EAS4101_S10_HW9S - EAS 4101 Aerodynamics Spring 2010 HW 9 1...

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
EAS 4101 – Aerodynamics – Spring 2010 – HW 9 1. wind tunnel at in which the stagnation conditions are at S.T.P. (as defined in Anderson). Assume that this magical wind tunnel permits the flow to be isentropically expanded to variable Mach numbers. Calculate and plot the static temperature, static pressure, static density, and expanded veloc 12 0 M ≤≤ . What assum re needed to derive these equations and when do they breakdown? Consider an air ity for ptions a Assumptions: Break down at T > 600K and T < 200K) Isentropic Thermally and Calorically Perfect ( 1 3.5 3.5 22 0 0 1 1 2.5 2.5 0 0 1 11 2 0 0 2 0 0 1 1 1 0.2 1 0.2 2 1 1 1 0.2 1 0.2 2 1 1 1 0.2 1 0.2 2 101325 / 1. p MM p p p T T T M T pN m γ ργ ρρ ρ ⎛⎞ ⎜⎟ −− ⎝⎠ ⎡⎤ 2 2 M M ⎤⎡ =+ →= + ⎦⎣ ⎢⎥ ⎣⎦ + + = = () ( ) 3 0 23 / 287 1.4 287 kg m TK V MV M a M R T M T a = =→= = = Page 1 of 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
EAS 4101 – Aerodynamics – Spring 2010 – HW 9 Page 2 of 2
Background image of page 2
EAS 4101 – Aerodynamics – Spring 2010 – HW 9 : 1 2 0 1 1 2 p M p γ =+ , 1 1 2 0 1 1 2 M ρ 2. Prove the following stagnation relations . In addition to stagnation flow, what other assumptions are required? Assumptions: Stagnation Flow Isentropic Flow Thermally and Calorically Perfect Gas Define a Stagnation Enthalpy: 2 0 2 V hh For a perfect gas: Page 3 of 3
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
EAS 4101 – Aerodynamics – Spring 2010 – HW 9 () 2 2 0 ; 1 1 22 p p V V TT C RC C 0 2 2 pp p p hC T C T C =→ =+ 2 2 0 11 p CR pv v C p vv p R R TC R T γ CC V T V T γγ =−→ = −→ =− = = Define , V aR T M a == 2 0 2 2 0 1 1 2 00 0 1 1 1 1 2 0 1 1 2 1 1 2 1 1 2 1 1 2 V T Ta T M T pT p M p T M T ρρ ⎛⎞ = + ⎜⎟ ⎝⎠ = + 2 1 3. Prove the following normal shock relations: 2 2 2 1 2 1 2 1 1 M M M + = , 2 1 2 2 1 2 21 2 M T M TM +− ⎡⎤ ⎢⎥ ++ ⎣⎦ , 2 2 1 1 2 1 P M P = + , and 2 1 2 2 1 M M ρ ργ + = . What assumptions are needed to derive this equation? ssumptions: Adiabatic Flow Steady Flow Inviscid Flow Neglect Body Forces One-Dimensional Flow Zero net work done on or by the system Thermally and Calorically Perfect Gas (Break Down for T<200K and T>600K) A Page 4 of 4
Background image of page 4
EAS 4101 – Aerodynamics – Spring 2010 – HW 9 Conservation of Mass: d ρ ∫∫∫ t () ˆ 0 VndA += ∫∫ i K A 11 1 2 2 2 2 1 ; VA VA A A ρρ == 11 2 2 VV = 12 2 2 1 1 1 1 2 2 a M a aa a M a =→ = Conservation of Momentum: Vd t ∀+ K 22 2 2 1 1 2 2 . sc o n s t = 1 2 1 2 2 2 1 2 2 21 1 2 2 ˆˆ 1 1 AA V V n dA pndA pp V V a p a a MM Ma γρ γ γγ ργρ ργ =− −= = ⎡⎤ + ÷ ⎢⎥ ⎣⎦ ⎛⎞ + ⎜⎟ ⎝⎠ + = + KK i Combining Conservation of Mass and Momentum: a 2 2 1 a 2 2 1 1 aM + = + 2 1 M M Conservation of Energy: Page 5 of 5
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
EAS 4101 – Aerodynamics – Spring 2010 – HW 9 22 21 VV hhq += ++ w 11 1 12 2 2 2 1 2 1 ; 2 1 pp p pv hC T C T
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 14

EAS4101_S10_HW9S - EAS 4101 Aerodynamics Spring 2010 HW 9 1...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online