Transcript Chapter 5
Chapter 5 Worked-Out Examples 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 Approach: Appendix D 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. 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. 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. 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 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. 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 p p • Use Cp 1 rV2 2 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. 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).