Question
Explain how you could vary the Mach number but not the Reynolds number in airflow past a sphere. For a constant Reynolds number of $300,000,$ estimate how much the drag coefficient will increase as the Mach number is increased from 0.3 to 1.0.
Step 1
The Mach number is the ratio of the speed of the object to the speed of sound in the fluid, while the Reynolds number is the ratio of inertial forces to viscous forces and is used to predict the onset of turbulence. The Mach number can be varied by changing the Show more…
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The National Transonic Facility (NTF) is a high-speed wind tunnel designed to operate with air at cryogenic temperatures to reduce viscosity, thus raising the unit Reynolds number $(R e / x)$ and reducing pumping power requirements. Operation is envisioned at temperatures of $-270^{\circ} \mathrm{F}$ and below. A schlieren photograph taken in the NTF shows a Mach angle of $57^{\circ}$ where $T=-270^{\circ} \mathrm{F}$ and $p=1.3$ psia. Evaluate the local Mach number and flow speed. Calculate the unit Reynolds number for the flow.
The drag characteristics of an airplane are to be determined by model tests in a wind tunnel operated at an absolute pressure of $1300 \mathrm{kPa}$. If the prototype is to cruise in standard air at 385 $\mathrm{km} / \mathrm{hr},$ and the corresponding speed of the model is not o differ by more than $20 \%$ from this (so that compressibility effects may be ignored), what range of length scales may be used if Reynolds number similarity is to be maintained? Assume the viscosity of air is unaffected by pressure, and the temperature of air in the tunnel is equal to the temperature of the air in which the airplane will fly.
The drag characteristics of an airplane are to be determined by model tests in a wind tunnel operated at an absolute pressure of 1300 kPa. If the prototype is to cruise in standard air at 385 $\mathrm{km} / \mathrm{hr},$ and the corresponding speed of the model is not to differ by more than $20 \%$ from this (so that compressibility effects may be ignored), what range of length scales may be used if Reynolds number similarity is to be maintained? Assume the viscosity of air is unaffected by pressure, and the temperature of air in the tunnel is equal to the temperature of the air in which the airplane will fly.
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