Answer Happy

A box-enclosed fan is pushing air downwards through a 1 m diameter blade span area. The whole system weighs 20 N and does not rotate. In order for the system to hover mid-air (i.e. stay stationary in the air), determine the following: • Consider g = 9.81 m/s2, and Pair = 1.25 kg/m3 • What are the valid assumptions (select all valid choices)? • What is the air exit velocity required? • What is the volumetric flow rate needed? • Hint: The inlet air speed is very small due to sucking stationary air from the surrounding. If the system is to accelerate upwards at constant value of 20 m/s2, determine the following: • Consider g = 9.81 m/s2, and Pair = 1.25 kg/m3 • What is the new air exit velocity needed? • What is the increase in the air exit velocity? • Hint 1: The inlet air speed is very small due to sucking stationary air from the surrounding. • Hint 2: Use the conservation of linear momentum with accelerating control volume equation provided below: E +FR-daredy = d. Boredy = | Tedy+Veï dà | PRÑ

• Hint 2: Use the conservation of linear momentum with accelerating control volume equation provided below: Es+ Fo - Sagres p av = di Saūp av + Ss Upū. dĀ Aref Select a total of 8 answers that match the above required quantities with the best approximations. Select 8 correct answer(s) 10.1 m/s Incompressible Flow 12.1 m/s 3.54 m3/s 7.87 m/s 6.89 m3/s 9.84 m/s 2.5 m/s Vincrease = 3.36 m/s =

2.5 m/s Vincrease = 3.36 m/s Vincrease = 5.87m/s | Non-uniform Velocity Profile across Control Surfaces Unsteady Flow Compressible Flow Vincrease = 1.42 m/s Uniform Velocity Profile across Control Surfaces Atmospheric pressure only at the outlet of the control volume 4.51 m/s Steady Flow 6.12 m/s Atmospheric pressure all around the control volume