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C. Simple region 10 9 Reflected wave 8 Nonsimple region Simple region Incident wave Figure 7.16 I Reflected expansion wave on an xt diagram. Evaluate the constant by applying Eq. (7.82) in region 4: 144 + y 2a4 = 0 y 1 = const (7.83) Combining Eqs. (7.82) and (7.83), 2-1-2-4(4) 1 - 2 (7.84) Equation (7.84) relatee 7.10 The driver and driven gases of a pressure-driven shock tube are both air at 300 K. If the diaphragm pressure ratio is P4/P1 = 5, calculate: a. Strength of the incident shock (p2/p1) b. Strength of the reflected shock (ps/p2) c. Strength of the incident expansion wave (p3/p4) 7.11 For the shock tube in Prob. 7.10, the lengths of the driver and driven sections are 3 and 9 m, respectively. On graph paper, plot the wave diagram (xt diagram) showing the wave motion in the shock tube, including the incident and reflected shock waves, the contact surface, and the incident and reflected expansion waves. To construct the nonsimple region of the reflected expansion wave, use the method of characteristics as outlined in Sec. 7.6. Use at least four characteristic lines to define the incident expansion wave, as shown in Fig. 7.16.

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%Given data
r1 = 1.4;
r4 = 1.4;
R1 = 287;
R4 = 287;
T1 = 300;
T4 = T1;
%Calculation of Speed of Sound
a1 = sqrt(r1*R1*T1);
a4 = sqrt(r4*R4*T4);
P4P1 = 5;
P2P1 = 45.5554;
%Shock wave Calculations
Ms = sqrt(((r1+1)*P2P1+(r1-1))/(2*r1));
Cs = Ms*a1;
V2 = (2*Cs/(r1+1))*(1-((a1/Cs)*(a1/Cs)));
rho2rho1 = (r1+1)*Ms*Ms/((2+(r1-1)*Ms*Ms));
T2T1 = P2P1/rho2rho1;
T2 = T1*T2T1;
M2 = V2/sqrt(r1*R1*T2);
a2 = sqrt(r1*R1*T2);
%reflected shock wave
Cr = ((r1+1)/4)*V2+ sqrt((((r1+1)/4)*V2)*(((r1+1)/4)*V2)+a2*a2);
Wr = Cr - V2;
%Contact deformity
P2P4 = P2P1/P4P1;
V3 = V2;
%Finding x(t)
for i=1:length(t)
    x4(i) = -a4*t(i); % Expansion head
    x5(i) = (-a4+(0.7*(r4-1)/2)*V3)*t(i); %Expansion wave
    x6(i) = (-a4+(0.3*(r4-1)/2)*V3)*t(i); %Expansion wave
    x3(i) = (-a4+((r4-1)/2)*V3)*t(i); % Expansion tail
    x2(i) = V2*t(i); %Contact deformity
    %Contact is assumed to cease at the wall
    if x2(i)>(9)
       x2(i)= 9;

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