p1138 - 50 CHAPTER 11 POTENTIAL FLOW 11.38 Chapter 11...

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50 CHAPTER 11. POTENTIAL FLOW 11.38 Chapter 11, Problem 38 Problem: As an airplane taxis down the runway in preparation for takeoff, the velocity onthefuse lageis | u | = U · s L · t τ where s is arc length and t is time. The quantities U , L and τ are reference velocity, length and time scales related by L = U τ . In this problem, we examine the error in using a Pitot-static tube to infer velocity if effects of the acceleration (unsteadiness) are ignored (this problem had to be corrected to get the DC-10 certified by the FAA). (a) Neglecting body forces and assuming the flow is incompressible, compute the pressure coefficient, C p , defined by C p ( p p s ) / ( 1 2 ρ U 2 ) where p s is the pressure at the stagnation point ( s =0 ). Note that the velocity potential near the stagnation point is φ = 1 2 U ( s 2 /L )( t/ τ ) . (b) Starting with the value for C p computed in Part (a), use the steady-flow version of Bernoulli’s Equation to infer the velocity at s = L
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p1138 - 50 CHAPTER 11 POTENTIAL FLOW 11.38 Chapter 11...

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