From b1f5c3f8d6671b4331cef1dcebdf63b7a43a3a2b Mon Sep 17 00:00:00 2001 From: priyanka Date: Wed, 24 Jun 2015 15:03:17 +0530 Subject: initial commit / add all books --- 551/CH13/EX13.1/1.sce | 24 ++++++++++++++ 551/CH13/EX13.10/10.sce | 44 ++++++++++++++++++++++++++ 551/CH13/EX13.11/11.sce | 25 +++++++++++++++ 551/CH13/EX13.12/12.sce | 29 +++++++++++++++++ 551/CH13/EX13.13/13.sce | 78 +++++++++++++++++++++++++++++++++++++++++++++ 551/CH13/EX13.14/14.sce | 39 +++++++++++++++++++++++ 551/CH13/EX13.15/15.sce | 32 +++++++++++++++++++ 551/CH13/EX13.17/17.sce | 10 ++++++ 551/CH13/EX13.18/18.sce | 15 +++++++++ 551/CH13/EX13.19/19.sce | 16 ++++++++++ 551/CH13/EX13.2/2.sce | 46 +++++++++++++++++++++++++++ 551/CH13/EX13.20/20.sce | 15 +++++++++ 551/CH13/EX13.21/21.sce | 81 +++++++++++++++++++++++++++++++++++++++++++++++ 551/CH13/EX13.22/22.sce | 46 +++++++++++++++++++++++++++ 551/CH13/EX13.23/23.sce | 19 +++++++++++ 551/CH13/EX13.24/24.sce | 9 ++++++ 551/CH13/EX13.25/25.sce | 46 +++++++++++++++++++++++++++ 551/CH13/EX13.26/26.sce | 66 ++++++++++++++++++++++++++++++++++++++ 551/CH13/EX13.27/27.sce | 32 +++++++++++++++++++ 551/CH13/EX13.28/28.sce | 41 ++++++++++++++++++++++++ 551/CH13/EX13.29/29.sce | 83 ++++++++++++++++++++++++++++++++++++++++++++++++ 551/CH13/EX13.3/3.sce | 63 +++++++++++++++++++++++++++++++++++++ 551/CH13/EX13.30/30.sce | 84 +++++++++++++++++++++++++++++++++++++++++++++++++ 551/CH13/EX13.31/31.sce | 27 ++++++++++++++++ 551/CH13/EX13.32/32.sce | 25 +++++++++++++++ 551/CH13/EX13.33/33.sce | 40 +++++++++++++++++++++++ 551/CH13/EX13.34/34.sce | 17 ++++++++++ 551/CH13/EX13.35/35.sce | 34 ++++++++++++++++++++ 551/CH13/EX13.36/36.sce | 21 +++++++++++++ 551/CH13/EX13.37/37.sce | 44 ++++++++++++++++++++++++++ 551/CH13/EX13.38/38.sce | 19 +++++++++++ 551/CH13/EX13.39/39.sce | 30 ++++++++++++++++++ 551/CH13/EX13.4/4.sce | 21 +++++++++++++ 551/CH13/EX13.40/40.sce | 36 +++++++++++++++++++++ 551/CH13/EX13.41/41.sce | 25 +++++++++++++++ 551/CH13/EX13.42/42.sce | 17 ++++++++++ 551/CH13/EX13.43/43.sce | 40 +++++++++++++++++++++++ 551/CH13/EX13.44/44.sce | 25 +++++++++++++++ 551/CH13/EX13.45/45.sce | 57 +++++++++++++++++++++++++++++++++ 551/CH13/EX13.46/46.sce | 27 ++++++++++++++++ 551/CH13/EX13.47/47.sce | 50 +++++++++++++++++++++++++++++ 551/CH13/EX13.48/48.sce | 50 +++++++++++++++++++++++++++++ 551/CH13/EX13.49/49.sce | 42 +++++++++++++++++++++++++ 551/CH13/EX13.5/5.sce | 17 ++++++++++ 551/CH13/EX13.7/7.sce | 8 +++++ 551/CH13/EX13.8/8.sce | 25 +++++++++++++++ 551/CH13/EX13.9/9.sce | 50 +++++++++++++++++++++++++++++ 47 files changed, 1690 insertions(+) create mode 100755 551/CH13/EX13.1/1.sce create mode 100755 551/CH13/EX13.10/10.sce create mode 100755 551/CH13/EX13.11/11.sce create mode 100755 551/CH13/EX13.12/12.sce create mode 100755 551/CH13/EX13.13/13.sce create mode 100755 551/CH13/EX13.14/14.sce create mode 100755 551/CH13/EX13.15/15.sce create mode 100755 551/CH13/EX13.17/17.sce create mode 100755 551/CH13/EX13.18/18.sce create mode 100755 551/CH13/EX13.19/19.sce create mode 100755 551/CH13/EX13.2/2.sce create mode 100755 551/CH13/EX13.20/20.sce create mode 100755 551/CH13/EX13.21/21.sce create mode 100755 551/CH13/EX13.22/22.sce create mode 100755 551/CH13/EX13.23/23.sce create mode 100755 551/CH13/EX13.24/24.sce create mode 100755 551/CH13/EX13.25/25.sce create mode 100755 551/CH13/EX13.26/26.sce create mode 100755 551/CH13/EX13.27/27.sce create mode 100755 551/CH13/EX13.28/28.sce create mode 100755 551/CH13/EX13.29/29.sce create mode 100755 551/CH13/EX13.3/3.sce create mode 100755 551/CH13/EX13.30/30.sce create mode 100755 551/CH13/EX13.31/31.sce create mode 100755 551/CH13/EX13.32/32.sce create mode 100755 551/CH13/EX13.33/33.sce create mode 100755 551/CH13/EX13.34/34.sce create mode 100755 551/CH13/EX13.35/35.sce create mode 100755 551/CH13/EX13.36/36.sce create mode 100755 551/CH13/EX13.37/37.sce create mode 100755 551/CH13/EX13.38/38.sce create mode 100755 551/CH13/EX13.39/39.sce create mode 100755 551/CH13/EX13.4/4.sce create mode 100755 551/CH13/EX13.40/40.sce create mode 100755 551/CH13/EX13.41/41.sce create mode 100755 551/CH13/EX13.42/42.sce create mode 100755 551/CH13/EX13.43/43.sce create mode 100755 551/CH13/EX13.44/44.sce create mode 100755 551/CH13/EX13.45/45.sce create mode 100755 551/CH13/EX13.46/46.sce create mode 100755 551/CH13/EX13.47/47.sce create mode 100755 551/CH13/EX13.48/48.sce create mode 100755 551/CH13/EX13.49/49.sce create mode 100755 551/CH13/EX13.5/5.sce create mode 100755 551/CH13/EX13.7/7.sce create mode 100755 551/CH13/EX13.8/8.sce create mode 100755 551/CH13/EX13.9/9.sce (limited to '551/CH13') diff --git a/551/CH13/EX13.1/1.sce b/551/CH13/EX13.1/1.sce new file mode 100755 index 000000000..450b4c5e2 --- /dev/null +++ b/551/CH13/EX13.1/1.sce @@ -0,0 +1,24 @@ +clc +T1=671; //K +T2=T1; +T3=313; //K +T4=T3; +W=130; //kJ + +disp("(i) Engine thermal efficiency =") +n_th=(T2-T3)/T2; +disp(n_th) + + +disp("(ii) Heat added =") +Q=W/n_th; +disp(Q) +disp("kJ") + + +disp("(iii) The entropy changes during heat rejection process") +Q_rejected=Q-W; +dS=Q_rejected/T3; +disp("dS=") +disp(dS) +disp("kJ/K") \ No newline at end of file diff --git