diff options
Diffstat (limited to '1187')
64 files changed, 1674 insertions, 0 deletions
diff --git a/1187/CH1/EX1.1/1.sce b/1187/CH1/EX1.1/1.sce new file mode 100755 index 000000000..9c2d34b13 --- /dev/null +++ b/1187/CH1/EX1.1/1.sce @@ -0,0 +1,15 @@ +clc
+p=2*10^5; // Pa
+T=300; // K
+R=287; // J/(kg.K)
+V=3; // m^3
+
+rho=p/(R*T);
+disp("(a) The density of air = ")
+disp(rho)
+disp("kg/m^3")
+
+m=rho*V;
+disp("(b) Its mass =")
+disp(m)
+disp("m^3")
\ No newline at end of file diff --git a/1187/CH1/EX1.2/2.sce b/1187/CH1/EX1.2/2.sce new file mode 100755 index 000000000..af508265e --- /dev/null +++ b/1187/CH1/EX1.2/2.sce @@ -0,0 +1,33 @@ +clc
+M_C=12;
+M_N=14;
+M_O=16;
+R=8314; // J/(kg.K)
+
+M_CO=M_C+M_O;
+R_CO=R/M_CO;
+
+M_CO2=M_C+2*M_O;
+R_CO2=R/M_CO2;
+
+M_NO=M_N+M_O;
+R_NO=R/M_NO;
+
+M_N2O=2*M_N+M_O;
+R_N2O=R/M_N2O;
+
+disp("Gas constant for CO = ")
+disp(R_CO)
+disp("J/(kg.K)")
+
+disp("Gas constant for CO2 = ")
+disp(R_CO2)
+disp("J/(kg.K)")
+
+disp("Gas constant for NO = ")
+disp(R_NO)
+disp("J/(kg.K)")
+
+disp("Gas constant for N2O = ")
+disp(R_N2O)
+disp("J/(kg.K)")
diff --git a/1187/CH1/EX1.3/3.sce b/1187/CH1/EX1.3/3.sce new file mode 100755 index 000000000..bfb7e967b --- /dev/null +++ b/1187/CH1/EX1.3/3.sce @@ -0,0 +1,10 @@ +clc
+d=0.004; // m
+rho=1000; // kg/m^3
+v=3; // m/s
+meu=10^(-3); // khm(m.s)
+
+Re=rho*v*d/meu;
+disp("Reynolds number =")
+disp(Re)
+disp("The Reynolds number is well in excess of 4000, so the flow is turbulent.")
\ No newline at end of file diff --git a/1187/CH10/EX10.1/1.sce b/1187/CH10/EX10.1/1.sce new file mode 100755 index 000000000..66375d01c --- /dev/null +++ b/1187/CH10/EX10.1/1.sce @@ -0,0 +1,26 @@ +clc
+
+Q=400; // m^3/s
+b2=20; // m
+g=9.81; // m/s^2
+b1=25; // m
+
+h2=(Q/b2/sqrt(g))^(2/3);
+// Since energy is conserved
+// h1 + u1^2/2g = h2 +u2^2/2g = h2 + h2/2 = 3h2/2
+
+// h1 + 1/2*g*(Q/(b1h1))^2 = 3*h2/2;
+
+// h1^3-5.16*h1^2+13.05 = 0;
+
+// By solving this cubic equation
+
+h1=4.52; // m
+
+disp("(a) The depth of the water under the brigde =")
+disp(h2)
+disp("m")
+
+disp("(b) the depth of water upstream =")
+disp(h1)
+disp("m")
diff --git a/1187/CH10/EX10.2/2.sce b/1187/CH10/EX10.2/2.sce new file mode 100755 index 000000000..33121a10d --- /dev/null +++ b/1187/CH10/EX10.2/2.sce @@ -0,0 +1,21 @@ +clc
+
+w=0.04; // thickness of block in m
+d=0.07; // depth of liquid in m
+b=0.4; // m
+g=9.81; // m/s^2
+
+H=d-w;
+
+Q=1.705*b*H^(3/2);
+
+u1=Q/d/b;
+h=u1^2/(2*g);
+
+H1=H+h;
+
+Q1=1.705*b*H1^(3/2);
+
+disp("Rate of flow = ")
+disp(Q1)
+disp("m^3/s")
\ No newline at end of file diff --git a/1187/CH10/EX10.3/3.sce b/1187/CH10/EX10.3/3.sce new file mode 100755 index 000000000..150a20e4d --- /dev/null +++ b/1187/CH10/EX10.3/3.sce @@ -0,0 +1,37 @@ +clc
