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

School

Universiti Teknologi Malaysia (UTM)

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Assignment Type

Individual Assignment

Subject

EUME3243N Fluid Mechanics

Uploaded by Malaysia Assignment Help

Date

05/15/2025

Answer All Questions

[TOTAL: 100 marks]

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.

Figure 1.

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)

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This wind tunnel experiment is designed before conducting it. There are a few variables of interest in this experiment that need to be studied and correlated to each other. You as an engineer, you need to complete all tasks below:

d) Consider the drag force (F_D) is a function of fluid properties, external effects and geometry properties based on the description of the wind tunnel experiment described above. Form all possible four Pi groups. (30 marks)

e) Explain the importance of each Pi groups determined. (20 marks)

[Total: 100 marks]

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