a/551/CH13/EX13.10/10.sce b/551/CH13/EX13.10/10.sce new file mode 100755 index 000000000..2c41c5b4a --- /dev/null +++ b/551/CH13/EX13.10/10.sce @@ -0,0 +1,44 @@ +clc +r=6; //v1/v2=v4/v3=r +p1=1; //bar +T1=300; //K +T3=1842; //K +y=1.4; + +disp("(i) Temperature and pressure after the isentropic expansion") +p2=p1*(r)^y; +T2=T1*r^(y-1); +p3=p2*(T3/T2); + +T4=T3/r^(y-1); +disp("T4=") +disp(T4) +disp("K") + +p4=p3/(r)^(y); +disp("p4 =") +disp(p4) +disp("bar") + +disp("(ii) Process required to complete the cycle") + +disp("Process required to complete the cycle is the constant pressure scavenging. The cycle is called Atkinson cycle") + +disp("(iii) Percentage improvement/increase in efficiency") +p5=1; //bar +T5=T3*(p5/p3)^((y-1)/y); + +n_otto=(1-1/r^(y-1))*100; +disp("n_otto = ") +disp(n_otto) +disp("%") + +n_atkinson=(1-y*(T5-T1)/(T3-T2))*100; +disp("n_atkinson=") +disp(n_atkinson) +disp("%") + +dn=n_atkinson - n_otto; //Improvement in efficiency +disp("Improvement in efficiency =") +disp(dn) +disp("%") \ No newline at end of file diff --git a/551/CH13/EX13.11/11.sce b/551/CH13/EX13.11/11.sce new file mode 100755 index 000000000..c3fc6cf66 --- /dev/null +++ b/551/CH13/EX13.11/11.sce @@ -0,0 +1,25 @@ +clc +p1=1; //bar +T1=343; //K +p2=7; //bar +Qs=465; //kJ/kg of air +cp=1; //kJ/kg K +cv=0.706; //kJ/kg K +y=1.41; + +disp("(i) Compression ratio of engine =") +r=(p2/p1)^(1/y); +disp(r) + + +disp("(ii) Temperature at the end of compression =") +T2=T1*(r)^(y-1); +t2=T2-273; +disp(t2) +disp("0C") + +disp("(iii) Temperature at the end of heat addition =") +T3=Qs/cv+T2; +t3=T3-273; +disp(t3) +disp("0C") diff --git a/551/CH13/EX13.12/12.sce b/551/CH13/EX13.12/12.sce new file mode 100755 index 000000000..2798c8b39 --- /dev/null +++ b/551/CH13/EX13.12/12.sce @@ -0,0 +1,29 @@ +clc + +y=1.4; +R=0.287; //kJ/kg K +T1=311; //K +T3=2223; //K +//p2/p1=15 + +disp("(i) Compression ratio =") +r=15^(1/1.4); +disp(r) + + +disp("(ii) Thermal efficiency =") +n_th=1-1/r^(y-1); +disp(n_th) + +disp("(iii) Work done") +T2=T1*(r)^(y-1); +T4=T3/r^(y-1); +cv=R/(y-1); + +Q_supplied=cv*(T3-T2); +Q_rejected=cv*(T4-T1); + +W=Q_supplied-Q_rejected; +disp("Work done=") +disp(W) +disp("kJ") \ No newline at end of file diff --git a/551/CH13/EX13.13/13.sce b/551/CH13/EX13.13/13.sce new file mode 100755 index 000000000..f941e0f20 --- /dev/null +++ b/551/CH13/EX13.13/13.sce @@ -0,0 +1,78 @@ +clc +V1=0.45; //m^3 +p1=1; //bar +T1=303; //K +p2=11; //bar +Qs=210; //kJ +n=210; //number of working cycles/min +R=287; //J/kg K +cv=0.71; //kJ/kg K +y=1.4; + +disp("(i) Pressures, temperatures and volumes at salient points") +r=(p2/p1)^(1/y); + +T2=T1*(r)^(y-1); +disp("T2=") +disp(T2) +disp("K") + +V2=T2/T1*p1/p2*V1; +disp("V2=") +disp(V2) +disp("m^3") + +m=p1*10^5*V1/R/T1; +T3=Qs/m/cv+T2; +disp("T3=") +disp(T3) +disp("K") + +p3=T3/T2*p2; +disp("p3=") +disp(p3) +disp("bar") + +V3=V2; +disp("V3=") +disp(V3) +disp("m^3") + +p4=p3/r^y; +disp("p4=") +disp(p4) +disp("bar") + +T4=T3/r^(y-1); +disp("T4=") +disp(T4) +disp("K") + +V4=V1; +disp("V4=") +disp(V4) +disp("m^3") + + +disp("(ii) Percentage clearance =") +%clearance=V2/(V1-V2)*100; +disp(%clearance) +disp("%") + + +disp("(iii) Efficiency =") +Qr=m*cv*(T4-T1); +n_otto=(Qs-Qr)/Qs; +disp(n_otto) + + +disp("(iv) Mean effective pressure =") +p_m=(Qs-Qr)/(V1-V2)/100; //bar +disp(p_m) +disp("bar") + + +disp("(v) Power developed =") +P=(Qs-Qr)*n/60; +disp(P) +disp("kW") \ No newline at end of file diff --git a/551/CH13/EX13.14/14.sce b/551/CH13/EX13.14/14.sce new file mode 100755 index 000000000..cdcd079d5 --- /dev/null +++ b/551/CH13/EX13.14/14.sce @@ -0,0 +1,39 @@ +clc + +// W=Qs-Qr=cv*(T3-T2) - cv*(T4-T1) +// T2=T1*(r^(y-1)) +// T3=T4*(r^(y-1)) +// W=cv*[T3-T1*r^(y-1) - T3/r^(y-1)+T1]; +// dW/dr=-T1*(y-1)*r^(y-2) - T3*(1-y)*r^(-y)=0 + +//By solving this we get + +disp("r=(T3/T1)^(1/2/(y-1))") + +disp("(b)Change in efficiency") + +T3=1220; //K +T1=310; //K + +// For air +y=1.4; +r1=(T3/T1)^(1/2/(y-1)); +n1=1-1/r1^(y-1); //air standard Efficiency +disp("Air standard Efficiency =") +disp(n1) + +//For helium +cp=5.22; //kJ/kg K +cv=3.13; //kJ/kg K +y=cp/cv; +r2=(T3/T1)^(1/2/(y-1)); + +n2=1-1/r2^(y-1); +disp("Air standard efficiency for helium =") +disp(n2) + +change=n1-n2; +disp("Change in efficiency=") +disp(change) + +disp("Hence change in efficiency is nil") \ No newline at end of file diff --git a/551/CH13/EX13.15/15.sce b/551/CH13/EX13.15/15.sce new file mode 100755 index 000000000..a7aeb5aad --- /dev/null +++ b/551/CH13/EX13.15/15.sce @@ -0,0 +1,32 @@ +clc +// W=cv*[T3-T1*r^(y-1) - T3/r^(y-1)+T1] +// r=(T3/T1)^(1/2/(y-1)) +// T2=T1*r^(y-1) +// T4=T3/r^(y-1) + +// T2=T1*[(T3/T1)^(1/2/(y-1))]^(y-1) + + +//T2=sqrt(T1*T3) + +//Similarly T4=T3/[(T3/T1)^(1/2/(y-1))]^(y-1) +//T4=sqrt(T1*T3) + +disp("T2=T4=sqrt(T1*T3)") + + +disp("(b) Power developed ") +T1=310; //K +T3=1450; //K +m=0.38; //kg +cv=0.71; //kJ/kg K + +T2=sqrt(T1*T3); +T4=T2; + +W1=cv*[(T3-T2) - (T4-T1)]; //Work done +W=m/60*W1; //Work done per second + +disp("Power =") +disp(W) +disp("kW") \ No newline at end of file diff --git a/551/CH13/EX13.17/17.sce b/551/CH13/EX13.17/17.sce new file mode 100755 index 000000000..ef5ba6174 --- /dev/null +++ b/551/CH13/EX13.17/17.sce @@ -0,0 +1,10 @@ +clc +r=15; +y=1.4; + +//V3-V2=0.06*(V1-V2) +rho=1.84; //cut off ratio rho=V3/V2 + +n_diesel=1-1/y/r^(y-1)*((rho^y-1)/(rho-1)); +disp("efficiency =") +disp(n_diesel) diff --git a/551/CH13/EX13.18/18.sce b/551/CH13/EX13.18/18.sce new file mode 100755 index 000000000..1fb6d1c68 --- /dev/null +++ b/551/CH13/EX13.18/18.sce @@ -0,0 +1,15 @@ +clc + +L=0.25; //m +D=0.15; //m +V2=0.0004; //m^3 +Vs=%pi/4*D^2*L; +V_total=Vs+V2; +y=1.4; +V3=V2+5/100*Vs; +rho=V3/V2; +r=(Vs+V2)/V2; //V1=Vs+V2 + +n_diesel=1-1/y/r^(y-1)*((rho^y-1)/(rho-1)); +disp("efficiency =") +disp(n_diesel) \ No newline at end of file diff --git a/551/CH13/EX13.19/19.sce b/551/CH13/EX13.19/19.sce new file mode 100755 index 000000000..25f36a543 --- /dev/null +++ b/551/CH13/EX13.19/19.sce @@ -0,0 +1,16 @@ +clc +r=14; //let clearance volume be unity +y=1.4; + +//When the fuel is cut-off at 5% +rho1=5/100*(r-1)+1; +n_diesel1=1-1/y/r^(y-1)*((rho1^y-1)/(rho1-1)); + +//When the fuel is cut-off at 8% +rho2=8/100*(r-1)+1; +n_diesel2=1-1/y/r^(y-1)*((rho2^y-1)/(rho2-1)); + +%loss=(n_diesel1-n_diesel2)*100; +disp("percentage loss in efficiency due to delay in fuel cut off =") +disp(%loss) +disp("%") \ No newline at end of file diff --git a/551/CH13/EX13.2/2.sce b/551/CH13/EX13.2/2.sce new file mode 100755 index 000000000..dcd8dac1a --- /dev/null +++ b/551/CH13/EX13.2/2.sce @@ -0,0 +1,46 @@ +clc +cv=0.721; //kJ/kg K +cp=1.008; //kJ/kg K +m=0.5; //kg +n_th=0.5; +Q_isothermal=40; //kJ +p1=7*10^5; //Pa +V1=0.12; //m^3 +R=287; //J/kg K + +disp("(i) The maximum and minimum temperatures") +T1=p1*V1/m/R; +disp("Maximun temperature =") +disp(T1) +disp("K") + +T2=(1-n_th)*T1; +disp("Minimum temperature =") +disp(T2) +disp("K") + + +disp("(ii) The volume at the end of isothermal expansion =") +V2=V1*%e^(Q_isothermal*10^3/m/R/T1); +disp(V2) +disp("m^3") + + +disp("(iii) The heat transfer for each of the four processes") + +Q1=Q_isothermal; +disp("Isothermal expansion") +disp(Q1) +disp("kJ") + +Q2=0; +disp("Adiabatic reversible expansion") +disp(Q2) + +Q3=-Q_isothermal; +disp("Isothermal compression") +disp(Q3) + +Q4=0; +disp("Adiabatic reversible compression") +disp(Q4) \ No newline at end of file diff --git a/551/CH13/EX13.20/20.sce b/551/CH13/EX13.20/20.sce new file mode 100755 index 000000000..9e2ade33a --- /dev/null +++ b/551/CH13/EX13.20/20.sce @@ -0,0 +1,15 @@ +clc + +pm=7.5; //bar +r=12.5; +p1=1; //bar +y=1.4; + +// pm = p1*r^y*[y*(rho-1) - r^(1-y)*(rho^y-1)]/(y-1)/(r-1) +//Solving above equation we get +rho=2.24; + +%cutoff=(rho-1)/(r-1)*100; +disp("%cutoff=") +disp(%cutoff) +disp("%") \ No newline at end of file diff --git a/551/CH13/EX13.21/21.sce b/551/CH13/EX13.21/21.sce new file mode 100755 index 000000000..3afd2c579 --- /dev/null +++ b/551/CH13/EX13.21/21.sce @@ -0,0 +1,81 @@ +clc +D=0.2; //m +L=0.3; //m +p1=1; //bar +T1=300; //K +R=287; +r=15; +y=1.4; + +disp("(i) Pressures and temperatures at salient points") +Vs=%pi/4*D^2*L; + +V1=r/(r-1)*Vs; +disp("V1=") +disp(V1) +disp("m^3") + +m=p1*10^5*V1/R/T1; + +p2=p1*r^y; +disp("p2=") +disp(p2) +disp("bar") + +T2=T1*r^(y-1); +disp("T2=") +disp(T2) +disp("K") + +V2=Vs/(r-1); +disp("V2=") +disp(V2) +disp("m^3") + +rho=8/100*(r-1) + 1; +V3=rho*V2; +disp("V3=") +disp(V3) +disp("m^3") + +T3=T2*V3/V2; +disp("T3=") +disp(T3) +disp("K") + +p3=p2; +disp("p3=") +disp(p3) +disp("bar") + +p4=p3*(rho/r)^y; +disp("p4=") +disp(p4) +disp("bar") + +T4=T3*(rho/r)^(y-1); +disp("T4=") +disp(T4) +disp("K") + +V4=V1; +disp("V4=") +disp(V4) +disp("m^3") + +disp("(ii) Theoretical air standard efficiency =") +n_diesel=1-1/y/r^(y-1)*((rho^y-1)/(rho-1)); +disp("efficiency =") +disp(n_diesel) + + +disp("(iii) Mean effective pressure =") +pm=(p1*r^y*(y*(rho-1) - r^(1-y)*(rho^y-1)))/(y-1)/(r-1); +disp(pm) +disp("bar") + +disp("(iv) Power of the engine =") +n=380; //number of cycles per min +P=n/60*pm*Vs*100; //kW +disp(P) +disp("kW") diff --git a/551/CH13/EX13.22/22.sce b/551/CH13/EX13.22/22.sce new file mode 100755 index 000000000..40d145d54 --- /dev/null +++ b/551/CH13/EX13.22/22.sce @@ -0,0 +1,46 @@ +clc +r1=15.3; //V1/V2 +r2=7.5; //V4/V3 +p1=1; //bar +T1=300; //K +n_mech=0.8; +C=42000; //kJ/kg +y=1.4; +R=287; +cp=1.005; +cv=0.718; +V2=1; ////Assuming V2=1 m^3 + +T2=T1*r1^(y-1); +p2=p1*r1^y; +T3=r1/r2*T2; +m=p2*10^5*V2/R/T2; +T4=T3/r2^(y-1); + +Q_added=m*cp*(T3-T2); +Q_rejected=m*cv*(T4-T1); +W=Q_added-Q_rejected; + +pm=W/(r1-1)/V2/100; +disp("Mean effective pressure =") +disp(pm) +disp("bar") + +ratio=p2/pm; +disp("Ratio of maximum pressure to mean effective pressure =") +disp(ratio) + +n_cycle=W/Q_added; +disp("Cycle efficiency =") +disp(n_cycle) + +n_thI=0.5; +n_cycle1=n_thI*n_cycle; + +n_thB=n_mech*n_cycle1; + +BP=1; +mf=BP/C/n_thB*3600; +disp("Fuel consumption per kWh =") +disp(mf) +disp("kg/kWh") \ No newline at end of file diff --git a/551/CH13/EX13.23/23.sce b/551/CH13/EX13.23/23.sce new file mode 100755 index 000000000..20d2f678f --- /dev/null +++ b/551/CH13/EX13.23/23.sce @@ -0,0 +1,19 @@ +clc +Vs=0.0053; //m^3 +Vc=0.00035; //m^3 +V3=Vc; +V2=V3; +p3=65; //bar +p4=65; //bar +T1=353; //K +p1=0.9; //bar +y=1.4; + +r=(Vs+Vc)/Vc; +rho=(5/100*Vs+V3)/V3; +p2=p1*(r)^y; +B=p3/p2; + +n_dual=1-1/r^(y-1)*[(B*rho^y-1)/((B-1)+B*y*(rho-1))]; +disp("Efficiency of the cycle =") +disp(n_dual) \ No newline at end of file diff --git a/551/CH13/EX13.24/24.sce b/551/CH13/EX13.24/24.sce new file mode 100755 index 000000000..71a4283dd --- /dev/null +++ b/551/CH13/EX13.24/24.sce @@ -0,0 +1,9 @@ +clc +r=14; +B=1.4; +rho=6/100*(r-1) + 1; +y=1.4; + +n_dual=1-1/r^(y-1)*[(B*rho^y-1)/((B-1)+B*y*(rho-1))] +disp("Efficiency of the cycle =") +disp(n_dual) \ No newline at end of file diff --git a/551/CH13/EX13.25/25.sce b/551/CH13/EX13.25/25.sce new file mode 100755 index 000000000..026f5cb9a --- /dev/null +++ b/551/CH13/EX13.25/25.sce @@ -0,0 +1,46 @@ +clc +D=0.25; //m +r=9; +L=0.3; //m +cv=0.71; //kJ/kg K +cp=1; //kJ/kg K +p1=1; //bar +T1=303; //K +p3=60; //bar +p4=p3; +n=3; //number of working cycles/ sec +y=1.4; +R=287; + +disp("(i) Air standard efficiency") +Vs=%pi/4*D^2*L; + +Vc=Vs/(r-1); +V1=Vs+Vc; +p2=p1*(r)^y; +T2=T1*r^(y-1); +T3=T2*p3/p2; +rho=4/100*(r-1)+1; +T4=T3*rho; + +T5=T4*(rho/r)^(y-1); +p5=p4*(r/rho)^(y); + +Qs=cv*(T3-T2)+cp*(T4-T3) + +Qr=cv*(T5-T1); + +n_airstandard=(Qs-Qr)/Qs; +disp("efficiency =") +disp(n_airstandard) + + +disp("(ii) Power developed by the engine") +m=p1*10^5*V1/R/T1; + +W=m*(Qs-Qr); + +P=W*n; +disp("P=") +disp(P) +disp("kW") \ No newline at end of file diff --git a/551/CH13/EX13.26/26.sce b/551/CH13/EX13.26/26.sce new file mode 100755 index 000000000..bcf833d65 --- /dev/null +++ b/551/CH13/EX13.26/26.sce @@ -0,0 +1,66 @@ +clc +p1=1; //bar +T1=363; //K +r=9; +p3=68; //bar +p4=68; //bar +Q=1750; //kJ/kg +y=1.4; +cv=0.71; +cp=1.0; + +disp("(i) Pressures and temperatures at salient points") +p2=p1*(r)^y; +disp("p2=") +disp(p2) +disp("bar") + +T2=T1*r^(y-1); +disp("T2=") +disp(T2) +disp("K") + +disp("p3=") +disp(p3) +disp("bar") + +disp("p4=") +disp(p4) +disp("bar") + +T3=T2*(p3/p2); +disp("T3=") +disp(T3) +disp("K") + +Q1=cv*(T3-T2); //heat added at constant volume +Q2=Q-Q1; //heat added at constant pressure + +T4=Q2/cp+T3; +disp("T4=") +disp(T4) +disp("K") + +rho=T4/T3; //V4/V3=T4/T3 + +p5=p4*(rho/r)^y; +disp("p5=") +disp(p5) +disp("bar") + +T5=T4*(rho/r)^(y-1); +disp("T5=") +disp(T5) +disp("K") + + +disp("(ii) Air standard efficiency =") +Qr=cv*(T5-T1); +n_airstandard=(Q-Qr)/Q; +disp(n_airstandard) + + +disp("(iii) Mean effective pressure =") +pm=1/(r-1)*(p3*(rho-1) + (p4*rho-p5*r)/(y-1) - (p2-p1*r)/(y-1)); +disp(pm) +disp("bar") diff --git a/551/CH13/EX13.27/27.sce b/551/CH13/EX13.27/27.sce new file mode 100755 index 000000000..edbbc6e33 --- /dev/null +++ b/551/CH13/EX13.27/27.sce @@ -0,0 +1,32 @@ +clc +T1=300; //K +r=15; +y=1.4; +//p3/p1=70 + +T2=T1*(r)^(y-1); + +//p2/p1=r^y +//p2=44.3*p1 + +T3=1400; //K; T3=T2*p3/p2 + +T4=T3 + (T3-T2)/y; + +//v1/v3=15 +//v4=0.084*v1 +//v5=v1 +//T5=T4*(v5/v1)^(y-1) +T5=656.9; //K + +n_airstandard=1-(T5-T1)/((T3-T2) + y*(T4-T3)); +disp("Efficiency =") +disp(n_airstandard) + +disp("Reasons for actual thermal efficiency being different from the theoretical value :") + +disp("1. In theoretical cycle working substance is taken air whereas in actual cycle air with fuel acts as working substance") + +disp("2. The fuel combustion phenomenon and associated problems like dissociation of gases, dilution of charge during suction stroke, etc. have not been taken into account") + +disp("3. Effect of variable specific heat, heat loss through cylinder walls, inlet and exhaust velocities of air/gas etc. have not been taken into account.") \ No newline at end of file diff --git a/551/CH13/EX13.28/28.sce b/551/CH13/EX13.28/28.sce new file mode 100755 index 000000000..ea5a48a84 --- /dev/null +++ b/551/CH13/EX13.28/28.sce @@ -0,0 +1,41 @@ +clc +T1=373; //K +p1=1; //bar +p3=65; //bar +p4=p3; +Vs=0.0085; //m^3 +ratio=21; //Air fuel ratio +r=15; +C=43890; //kJ/kg +cp=1; +cv=0.71; +V2=0.0006; //m^3 +V1=0.009; //m^3 +y=1.41; +V5=V1; +V3=V2; +R=287; + +p2=p1*(r)^y; +T2=T1*r^(y-1); +T3=T2*p3/p2; +m=p1*10^5*V1/R/T1; + +Q1=m*cv*(T3-T2); //Heat added during constant volume process 2-3 +amt=Q1/C; //Amount of fuel added during the constant volume process 2-3 +total=m/ratio; //Total amount of fuel added +quantity=total-amt; //Quantity of fuel added during the process 3-4 + +Q2=quantity*C; //Heat added during constant pressure process + +T4=Q2/(m+total)/cp+T3; +V4=V3*T4/T3; +T5=T4*(V4/V5)^(y-1); + +Q3=(m+total)*cv*(T5-T1); //Heat rejected during constant volume process 5-1 + +W=(Q1+Q2) - Q3; + +n_th=W/(Q1+Q2); +disp("Thermal efficiency =") +disp(n_th) \ No newline at end of file diff --git a/551/CH13/EX13.29/29.sce b/551/CH13/EX13.29/29.sce new file mode 100755 index 000000000..69fc24891 --- /dev/null +++ b/551/CH13/EX13.29/29.sce @@ -0,0 +1,83 @@ +clc +T1=303; //K +p1=1; //bar +rc=9; +re=5; +n=1.25; +D=0.25; //m +L=0.4; //m +R=287; +cv=0.71; +cp=1; +num=8; //no. 0f cycles/sec + +disp("(i) Pressure and temperatures at all salient points =") +p2=p1*(rc)^n; +disp("p2=") +disp(p2) +disp("bar") + +T2=T1*(rc)^(n-1); +disp("T2=") +disp(T2) +disp("K") + +//T4=1.8*T3 +//Heat liberated at constant pressure= 2 × heat liberated at constant volume +//cp*(T4-T3)=2*cv*(T3-T2) +//T4/T3=1.8 + +rho=rc/re; +T3=1201.9; //K +disp("T3=") +disp(T3) +disp("K") + +p3=p2*T3/T2; +disp("p3=") +disp(p3) +disp("bar") + +p4=p3; +disp("p4=") +disp(p4) +disp("bar") + +T4=1.8*T3; +disp("T4=") +disp(T4) +disp("K") + +p5=p4*(1/re)^(n); +disp("p5=") +disp(p5) +disp("bar") + +T5=T4*(1/re)^(n-1) +disp("T5=") +disp(T5) +disp("K") + + +disp("(ii) Mean effective pressure = ") +pm=1/(rc-1)*[p3*(rho-1)+(p4*rho-p5*rc)/(n-1)-(p2-p1*rc)/(n-1)]; +disp(pm) +disp("bar") + +disp("(iii) Efficiency of the cycle") +Vs=%pi/4*D^2*L; +W=pm*10^5*Vs/1000; + +V1=rc/(rc-1)*Vs +m=p1*10^5*V1/R/T1; +Q=m*(cv*(T3-T2) + cp*(T4-T3)); + +Efficiency=W/Q; +disp("Efficiency =") +disp(Efficiency) + + +disp("(iv) Power of the engine =") +P=W*num; +disp(P) +disp("kW") \ No newline at end of file diff --git a/551/CH13/EX13.3/3.sce b/551/CH13/EX13.3/3.sce new file mode 100755 index 000000000..a320b137f --- /dev/null +++ b/551/CH13/EX13.3/3.sce @@ -0,0 +1,63 @@ +clc +p1=18*10^5; //Pa +T1=683; //K +T2=T1; +r1=6; //ratio V4/V1; Isentropic compression +r2=1.5; //ratio V2/V1; Isothermal expansion +y=1.4; +V1=0.18; //m^3 + +disp("(i) Temperatures and pressures at the main points in the cycle") + +T4=T1/(r1)^(y-1); +disp("T4=") +disp(T4) +disp("K") + +T3=T4; +disp("T3=") +disp(T3) +disp("K") + +p2=p1/r2; +disp("p2=") +disp(p2/10^5) +disp("bar") + +p3=p2/(r1)^y; +disp("p3=") +disp(p3/10^5) +disp("bar") + +p4=p1/(r1)^y; +disp("p4=") +disp(p4/10^5) +disp("bar") + + +disp("(ii) Change in entropy =") +dS=p1*V1/T1/10^3*log(r2); +disp(dS) +disp("kJ/K") + + +disp("(iii) Mean thermal efficiency of the cycle") +Qs=T1*(dS); +Qr=T4*(dS); + +n=1-Qr/Qs; +disp("n=") +disp(n) + + +disp("(iv) Mean effective pressure of the cycle =") +pm=(Qs-Qr)/8/V1/100; //bar +disp(pm) +disp("bar") + + +n=210; //cycles per minute +disp("(v) Power of the engine =") +P=(Qs-Qr)*n/60; //kW +disp(P) +disp("kW") \ No newline at end of file diff --git a/551/CH13/EX13.30/30.sce b/551/CH13/EX13.30/30.sce new file mode 100755 index 000000000..f8823db0f --- /dev/null +++ b/551/CH13/EX13.30/30.sce @@ -0,0 +1,84 @@ +clc +v=10:1:100; +function p=f(v) + p=1/v^1.4; +endfunction +plot(v,f) + +v=[10 20] +p=[f(10) f(10)] +plot(v,p,'r') + +v=20:1:100; +function p=fa(v) + p=2.6515/v^1.4; +endfunction +plot(v,fa,'g') + +v=[100 100] +p=[f(100) fa(100)] +plot(v,p,'--p') + +v=[15 15] +p=[f(15) 0.040] +plot(v,p,'--') + +v=[20 20] +p=[f(20) 0.040] +plot(v,p,'--r') + +xtitle("p-v diagram", "v", "p") +legend("1-2b","2b-3", "3-4", "4-1", "2a-3a", "2-3") + +//The air-standard Otto, Dual and Diesel cycles are drawn on common p-v and T-s diagrams for the same maximum pressure and maximum temperature, for the purpose of comparison. +// Otto 1-2-3-4-1 +// Dual 1-2a-3a-3-4-1 +// Diesel 1-2b-3-4-1 + + +xset('window', 1) + +s=10:1:50; +function T=fb(s) + T=s^2 +endfunction +plot(s,fb) + +s=10:1:50; +function T=fc(s) + T=(s+30)^2 +endfunction +plot(s,fc,'r') + +s=[12 12]; +T=[fb(12) fc(12)]; +plot(s,T,'--p') + +s=[45 45]; +T=[fb(45) fc(45)] +plot(s,T,'m') + +s=10:1:27; +T=5*(s)^2; +plot(s,T,'g') + +s=10:1:20; +T=7*s^2; +plot(s,T,'--r') + +xtitle("T-s diagram", "s", "T") +legend("1-4", "2b-3", "1-2b", "3-4", "2-3", "2a-3a") + +// The construction of cycles on T-s diagram proves that for the given conditions the heat rejected is same for all the three cycles (area under process line 4-1). +// η=1-(Heat rejected)/(Heat supplied)=1-constant/Qs + +// The cycle with greater heat addition will be more efficient. +// From the T-s diagram + +// Qs(diesel) = Area under 2b-3 +// Qs(dual) = Area under 2a-3a-3 +// Qs(otto) = Area under 2-3. + +// Qs(diesel) > Qs(dual) > Qs(otto) + +disp("Thus, ηdiesel > ηdual > ηotto") \ No newline at end of file diff --git a/551/CH13/EX13.31/31.sce b/551/CH13/EX13.31/31.sce new file mode 100755 index 000000000..9fac4a29d --- /dev/null +++ b/551/CH13/EX13.31/31.sce @@ -0,0 +1,27 @@ +clc +cp=0.92; +cv=0.75; +y=1.22; //y=cp/cv +p1=1; //bar +p2=p1; +p3=4; //bar +p4=16; //bar +T2=300; //K + +T3=T2*(p3/p2)^((y-1)/y); +T4=p4/p3*T3; +T1=T4/(p4/p1)^((y-1)/y); + +disp("(i) Work done per kg of gas ") +Q_supplied=cv*(T4-T3); +Q_rejected=cp*(T1-T2); + +W=Q_supplied-Q_rejected; +disp("W=") +disp(W) +disp("kJ/kg") + + +disp("(ii) Efficiency of the cycle =") +n=W/Q_supplied; +disp(n) \ No newline at end of file diff --git a/551/CH13/EX13.32/32.sce b/551/CH13/EX13.32/32.sce new file mode 100755 index 000000000..a2a9536c3 --- /dev/null +++ b/551/CH13/EX13.32/32.sce @@ -0,0 +1,25 @@ +clc +p1=101.325; //kPa +T1=300; //K +rp=6; +y=1.4; + +T2=T1*rp^((y-1)/y); + +//T3/T4=rp^((y-1)/y) +//T4=T3/1.668 + +//W_T=2.5*W_C + +T3=2.5*(T2-T1)/(1-1/1.668); +disp("(i) Maximum temperature in the cycle =") +disp(T3) +disp("K") + + +disp("(ii) Cycle efficiency") +T4=T3/1.668; + +n_cycle=((T3-T4) - (T2-T1))/(T3-T2); +disp(" Cycle efficiency =") +disp(n_cycle) \ No newline at end of file diff --git a/551/CH13/EX13.33/33.sce b/551/CH13/EX13.33/33.sce new file mode 100755 index 000000000..01a6ec8fa --- /dev/null +++ b/551/CH13/EX13.33/33.sce @@ -0,0 +1,40 @@ +clc +p1=1; //bar +p2=5; //bar +T3=1000; //K +cp=1.0425; //kJ/kg K +cv=0.7662; //kJ/kg K +y=cp/cv; + +disp("(i)Temperature entropy diagram") + +s=10:1:50; +function T=fb(s) + T=s^2 +endfunction +plot(s,fb,'--') + +s=10:1:50; +function T=fc(s) + T=(s+30)^2 +endfunction +plot(s,fc,'r') + +s=[12 12]; +T=[fb(12) fc(12)]; +plot(s,T,'m') + +s=[45 45]; +T=[fb(45) fc(45)] +plot(s,T,'g') + + +xtitle("T-s diagram", "s", "T") +legend("p1=1 bar", "p2=5 bar", "1-2", "3-4") + +disp("(ii) Power required =") +T4=T3*(p1/p2)^((y-1)/y); +P=cp*(T3-T4); +disp("P=") +disp(P) +disp("kW") \ No newline at end of file diff --git a/551/CH13/EX13.34/34.sce b/551/CH13/EX13.34/34.sce new file mode 100755 index 000000000..68cc266ce --- /dev/null +++ b/551/CH13/EX13.34/34.sce @@ -0,0 +1,17 @@ +clc +m=0.1; //kg/s +p1=1; //bar +T4=285; //K +p2=4; //bar +cp=1; //kJ/kg K +y=1.4; + +T3=T4*(p2/p1)^((y-1)/y); +disp("Temperature at turbine inlet =") +disp(T3) +disp("K") + +P=m*cp*(T3-T4); +disp("Power developed =") +disp(P) +disp("kW") \ No newline at end of file diff --git a/551/CH13/EX13.35/35.sce b/551/CH13/EX13.35/35.sce new file mode 100755 index 000000000..4777574cb --- /dev/null +++ b/551/CH13/EX13.35/35.sce @@ -0,0 +1,34 @@ +clc +y=1.4; +cp=1.005; //kJ/kg K +p1=1; //bar +T1=293; //K +p2=3.5; //bar +T3=873; //K +rp=p2/p1; + +disp("(i) Efficiency of the cycle =") +n_cycle=1-1/rp^((y-1)/y); +disp(n_cycle) + + +disp("(ii) Heat supplied to air =") +T2=T1*(p2/p1)^((y-1)/y); +Q1=cp*(T3-T2); +disp(Q1) +disp("kJ/kg") + +disp("(iii) Work available at the shaft =") +W=n_cycle*Q1; +disp(W) +disp("kJ/kg") + +disp("(iv) Heat rejected in the cooler =") +Q2=Q1-W; +disp(Q2) +disp("kJ/kg") + +disp("(v) Temperature of air leaving the turbine =") +T4=T3/rp^((y-1)/y); +disp(T4) +disp("K") \ No newline at end of file diff --git a/551/CH13/EX13.36/36.sce b/551/CH13/EX13.36/36.sce new file mode 100755 index 000000000..fa9d3e541 --- /dev/null +++ b/551/CH13/EX13.36/36.sce @@ -0,0 +1,21 @@ +clc +T1=303; //K +T3=1073; //K +C=45000; //kJ/kg +cp=1; //kJ/kg K +y=1.4; + +T2=sqrt(T1*T3); +T4=T2; + +//W_turbine-W_compressor=m_f*C*n=100; + +m_f=100/C/(1-(T4-T1)/(T3-T2)); +disp("m_f=") +disp(m_f) +disp("kg/s") + +m_a=(100-m_f*(T3-T4))/(T3-T4-T2+T1); +disp("m_a=") +disp(m_a) +disp("kg/s") \ No newline at end of file diff --git a/551/CH13/EX13.37/37.sce b/551/CH13/EX13.37/37.sce new file mode 100755 index 000000000..bfa324954 --- /dev/null +++ b/551/CH13/EX13.37/37.sce @@ -0,0 +1,44 @@ +clc +T1=300; //K +p1=1; //bar +rp=6.25; +T3=1073; //K +n_comp=0.8; +n_turbine=0.8; +cp=1.005; //kJ/kg K +y=1.4; + +T2=T1*(rp)^((y-1)/y); + +//Let T2'=T2a +T2a=(T2-T1)/n_comp + T1; + +W_comp=cp*(T2a-T1); +disp("Compressor work =") +disp(W_comp) +disp("kJ/kg") + +T4=T3/rp^((y-1)/y); +T4a=T3-n_turbine*(T3-T4); + +W_turbine=cp*(T3-T4a); +disp("Turbine work =") +disp(W_turbine) +disp("kJ/kg") + +Q_s=cp*(T3-T2a); +disp("Heat supplied =") +disp(Q_s) +disp("kJ/kg") + +W_net=W_turbine - W_comp; + +n_cycle=W_net/Q_s*100; +disp("n_cycle") +disp(n_cycle) +disp("%") + +t4a=T4a-273; +disp("Turbine exhaust temperature =") +disp(t4a) +disp("0C") \ No newline at end of file diff --git a/551/CH13/EX13.38/38.sce b/551/CH13/EX13.38/38.sce new file mode 100755 index 000000000..761e53e8b --- /dev/null +++ b/551/CH13/EX13.38/38.sce @@ -0,0 +1,19 @@ +clc +n_turbine=0.85; +n_compressor=0.80; +T3=1148; //K +T1=300; //K +cp=1; //kJ/kg K +y=1.4; +p1=1; //bar +p2=4; //bar +C=42000; //kJ/kg K +n_cc=0.90; + +T2=T1*(p2/p1)^((y-1)/y); + +T2a=(T2-T1)/n_compressor + T1; + +ratio=0.9*C/cp/(T3-T2a) - 1; //ratio=ma/mf +disp("A/F ratio =") +disp(ratio) \ No newline at end of file diff --git a/551/CH13/EX13.39/39.sce b/551/CH13/EX13.39/39.sce new file mode 100755 index 000000000..95ecf0c81 --- /dev/null +++ b/551/CH13/EX13.39/39.sce @@ -0,0 +1,30 @@ +clc +cp=1.005; //kJ/kg K +y1=1.4; +y2=1.333; +p1=1; //bar +p4=p1; +T1=300; //K +p2=6.2; //bar +p3=p2; +n_compressor=0.88; +C=44186; //kJ/kg +ratio=0.017; //Fuel-air ratio; kJ/kg of air +n_turbine=0.9; // +cpg=1.147; + +T2=T1*(p2/p1)^((y1-1)/y1); +T2a=(T2-T1)/n_compressor + T1; //T2' + +T3=ratio*C/(1+ratio)/cp + T2a; +T4=T3*(p4/p3)^((y2-1)/y2); +T4a=T3-n_turbine*(T3-T4); +W_compressor=cp*(T2a-T1); +W_turbine=cpg*(T3-T4a); +W_net=W_turbine-W_compressor; +Qs=ratio*C; + +n_th=W_net/Qs*100; +disp("Thermal efficiency =") +disp(n_th) +disp("%") \ No newline at end of file diff --git a/551/CH13/EX13.4/4.sce b/551/CH13/EX13.4/4.sce new file mode 100755 index 000000000..9ca5049cd --- /dev/null +++ b/551/CH13/EX13.4/4.sce @@ -0,0 +1,21 @@ +clc + +// First case +//(T1-T2)/T1=1/6 +//T1=1.2*T2 + + +// Second case +//(T1-(T2-(70+273)))/T3=1/3 + +T2=1029/0.6; +T1=1.2*T2; + +disp("Temperature of the source =") +disp(T1) +disp("K") + + +disp("Temperature of the sink=") +disp(T2) +disp("K") \ No newline at end of file diff --git a/551/CH13/EX13.40/40.sce b/551/CH13/EX13.40/40.sce new file mode 100755 index 000000000..564dc84c9 --- /dev/null +++ b/551/CH13/EX13.40/40.sce @@ -0,0 +1,36 @@ +clc +cp=1; //kJ/kg K +y=1.4; +C=41800; //kJ/kg +p1=1; //bar +T1=293; //K +p2=4; //bar +p4=p1; +p3=p2; +n_compressor=0.80; +n_turbine=0.85; +ratio=90; //Air-Fuel ratio +m_a=3; //kg/s + +disp("(i)Power developed ") +T2=T1*(p2/p1)^((y-1)/y); +T2a=(T2-T1)/n_compressor + T1; +T3=C/(1+ratio)/cp + T2a; +T4=T3*(p4/p3)^((y-1)/y); +T4a=T3-n_turbine*(T3-T4); + +W_turbine=(ratio+1)/ratio*cp*(T3-T4a); +W_compressor=cp*(T2a-T1); +W_net=W_turbine-W_compressor; +Qs=1/ratio*C; + +P=m_a*W_net; +disp("Power=") +disp(P) +disp("kW/kg of air") + + +disp("(ii) Thermal efficiency of cycle =") +n_thermal=W_net/Qs; +disp(n_thermal) +disp("%") \ No newline at end of file diff --git a/551/CH13/EX13.41/41.sce b/551/CH13/EX13.41/41.sce new file mode 100755 index 000000000..84555c48d --- /dev/null +++ b/551/CH13/EX13.41/41.sce @@ -0,0 +1,25 @@ +clc +T1=288; //K +T3=883; //K +rp=6; //rp=p2/p1 +n_compressor=0.80; +n_turbine=0.82; +m_a=16; //kg/s +cp1=1.005; //kJ/kg K, For compression process +y1=1.4; // For compression process +cp2=1.11; //kJ/kg K +y2=1.333; + +T2=T1*(rp)^((y1-1)/y1); +T2a=(T2-T1)/n_compressor + T1; +T4=T3/rp^((y2-1)/y2); +T4a=T3-n_turbine*(T3-T4); + +W_compressor=cp1*(T2a-T1); +W_turbine=cp2*(T3-T4a); +W_net=W_turbine-W_compressor; + +Power=m_a*W_net; +disp("Power =") +disp(Power) +disp("kW") \ No newline at end of file diff --git a/551/CH13/EX13.42/42.sce b/551/CH13/EX13.42/42.sce new file mode 100755 index 000000000..ac605c087 --- /dev/null +++ b/551/CH13/EX13.42/42.sce @@ -0,0 +1,17 @@ +clc +cp=1.11; +T3=883; //K +T2a=529; //K +W_turbine=290.4; //kJ/kg +W_net=48.2; //kJ/kg + +Qs=cp*(T3-T2a); + +n_thermal=W_net/Qs*100; +disp("Thermal efficiency =") +disp(n_thermal) +disp("%") + +W_ratio=W_net/W_turbine; //Work ratio=net work output/Gross work output +disp("Work ratio =") +disp(W_ratio) \ No newline at end of file diff --git a/551/CH13/EX13.43/43.sce b/551/CH13/EX13.43/43.sce new file mode 100755 index 000000000..144665e27 --- /dev/null +++ b/551/CH13/EX13.43/43.sce @@ -0,0 +1,40 @@ +clc +p1=1; //bar +p2=5; //bar +p3=4.9; //bar +p4=1; //bar +T1=293; //K +T3=953; //K +n_compressor=0.85; +n_turbine=0.80; +n_combustion=0.85; +y=1.4; +cp=1.024; //kJ/kg K +P=1065; //kW + +disp("(i) The quantity of air circulation") +T2=T1*(p2/p1)^((y-1)/y); +T2a=(T2-T1)/n_compressor + T1; +T4=T3*(p4/p3)^((y-1)/y); +T4a=T3-n_turbine*(T3-T4); + +W_compressor=cp*(T2a-T1); +W_turbine=cp*(T3-T4a); +W_net=W_turbine-W_compressor; + +m_a=P/W_net; +disp("m_a =") +disp(m_a) +disp("kg") + + +disp("(ii) Heat supplied per kg of air circulation =") +Qs=cp*(T3-T2a)/n_combustion; +disp(Qs) +disp("kJ/kg") + + +disp("(iii) Thermal efficiency of the cycle =") +n_thermal=W_net/Qs*100; +disp(n_thermal) +disp("%") \ No newline at end of file diff --git a/551/CH13/EX13.44/44.sce b/551/CH13/EX13.44/44.sce new file mode 100755 index 000000000..89a9f4fe8 --- /dev/null +++ b/551/CH13/EX13.44/44.sce @@ -0,0 +1,25 @@ +clc +m_a=20; //kg/s +T1=300; //K +T3=1000; //K +rp=4; //rp=p2/p1 +cp=1; //kJ/kg K +y=1.4; + +T2=T1*(rp)^((y-1)/y); +T4=T3-T2+T1; + +//p5/p4=(p5/p3)*(p3/p4) +//let p3/p4=r1 +r1=(T3/T4)^(y/(y-1)); + +//r2=p5/p4; +r2=1/4*r1; +P_ratio=1/r2; //Pressure ratio of low pressure turbine +disp("Pressure ratio of low pressure turbine =") +disp(P_ratio) + +T5=T4/(P_ratio)^((y-1)/y); +disp("Temperature of the exhaust from the unit =") +disp(T5) +disp("K") \ No newline at end of file diff --git a/551/CH13/EX13.45/45.sce b/551/CH13/EX13.45/45.sce new file mode 100755 index 000000000..f40ffe5bd --- /dev/null +++ b/551/CH13/EX13.45/45.sce @@ -0,0 +1,57 @@ +clc +T1=288; //K +p1=1.01; //bar +rp=7; +p2=rp*p1; +p3=p2; +p5=p1; +n_compressor=0.82; +n_turbine=0.85; +n_turbine=0.85; +T3=883; //K +cpa=1.005; +cpg=1.15; +y1=1.4; +y2=1.33; + +disp("(i) Pressure and temperature of the gases entering the power turbine =") + +T2=T1*rp^((y1-1)/y1); +T2a=(T2-T1)/n_compressor + T1; + +W_compressor=cpa*(T2a-T1); + +T4a=(cpg*T3-W_compressor)/cpg; +disp("Temperature of gases entering the power turbine =") +disp(T4a) +disp("K") + +T4=T3-(T3-T4a)/n_turbine; + +p4=p3/(T3/T4)^(y2/(y2-1)); +disp("Pressure of gases entering the power turbine =") +disp(p4) +disp("bar") + + +disp("(ii) Net power developed per kg/s mass flow") +T5=T4a/(p4/p5)^((y2-1)/y2); +T5a=T4a-n_turbine*(T4a-T5); + +W_turbine=cpg*(T4a-T5a); +disp(" Net power developed per kg/s mass flow =") +disp(W_turbine) +disp("kW") + + +disp("(iii) Work ratio =") +W_ratio=W_turbine/(W_turbine+W_compressor); +disp(W_ratio) + + +disp("(iv) Thermal efficiency of the unit") +Qs=cpg*(T3-T2a); +n_thermal=W_turbine/Qs*100; +disp("n_thermal =") +disp(n_thermal) +disp("%") \ No newline at end of file diff --git a/551/CH13/EX13.46/46.sce b/551/CH13/EX13.46/46.sce new file mode 100755 index 000000000..2e064a6db --- /dev/null +++ b/551/CH13/EX13.46/46.sce @@ -0,0 +1,27 @@ +clc +T1=288; //K +rp=4; //rp=p2/p1=p3/p4 +n_compressor=0.82; +e=0.78; //Effectiveness of the heat exchanger +n_turbine=0.70; +T3=873; //K +y=1.4; +R=0.287; + +T2=T1*(rp)^((y-1)/y); +T2a=(T2-T1)/n_compressor + T1; +T4=T3/rp^((y-1)/y); +T4a=T3-n_turbine*(T3-T4); + +cp=R*y/(y-1); +W_compressor=cp*(T2a-T1); +W_turbine=cp*(T3-T4a); +W_net=W_turbine-W_compressor; + +T5=e*(T4a-T2a) + T2a; +Qs=cp*(T3-T5); + +n_cycle=W_net/Qs*100; +disp("Efficiency =") +disp(n_cycle) +disp("%") \ No newline at end of file diff --git a/551/CH13/EX13.47/47.sce b/551/CH13/EX13.47/47.sce new file mode 100755 index 000000000..75b6f70a2 --- /dev/null +++ b/551/CH13/EX13.47/47.sce @@ -0,0 +1,50 @@ +clc + +//Simple cycle +p2=4; //bar +p1=1; //bar +T1=293; +n_compressor=0.8; +n_turbine=0.85; +ratio=90; //Air