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Chapter 5 Worked-Out Examples

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**5.2 NACA 1412 airfoil 3 foot chord 5 degree alpha**

100 ft/sec freestream speed at sea level Compute lift, drag forces, and moment about quarter-chord per unit span

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Approach: Appendix D

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**Approach First compute Reynolds number**

Look up Cl, Cd, Cm at closest Reynolds number. In real world applications, a computer program will interpolate between Reynolds numbers. Find L’, D’, and M at quarter chord using relationships that define these in terms of Cl, Cd, and Cm.

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**Problem 5.3 NACA 23012 airfoil Chord 0.3 m**

Freestream velocity 42 m/sec at 1 atm, 303 degree K. Find density r from equation of state. 8 degree angle of attack. We are asked to compute L’, D’, and M’ Same approach as 5.2, different airfoil, SI units.

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Problem 5.4 Same airfoil as 5.3, same freestream velocity, pressure, density, and temperature. We are given L’, asked to find alpha Approach: Find Cl first Look up the chart in appendix D for this airfoil to see at which angle of attack will this Cl result.

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**Problem 5.5 Wing made of NACA 0009 airfoil**

Given freestream velocity, freestream conditions, alpha. Given total lift L for the entire wing. Asked to find wing area S. Approach: Compute Reynolds number Look up Cl at this Reynolds number and alpha from appendix D This wing has the same Cl everywhere. Thus, CL of the wing is same as Cl of the airfoil. Find S from L = ½ * r * V ∞ * V∞ * CL * S

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Problem 5.6 We are asked to find max L/D for an airfoil (NACA 2412) at a Reynolds number of 9. Approach: L/D = Cl / Cd since density, chord, etc. all cancel. Select several angles of attack. Look up Cl and Cd at these alphas for this airfoil at this Reynolds number. Compute Cl/Cd for each of these angles of attack. See when maximum value occurs.

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**Problem 5.7 Given freestream velocity**

Standard sea level conditions (we know density and pressure p∞). We are given p at a point on the surface. Asked to find pressure coefficient Cp Use

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**Problem 5.8 Given freestream velocity V∞ of an airplane**

Given local velocity V at some point on the body. Asked to find pressure coefficient Cp Use Bernoulli’s equation. Manipulate it to arrive at Cp= 1 – [V/V∞]2 Find Cp from supplied info.

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Problem 5.9 Same approach as 5.8, since speed of the flow (160 feet/sec) is low compared to sound speed (~1100 ft/sec).

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