values

Fx = 78470(0.025)+65230(0.025)+1.01x998.2x0.025x102+1.03x998.2x0.025x102 = 8683 N

Force of the fluid acting on the wall , positive = to the right

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