Fuel ratio +C=41800; //kJ/kg +cp=1.024; +p4=1.01; //bar +p3=3.9; //bar +y=1.4; +e=0.72; //thermal ratio + +T2=T1*(p2/p1)^((y-1)/y); +T2a=(T2-T1)/n_compressor + T1; +T3=C/cp/(ratio+1)+471; +T4=T3*(p4/p3)^((y-1)/y); + +T4a=T3-n_turbine*(T3-T4); + +n_thermal1=((T3-T4a)-(T2a-T1))/(T3-T2a)*100; +disp("Thermal efficiency of simple cycle=") +disp(n_thermal1) +disp("%") + + +//Heat exchanger cycle + +T2a=471; // K (as for simple cycle) +T3=919.5; // K (as for simple cycle) +p3=4.04-0.14-0.05; //bar +p4=1.01+0.05; //bar + +T4=T3*(p4/p3)^((y-1)/y); +T4a=T3-n_turbine*(T3-T4); + +T5=e*(T4a-T2a) + T2a; + +n_thermal2=((T3-T4a) - (T2a-T1))/(T3-T5)*100; +disp("Thermal efficiency of heat exchanger cycle =") +disp(n_thermal2) +disp("%") + +dn=n_thermal2-n_thermal1; +disp("Increase in thermal efficiency =") +disp(dn) +disp("%") \ No newline at end of file diff --git a/551/CH13/EX13.48/48.sce b/551/CH13/EX13.48/48.sce new file mode 100755 index 000000000..722ff5907 --- /dev/null +++ b/551/CH13/EX13.48/48.sce @@ -0,0 +1,50 @@ +clc +T1=293; //K +T6=898; //K +T8=T6; +n_c=0.8; //Efficiency of each compressor stage +n_t=0.85; //Efficiency of each turbine stage +n_mech=0.95; +e=0.8; +cpa=1.005; //kJ/kg K +cpg=1.15; //kJ/kg K +y1=1.4; +y2=1.333; + +disp("(i) Thermal efficiency") +T3=T1; + +// p2/p1=sqrt(9)=3 +T2=T1*(3)^((y1-1)/y1); +T2a=(T2-T1)/n_c + T1; +T4a=T2a; +W_c=cpa*(T2a-T1); //Work input per compressor stage +W_t=2*W_c/n_mech; //Work output of H.P. turbine +T7a=T6-W_t/cpg; +T7=T6-(T6-T7a)/n_t; + +// (p6/p7)=(T6/T7)^(y2/(y2-1))=4.82; +// p8/p9=9/4.82=1.86 +T9=T8/(1.86)^((y2-1)/y2); +T9a=T8-n_t*(T8-T9); + +W=cpg*(T8-T9a)*n_mech; //Net work output +T5=e*(T9a-T4a)+T4a; + +Q=cpg*(T6-T5)+cpg*(T8-T7a); //Heat supplied +n_thermal=W/Q*100; +disp("n_thermal =") +disp(n_thermal) +disp("%") + +disp("(ii) Work ratio") +Gross_work=W_t+W/n_mech; +W_ratio=W/Gross_work; +disp("Work ratio=") +disp(W_ratio) + + +disp("(iii) Mass flow rate =") +m=4500/W; +disp(m) +disp("kg/s") \ No newline at end of file diff --git a/551/CH13/EX13.49/49.sce b/551/CH13/EX13.49/49.sce new file mode 100755 index 000000000..5acd314c1 --- /dev/null +++ b/551/CH13/EX13.49/49.sce @@ -0,0 +1,42 @@ +clc +T1=293; //K +T5=1023; //K +T7=T5; +p1=1.5; //bar +p2=6; //bar +n_c=0.82; +n_t=0.82; +e=0.70; +P=350; //kW +cp=1.005; //kJ/kg K +y=1.4; + +T3=T1; +px=sqrt(p1*p2); +T2=T1*(px/p1)^((y-1)/y); +T2a=T1+(T2-T1)/n_c; +T4a=T2a; +p5=p2; +T6=T5/(p5/px)^((y-1)/y); +T6a=T5-n_t*(T5-T6); +T8a=T6a; +Ta=T4a+e*(T8a-T4a); +W_net=2*cp*[(T5-T6a)-(T2a-T1)]; + +Q1=cp*(T5-T4a)+cp*(T7-T6a); //Without regenerator +Q2=cp*(T5-Ta)+cp*(T7-T6a); + +disp("n_thermal without regenerator =") +n1=W_net/Q1*100; +disp(n1) +disp("%") + +disp("n_thermal woth regenerator =") +n2=W_net/Q2*100; +disp(n2) +disp("%") + +disp("(iii) Mass of fluid circulated =") +m=P/W_net; +disp(m) +disp("kg/s") \ No newline at end of file diff --git a/551/CH13/EX13.5/5.sce b/551/CH13/EX13.5/5.sce new file mode 100755 index 000000000..5f2622c9b --- /dev/null +++ b/551/CH13/EX13.5/5.sce @@ -0,0 +1,17 @@ +clc + +T1=1990; //K +T2=850; //K +Q=32.5/60; //kJ/s +P=0.4; //kW + +n_carnot=(T1-T2)/T1; +disp("most efficient engine is one that works on Carnot cycle") +disp(n_carnot) + +n_th=P/Q; +disp("n_thermal =") +disp(n_th) + +disp("which is not feasible as no engine can be more efficient than that working on Carnot") +disp("Hence claims of the inventor is not true.") \ No newline at end of file diff --git a/551/CH13/EX13.7/7.sce b/551/CH13/EX13.7/7.sce new file mode 100755 index 000000000..9db6085ef --- /dev/null +++ b/551/CH13/EX13.7/7.sce @@ -0,0 +1,8 @@ +clc + +n=0.6; +y=1.5; + +r=(1/(1-n))^(1/(y-1)); +disp("Compression ratio =") +disp(r) \ No newline at end of file diff --git a/551/CH13/EX13.8/8.sce b/551/CH13/EX13.8/8.sce new file mode 100755 index 000000000..cb0fb3984 --- /dev/null +++ b/551/CH13/EX13.8/8.sce @@ -0,0 +1,25 @@ +clc + +D=0.25; //m +L=0.375; //m +Vc=0.00263; //m^3 +p1=1; //bar +T1=323; //K +p3=25; //bar +Vs=%pi/4*D^2*L; +r=(Vs+Vc)/Vc; +y=1.4; + +disp("(i) Air standard efficiency=") +n_otto=1-1/(r^(y-1)); +disp(n_otto) + + +disp("(ii) Mean effective pressure ") +p2=p1*(r)^(y); +r_p=p3/p2; + +p_m=p1*r*(r^(y-1) - 1)*(r_p - 1)/(y-1)/(r-1); +disp("Mean effective pressure =") +disp(p_m) +disp("bar") \ No newline at end of file diff --git a/551/CH13/EX13.9/9.sce b/551/CH13/EX13.9/9.sce new file mode 100755 index 000000000..39612f0f3 --- /dev/null +++ b/551/CH13/EX13.9/9.sce @@ -0,0 +1,50 @@ +clc +cv=0.72; //kJ/kg K +y=1.4; +p1=1; //bar +T1=300; //K +Q=1500; //kJ/kg +r=8; +y=1.4; + +disp("(i) Pressures and temperatures at all points") +T2=T1*(r)^(y-1); +disp("T2=") +disp(T2) +disp("K") + +p2=p1*(r)^y; +disp("p2=") +disp(p2) +disp("bar") + +T3=Q/cv + T2; +disp("T3=") +disp(T3) +disp("K") + +p3=p2*T3/T2; +disp("p3=") +disp(p3) +disp("bar") + +T4=T3/r^(y-1); +disp("T4=") +disp(T4) +disp("K") + +p4=p3/r^(y); +disp("p4=") +disp(p4) +disp("bar") + + +disp("(ii) Specific work and thermal efficiency") +SW=cv*[(T3-T2) - (T4-T1)]; +disp("Specific work =") +disp(SW) +disp("kJ/kg") + +n_th=1-1/r^(y-1); +disp("Thermal efficiency =") +disp(n_th) \ No newline at end of file -- cgit