Repeat Problem 9.13 using
a. Newtonian theory
b. Modified newtonian theory
Compare these results with those obtained from exact shock-expansion theory (Problem 9.13). From this comparison, what comments can you make about the accuracy of newtonian and modified newtonian theories at low supersonic Mach numbers?
(a)
The value of lift and wave-drag coefficients using Newtonian theory.
The comparison between the results obtain from exact shock-expansion theory.
Answer to Problem 14.1P
The lift and wave-drag coefficient at
The lift and wave-drag coefficient at
The lift and wave-drag coefficient at
Explanation of Solution
Given:
The angle of attack is
The angle of attack is
The angle of attack is
Formula used:
The expression for the lift coefficient is given as,
The expression for the wave-drag coefficient is given as,
Calculation:
The value of lift and wave-drag coefficient at
The lift coefficient can be calculated as,
The wave-drag coefficient can be calculated as,
The value of lift and wave-drag coefficient at
The lift coefficient can be calculated as,
The wave-drag coefficient can be calculated as,
The value of lift and wave-drag coefficient at
The lift coefficient can be calculated as,
The wave drag coefficient can be calculated as,
Conclusion:
Therefore, the lift and wave-drag coefficient at
Therefore, the lift and wave-drag coefficient at
Therefore, the lift and wave-drag coefficient at
(b)
The value of lift and wave-drag coefficients using modified Newtonian theory.
The comparison between the results obtain from exact shock-expansion theory.
Answer to Problem 14.1P
The lift and wave-drag coefficient at
The lift and wave-drag coefficient at
The lift and wave-drag coefficient at
Explanation of Solution
Given:
The angle of attack is
The angle of attack is
The angle of attack is
Formula used:
The expression for the lift coefficient is given as,
The expression for the wave-drag coefficient is given as,
Calculation:
The value of lift and wave-drag coefficient at
The lift coefficient can be calculated as,
The wave drag coefficient can be calculated as,
The value of lift and wave-drag coefficient at
The lift coefficient can be calculated as,
The wave drag coefficient can be calculated as,
The value of lift and wave-drag coefficient at
The lift coefficient can be calculated as,
The wave drag coefficient can be calculated as,
On comparing values obtained using Newtonian and modified Newtonian theory with shock expansion theory (prob 9.13), we can see that the error % goes up to 90% for
Conclusion:
Therefore, the lift and wave-drag coefficient at
Therefore, the lift and wave-drag coefficient at
Therefore, the lift and wave-drag coefficient at
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