**Question 1 (30 marks)**

The aerodynamic drag of a new sports car is to be predicted at a speed of 75 km/h at an air temperature of 25°C. Automotive engineers build a one-fifth scale model of the car to test in a wind tunnel. It is winter and the wind tunnel is located in an unheated building. The temperature of the wind tunnel air is only 5°C.

a) Determine how fast the engineers should run the wind tunnel in order to achieve similarity between the model and the prototype. (15 marks)

b) If the drag force on the model is 40 N, predict the drag force on the full-size car. (15 marks)**Question 2 (75 marks)**

The bathroom plumbing of a building consists of 1.5 cm diameter commercial steel pipes with threaded connectors, as shown in Fig. 1.

(a) If the gage pressure at the inlet of the system is 200 kPa during a shower and the toilet reservoir is full (no flow in that branch), determine the flow rate of water through the shower head. (40 marks)

(b) Determine the effect of flushing of the toilet on the flow rate through the shower head. (30 marks writing the equations +5 marks solving the equations)

Take the loss coefficients of the shower head and the reservoir to be 12 and 14, respectively.

Figure 1

**Question 3 (45 marks)**

A 2-m-high, 4-m-wide rectangular advertisement panel is attached to a 4-m-wide, 0.15-m-high rectangular concrete block (density=2300 kg/m3) by two 5-cm-diameter, 4-m-high (exposed part) poles, as shown in Figure 2. If the sign is to withstand 150 km/h winds from any direction, determine,

(a) The maximum drag force on the panel, (15 marks)

(b) The drag force acting on the poles, and (15 marks)

(c) The minimum length L of the concrete block for the panel to resist the winds.

(15 marks)

Take the density of air to be 1.30 kg/m3.