Given m,p→)fc,v,T设计计算 Given p,f→mn,c,v,T校核计算 (1) Continuity Equation(连续性方程) C-m v f·de+c.d=m·dhy ac C If y c then c must be adopted K then df<o c must be adopted
Given p, f m,c, v,T m,p f, c, v,T 校核计算 设计计算 → Given → (1) Continuity Equation (连续性方程） If then , c , must be adopted; If then , c , must be adopted; f c = m v f dc + c df = m dv c dc v dv f df = − c dc v dv df 0 c dc v dv df 0 (A)
For incompressible fluid 0 df dc f' C C (2). Energy Equation(能量方程) 0 0 0 8gdh+ dc2+g.dit Ws =-dh 2 c2=2(h1-h2) c2=V2(hn-h2)+c2
For incompressible fluid , (2). Energy Equation (能量方程) = 0 v dv c dc f df = − f c f , c q dh dc g dz +ws = + + 2 2 1 0 0 0 dh dc = − 2 2 2( ) 1 2 2 1 2 c2 − c = h − h 2 2 1 2 1 c = 2(h − h ) + c
For reversible process(可逆过程) dh=-w,=vdp C 1 2 Cac =-vap(B) If C thenp;如果C变大(C>0,则p必减少(dp<0) If C thenp itr果C变小(d<,则p必变小(dp>0 (3)Process Equation k k= For ideal gas(对理想气体)c For real gas, k is an empirical constant.〔对实际气体来二 说k是经验常数)
For reversible process (可逆过程) If then ; If then ; (3) Process Equation For ideal gas(对理想气体) For real gas, k is an empirical constant.(对实际气体来 说,k是经验常数) dh = −wt = vdp vdp dc = − 2 2 cdc = −vdp c p c p pv C k = v p c c k = (B) 如果 c 变大（ dc >0),则p必减少(dp<0); 如果 c 变小（ dc <0),则p必变小(dp>0)
k h1+1 p=0 vdp= kdv k (C) Eq (BX kpv cac= C C M p kp From Eq (c) du
0 1 + = − kpv dv v dp k k − vdp = kpdv p dp v dv k = − (C ) Eq. (B)× 2 c kp dp c kpv cdc c k p 2 2 = − a = kpv 2 dp M dc c k p 2 1 = − dv v k p From Eq.(C) dp = −
dc dy M ( D) Substitute Eq. D) into Eq (A) (M2-1 l) M 1> Supersonic region dc>0, then df>0 M<1 Subsonic region If dc>o, then df<o
v dv c dc M = 2 (D) Substitute Eq.(D) into Eq.(A) c dc M f df ( 1) 2 = − M 1 If dc 0, then df 0 Supersonic region M 1 Subsonic region If dc 0, then df 0