HW3soln - EAS 4101 S08 HW solutions 3rd Homework 1 3.6 p0 =...

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EAS 4101 S08 HW solutions Page 1 of 14 HW#3 02/13/08 3 rd Homework 1. 3.6 2 0 5 0 1 2 2( ) 2(1.07 1.01) 10 98.8m/s 1.23 pp V V ρ ∞∞ =+ −× == =

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EAS 4101 S08 HW solutions Page 2 of 14 HW#3 2.
EAS 4101 S08 HW solutions Page 3 of 14 HW#3

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EAS 4101 S08 HW solutions Page 4 of 14 HW#3 3.
EAS 4101 S08 HW solutions Page 5 of 14 HW#3 4.

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EAS 4101 S08 HW solutions Page 6 of 14 HW#3 5. Given: Hurricane flow over a Quonset hut of weight W , radius R and length l , with the stream function being () 2 2 , sin 1 , and 0 R rV r r R r θ θθ π ⎡⎤ Ψ= ⎢⎥ ⎣⎦ Find: a) List the appropriate assumptions. b) Determine the velocity, ( ) ( )( ) ˆˆ ,, , rr VR V R e V R e =+ JK c) What is the maximum and minimum velocity on the surface of the hut? d) Is this flow irrotational? e) What is the gage pressure distribution on the surface of the hut ( i.e. , , pR )? f) Integrate the pressure over the surface to find the lift force on the hut. g) Determine V that will lift the hut off of its foundation. h) Integrate the pressure over the surface to find the drag force on the hut. Schematic: p(inf) R θ V(inf), p(inf) e r e θ
EAS 4101 S08 HW solutions Page 7 of 14 HW#3 SOLUTION: a) Assume 2-D flow, incompressible, inviscid, steady, flow along a streamline, neglect z Δ , inside of hut is at atmospheric pressure. b) Using the definition of the stream function, the velocity components are computed to be 22 2 23 2 1 cos 1 cos 1 sin 1 sin 2 sin 1 r RR VV r V rr r R V r V r θ θθ ∞∞ ⎡⎤ ⎛⎞ =− = ⎢⎥ ⎜⎟ ⎝⎠ ⎣⎦ + + Thus the velocity at the surface of the hut is ( ) ( ) ˆ ,2 s i n VR V e c) The maximum and minimum velocities at the surface of the hut occur when sin is a maximum and minimum, respectively, thus ( ) () max min ˆ ,9 0 2 , 0 ,180 0 V e = °= d) Computing the curl of the velocity field, 1 ˆ z r V V Ve rz ∇× = ∂∂ JK 0 ˆ e zr = +− 0 11 ˆ r rV V k = where 2 2 2 2 sin 1 sin 2 sin 1 sin 1 r rV R r V r r V R V r +

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EAS 4101 S08 HW solutions Page 8 of 14 HW#3 therefore 0 the flow is irrotational V ∇× = → JK , then again, you knew this because it was an ideal flow problem.
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HW3soln - EAS 4101 S08 HW solutions 3rd Homework 1 3.6 p0 =...

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