Air flows through a horizontal nozzle as shown below. The nozzle, which is conne

Question

Air flows through a horizontal nozzle as shown below. The nozzle, which is connected to the pipe by flanges), has an inlet diameter D_1 = 60 mm and an exit diameter D_2 = 10 mm. The inlet absolute pressure is P_1 = 105 kPa, and the air exhausts into the atmosphere so the exit pressure is P_2 = P_atm = 101.3 kPa. Assume that the air has a constant density of rho_air= 1.2 kg m^-3, and neglect the weight of the nozzle. Find the air velocity at the nozzle outlet (Vi). Find the force F applied by the flange to hold the nozzle in place.

Explanation / Answer

Use bernoulli for this:

E1=E2

P1/density x g + v1^2 / 2g = P2 / density x g + v2^2 / 2g

105x10^3 / 1.2x9.81 + v1^2 / 2x9.81 = 101.3x10^3 / 1.2x9.81 + v2^2 / 2x9.81

and the flow is the same

v1(60x10^-3)^2 = v2 (10x10^-3)^2

so solving this we have:

v1=11.61 m/s

v2=418.29 m/s

F= density x A x V2^ = 1.2 x (10^-3)^2 ( pi ) ( 1/4) ( 418.29^2) = 1.55x10^9 N

Good luck! bye

:)

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