The ducted fan unit shown in the figure has a mass m = 100 kg and is supported in the vertical position on its flange at A. The unit draws in air with a density of 1.2 kg/m³ and a velocity v₁ = 5 m/s through an inlet with diameter D₁ = 1 m. It discharges air through two outlets at the bottom of the fan. The mass flow rate through each outlet is ½ of the entering mass flow rate, and the velocity at each outlet is V₂ V3 = 15 m/s. Both inlet and outlet pressures are atmospheric. Determine the vertical force R, in newtons, applied to the flange of the fan unit by the supports (at A). D₁1.00 m V3= 15 m/s

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Fluid Dynamics

The study of the flow of gases and liquids, usually in and around solid surfaces, is known as fluid dynamics in physics and engineering. Fluid dynamics, for example, can be used to evaluate the movement of air through an airplane wing or the surface of a vehicle. It can also be used in ship design to increase the speed at which ships pass through water.