+
+h1=0.45; // m
+g=9.81; // m/s^2
+b1=0.8; // m
+h2=0.35; // m
+b2=0.3; // m
+disp("(a) the flow rate")
+Q=sqrt((h1-h2)*2*g/((1/(h1*b1)^2)-(1/(h2*b2)^2)));
+disp("(a) Flow rate =")
+disp(Q)
+disp("m^3/s")
+
+disp("(b) the Froude number at the throat")
+Fr2=Q/(sqrt(g)*b2*h2^(3/2));
+disp("The Froude number at the throat =")
+disp(Fr2)
+
+disp("(c) the depth of water at the throat")
+
+// (h1/h2)^(3) + 1/2*(b2/b1)^2 = 3/2*(h1/h2)^2
+
+// The solution for the above eqn is as follows
+// (h1/h2) = 0.5 + cos(2arcsin(b2/b1)/3)
+
+// h1/h2=1.467
+
+h2_new=h1/1.467;
+disp("Depth of water at the throat =")
+disp(h2_new)
+disp("m")
+
+disp("(d)the new flow rate")
+Q=sqrt(g)*b2*h2_new^(3/2);
+disp("New flow rate =")
+disp(Q)
+disp("m^3/s")
diff --git a/1187/CH10/EX10.4/4.sce b/1187/CH10/EX10.4/4.sce new file mode 100755 index 000000000..69d92fb74 --- /dev/null +++ b/1187/CH10/EX10.4/4.sce @@ -0,0 +1,18 @@ +clc
+
+Q=8.75; // m^3/s
+w=5; // m
+n=0.0015;
+s=1/5000;
+
+// Q/(w*h0) = u = m^(2/3)*i^(1/2)/n = 1/0.015*(w*h0/(w+2*h0))^(2/3)*sqrt(s);
+// Solution by trial gives h0
+h0=1.8; // m
+
+q=1.75;
+g=9.81;
+hc=(q^2/g)^(1/3); // critical depth
+
+disp("Depth =")
+disp(h0)
+disp("m")
\ No newline at end of file diff --git a/1187/CH10/EX10.5/5.sce b/1187/CH10/EX10.5/5.sce new file mode 100755 index 000000000..e4801909a --- /dev/null +++ b/1187/CH10/EX10.5/5.sce @@ -0,0 +1,14 @@ +clc
+
+g=9.81; // m/s^2
+T=5; // s
+h=4; // m
+
+// lambda=g*T^2/(2*%pi)*tanh(2*%pi*h/lambda1);
+// by trial method , we get
+lambda1=28.04;
+
+lambda=g*T^2/(2*%pi)*tanh(2*%pi*h/lambda1);
+disp("Wavelength =")
+disp(lambda)
+disp("m")
\ No newline at end of file diff --git a/1187/CH10/EX10.6/6.sce b/1187/CH10/EX10.6/6.sce new file mode 100755 index 000000000..42953504e --- /dev/null +++ b/1187/CH10/EX10.6/6.sce @@ -0,0 +1,16 @@ +clc
+
+g=9.81; // m/s^2
+T=12; // s
+
+c=g*T/(2*%pi);
+
+lambda=c*T;
+
+disp("Phase velocity =")
+disp(c)
+disp("m/s")
+
+disp("Wavelength =")
+disp(lambda)
+disp("m")
\ No newline at end of file diff --git a/1187/CH10/EX10.7/7.sce b/1187/CH10/EX10.7/7.sce new file mode 100755 index 000000000..fa3cc8007 --- /dev/null +++ b/1187/CH10/EX10.7/7.sce @@ -0,0 +1,23 @@ +clc
+
+c=18.74; // m/s
+lambda=225; // m
+
+disp("(a)Estimate the time elapsed since the waves were generated in a storm occurring 800 km out to sea. ")
+
+x=800*10^3; // m
+cg=c/2;
+
+t=x/cg;
+
+disp("time elapsed =")
+disp(t/3600)
+disp("hours")
+
+disp("(b)Estimate the depth at which the waves begin to be significantly influenced by the sea bed as they approach the shore.")
