You have purchased a wind tunnel for testing the aerodynamics of nose cones. The tunnel is shaped like a venturi tube for measuring the flow of the air. But wait, something is wrong! The company didn't send the datasheet for the tube, and they won't return your calls! How are you supposed to confirm the tube flow?
The main tubes of the wind tunnel have a diameter of 3m. The restricted portion of the tunnel has a smaller diameter of 2m. At full power, your pressure gauges are measuring 1200 Pa at the inlet and 200 Pa at the outlet. The wind tunnel is 60m long and made of structural steel.
Density of Air = 1.18 kg/m^3
Dynamic Viscosity of Air = 16.84x10^-6 Pa-s
a) Draw and label an orifice with a manometer attached.
b) Derive the equation for flow through an orifice.
c) What is the theoretical flow rate through your wind tunnel?
d) Given the theoretical flow, what is your flow velocity? What is your Reynolds number?
e) Use your answers from (c) and (d), and the table in Figure 2, what is your discharge coefficient?
f) Given your answers from (c), (d), and (e), what is the actual flow rate in the wind tunnel?
g) Using the Moody Chart in Figure 3, what is the relative roughness of your tunnel walls? What is the friction factor?
h) Given your answer to (g), what is the pressure drop per unit length? What is the total pressure drop?
i) Calculate the flow coefficient of your wind tunnel orifice
Discharge Coefficient - Cd
Reynolds Number - Re
105 106 0.595 0.594 0.603 0.598 0.608 0.603 0.61 0.608 0.614 0.609
Diameter Ratio - d=D/D
104 0.60 0.61 0.62 0.63 0.64
107 0.594 0.598 0.603 0.608 0.609
0.2 0.4 0.5 0.6 0.7
Figure 2 - Discharge Coefficient
Moody Diagram: Transition Region
0.1 0.09 0.08 0.07 0.06 0.05
0.05 0.04 0.03 0.02 0.015 0.01
0.04
0.03
0.005
Laminar Flow 64
0.002 0.001 510 210 104
Material Concrete, coarse
g (mm) 0.25 0.025 0.0025 0.0025 Complete Turbulence:
0.015
Drain tubing Plastic Pex 0.01 Iron, cast Sewers, old Steel, metal lined Steel, rusted
10^-5 5x10^-6 10^-6 10^8
0.025 1.0
Friction Factor =
AP
Smooth Pipe 105 106 107 Reynolds Number, Re = pVd
10^3
10^4
Figure 3 - Moody Chart (Wikipedia.org/wiki/Moody_Chart)
