University:
Duke University
Course:
PHYSICS 151L | Introductory Mechanics
Academic year:

2023
Views:

239

Pages:

2
Author:

Pemuda H

Momentum Conservation Equation (3.1.2) Spv (JR)do = F + Fs jot do Pwy P+ dp TraT Kdx- dw=dPs, -pvio + (p+dp) (v+dv)² ↑ (o + do) = F+ -ρνστ + (ρν + ραν + ναρ) (σν + νασ +σαν) + -pv²oi + (pv²o +pv²ασ +ρυσαν + ρσναν + ν²σαρ) = F + F -ρν²σί + ν (ρνο + ρνασ +ρσαν + ρσαν + σναρ) = F + F = 0 (mass conservation) -ρυσι + νερνο + ρσαν) ↑ = Fv + Fs ρυσανί= F+ =pf (o+o+do) axi = pfodxi ==pf( 2 ←← =-Gwcdxi + FP cdx is circumference of wall Fp=- Spñdo - poi - (p+dp) (o+do) i =î (ρό - ρε -ρασ-σαρ) Fs=-Twcdxi - (pdo+odp)î pvodv=pfodx - Twcdx-pdo-odp dv do ap prodx=pfo - Twc-pax - o de C First Low of Thermodynamics (Energy Conservation) (3.1.3) Q = Pss + Sp (h+v²+ge) vñdo = p (n+½v²) (-v) o+ (p+dp) (h+dh+ ½ (v+dv)²) (v+dv)(o+do) =-pvo(n+2)+(p+dp)(n+an+ 2 (v² + 2 vdv) (vo +νασ + σαν) = -pro (K+2) + (pvo +ρνασ + ρσαν + σναρ) (μ+dh+/½+vdv) = 0 αά-αρs,s = ρνσ (dh+vdv) = m (dh+vdv) do do = da Stagnation State (3.1.3.1) Fluid brought to rest adiabatically, with no work, and reversibly. O= ah+vdv h+ ½ v² = constant = n' * = h = ho Stagnation h T = CPT+2=CpTo A combination of static and stagnation means isentropic () = Po P Speed of Sound (3.2.1) a = NORT if isentropic dv do 10 p=0 since a shockwave is very small, do can be neglected v=a +=0 dv a P ρυσαν = - Twe dx-p do + pffdx dv = - pro do = - padv=-dp dp - pa a=0 => a = P pr = const Isentropic dp = const. d(pr) = const. rpdp = pr. rpdp = redo 8-1 = = P ⇒ P dp = = 8RT a= NORT Max Velocity (3.2.2) v2 ho = h + v = Nz(ho-h) = √2 Cp (To-T) = √2R(T-T) N So V max =N2RTO

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