+
+h1=lambda/2;
+
+h2=lambda/(2*%pi)*atanh(0.99);
+
+printf("The answers show that h lies in the range between about %f m and %f m", h2,h1)
\ No newline at end of file diff --git a/1187/CH11/EX11.1/1.sce b/1187/CH11/EX11.1/1.sce new file mode 100755 index 000000000..da711b045 --- /dev/null +++ b/1187/CH11/EX11.1/1.sce @@ -0,0 +1,37 @@ +clc
+
+disp("(a) the density at plane 1")
+
+p1=1.5*10^5; // N/m^2
+R=287; // J/kg.K
+T1=271; // K
+
+rho1=p1/R/T1;
+disp("Density at plane 1 =")
+disp(rho1)
+disp("kg/m^3")
+
+disp("(b) the stagnation temperature")
+
+u1=270; // m/s
+cp=1005; // J/Kg.K
+
+T0=T1+u1^2/(2*cp);
+disp("The stagnation temperature =")
+disp(T0)
+disp("K")
+
+disp("(c) the temperature and density at plane 2")
+
+u2=320; // m/s
+p2=1.2*10^5; // N/m^2
+
+T2=T0-u2^2/(2*cp);
+disp("Temperature = ")
+disp(T2)
+disp("K")
+
+rho2=p2/(R*T2);
+disp("density =")
+disp(rho2)
+disp("kg/m^3")
diff --git a/1187/CH11/EX11.2/2.sce b/1187/CH11/EX11.2/2.sce new file mode 100755 index 000000000..e82a3c491 --- /dev/null +++ b/1187/CH11/EX11.2/2.sce @@ -0,0 +1,37 @@ +clc
+
+disp("(a) the angle through which the airstream is deflected")
+
+y=1.4;
+R=287; // J/kg.K
+T1=238; // K
+u1=773; // m/s
+beta1=38; // degrees
+cp=1005; // J/kg.K
+
+a1=sqrt(y*R*T1);
+M1=u1/a1;
+
+beta2=atand(tand(beta1)*((2+(y-1)*M1^2*(sind(beta1))^2)/((y+1)*M1^2*(sind(beta1))^2)));
+
+deflection_angle=beta1-beta2;
+disp("Deflection angle =")
+disp(deflection_angle)
+disp("degrees")
+
+disp("(b) the final Mach number")
+
+u2=u1*cosd(beta1)/cosd(beta2);
+
+T2=T1+1/(2*cp)*(u1^2-u2^2);
+a2=sqrt(y*R*T2);
+
+M2=u2/a2;
+
+disp("Final Mach number =")
+disp(M2)
+
+disp("(c) the pressure ratio across the wave.")
+ratio=T2/T1*(tand(beta1)/tand(beta2));
+disp("Pressure ratio =")
+disp(ratio)
\ No newline at end of file diff --git a/1187/CH11/EX11.3/3.sce b/1187/CH11/EX11.3/3.sce new file mode 100755 index 000000000..a17acd6c7 --- /dev/null +++ b/1187/CH11/EX11.3/3.sce @@ -0,0 +1,14 @@ +clc
+
+M1=1.8;
+theta1=20.73; // degrees
+theta2=30.73; // degrees
+M2=2.162;
+p1=50; // kPa
+y=1.4;
+
+p2=p1*((1+(y-1)/2*M1^2)/(1+(y-1)/2*M2^2))^(y/(y-1));
+
+disp("Pressure after the bend =")
+disp(p2)
+disp("kPa")
\ No newline at end of file diff --git a/1187/CH11/EX11.4/4.sce b/1187/CH11/EX11.4/4.sce new file mode 100755 index 000000000..63f8adb3e --- /dev/null +++ b/1187/CH11/EX11.4/4.sce @@ -0,0 +1,37 @@ +clc
+
+p=28*10^3; // N/m^2
+y=1.4;
+M1=2.4;
+M2=1;
+T0=291; // K
+R=287; // J/kg.K
+
+disp("(a) the pressures in the reservoir and at the nozzle throat")
+
+p0=p*(1+(y-1)/2*M1^2)^(y/(y-1));
+pc=p0*(1+(y-1)/2*M2^2)^(-y/(y-1));
+
+disp("Pressure in the reservoir =")
+disp(p0)
+disp("N/m^2")
+
+disp("Pressure at the nozzle throat =")
+disp(pc)
+disp("N/m^2")
+
+disp("(b) the temperature and velocity of the air at the exit.")
