EUME3243N Wind Tunnel Experiment Assignment: Fluid Dynamics and Pi Group Analysis Using Student ID Variables

A small rounded object is tested in a (2 – 0.1c + 0.02e) m diameter wind tunnel as shown in Figure 1. The pressure is uniform across section ① and ②. The upstream pressure is (40 + 0.2c – 0.01d) mm H₂O (gage), the downstream pressure is (15 + 0.4e – 0.05d) mm H₂O (gage), and the mean air speed is (5 + b + 0.1d) m/s. The velocity profile at section ② is linear; it varies from zero at the tunnel centerline to a maximum at the tunnel wall.

This wind tunnel test is conducted in 1 atmospheric (1 atm or 101.325 kPa) and 25℃ condition. Neglect viscous resistance at the tunnel wall. Calculate:

a) Derive the mass flow rate from conservation of mass equation then determine the mass flow rate of the wind tunnel. Assume the gas constant for air, R_air = 286.9 N.m/kg.°K. (10 marks)

b) The maximum velocity at section ②. (15 marks)

c) The drag of the round object and its supporting vane. (25 marks)