Discussion
A thin airfoil is mounted in a low-speed, subsonic wind tunnel, in which the Mach number is 0.1. At a point on the airfoil, the pressure coefficient is measured to be -1.2. If the flow velocity is increased such that the free-stream Mach number is 0.6, the pressure coefficient at the same point on the airfoil will approximately be:
Answer: C
The pressure coefficient will be about -1.5.
The Prandtl-Glauert rule scales a thin airfoil's pressure coefficient with Mach number: \(C_{p} = C_{p,0}/\sqrt{1 - M^{2}}\), where \(C_{p,0}\) is the incompressible value. First recover \(C_{p,0}\) from the reading at M = 0.1, then scale it to M = 0.6:
\[ \begin{aligned} C_{p,0} &= -1.2\sqrt{1 - 0.01} \approx -1.194 \\ C_{p} &= \frac{-1.194}{\sqrt{1 - 0.36}} \\ &= \frac{-1.194}{0.8} \\ &\approx -1.49 \end{aligned} \]
At M = 0.1 the correction is negligible, so the answer is essentially -1.2 divided by 0.8. -0.75 multiplies by a factor less than 1 instead, as if compressibility weakened the suction; it strengthens it. -2.9 and -3.5 are far larger than any compressibility correction gives at M = 0.6 (even the Karman-Tsien rule gives only about -1.75).
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development