+
+T=T0*(1+(y-1)/2*M1^2)^(-1);
+
+disp("Temperature =")
+disp(T)
+disp("K")
+
+a=sqrt(y*R*T)
+
+u=M1*a;
+
+disp("Velocity =")
+disp(u)
+disp("m/s")
diff --git a/1187/CH11/EX11.5/5.sce b/1187/CH11/EX11.5/5.sce new file mode 100755 index 000000000..03c454d26 --- /dev/null +++ b/1187/CH11/EX11.5/5.sce @@ -0,0 +1,25 @@ +clc
+
+M_He=1.8;
+y_He=5/3;
+y_air=1.4;
+p2=30; // kPa
+
+// (A/At)=(1+(y-1)/2*M^2)^((y+1)/(y-1))/M^2*(2/(y+1))^((y+1)/(y-1))
+
+// = (1+1/3*1.8^2)^(4)/1.8^(2)*(3/4)^(4) = 1.828 for helium
+
+// = (1+0.2*M^2)^6/M^2*1/1.2^6 for air
+// Hence by trial
+
+M1=1.715;
+disp("Mach number before the shock =")
+disp(M1)
+
+p1=p2/((2*y_air*M1^2-(y_air-1))/(y_air+1));
+
+p0_1=p1*(1+(y_air-1)/2*M1^2)^(y_air/(y_air-1));
+
+disp("Stagnation Pressure =")
+disp(p0_1)
+disp("kPa")
diff --git a/1187/CH11/EX11.6/6.sce b/1187/CH11/EX11.6/6.sce new file mode 100755 index 000000000..c42e1a6ff --- /dev/null +++ b/1187/CH11/EX11.6/6.sce @@ -0,0 +1,44 @@ +clc
+
+p0=510; // kPa
+pA=500; // kPa
+pB=280; // kPa
+d=0.02; // m
+l_max=12; // m
+
+disp("(a) the value of the friction factor for the pipe")
+
+// At A, pA/p0 = 500/510 = 0.980. From the Isentropic Flow Tables (Appendix 3), M_A = 0.17.
+// From the Fanno Flow Tables (Appendix 3)for M_A = 0.17 and γ = 1.4, pc/pA = 0.1556 and (fl_maxP/A)_A = 21.37
+
+pC=pA*0.1556;
+
+// From the Fanno Tables at pc/pB = 0.278,M_B = 0.302 and (fl_maxP/A)B = 5.21.
+// For a circular pipe P/A=4/d
+M_B=0.302;
+f=(21.37-5.21)/l_max/4*d;
+
+disp("friction factor =")
+disp(f)
+
+disp("(b) the overall length of the pipe, L, if the flow exhausts to atmosphere")
+
+p=100; // kPa
+
+// At exit, pc/p = 77.8/100 = 0.778. From the Fanno Tables, (fl_maxP/A) = 0.07
+L=l_max*(21.37-0.07)/(21.37-5.21);
+
+disp("Overall Length =")
+disp(L)
+disp("m")
+
+disp("(c) the mass flow rate if the reservoir temperature is 294 K.")
+T0=294; // K
+R=287; // J/kg.K
+y=1.4;
+M=0.302;
+
+m=%pi/4*d^2*pB*10^3*M_B*(y*(1+(y-1)*M^2/2)/R/T0)^(1/2);
+disp("mass flow rate =")
+disp(m)
+disp("kg/s")
diff --git a/1187/CH11/EX11.7/7.sce b/1187/CH11/EX11.7/7.sce new file mode 100755 index 000000000..668052168 --- /dev/null +++ b/1187/CH11/EX11.7/7.sce @@ -0,0 +1,38 @@ +clc
+
+p1=8*10^5; // N/m^2
+p2=5*10^5; // N/m^2
+f=0.006;
+l=145; // m
+m=0.32; // kg/s
+R=287; // J/kg.K
+T=288; // K
+y=1.4;
+
+d=(4*f*l*m^2*R*T/(%pi/4)^2/(p1^2-p2^2))^(1/5);
+disp("(a) Diameter of pipe =")
+disp(d)
+disp("m")
+
+rho=p1/R/T;
+A=%pi/4*d^2;
+u=m/rho/A;
+
+a=sqrt(y*R*T);
+
+M1=u/a;
+M2=p1/p2*M1;
+
+disp("(b) Entry and Exit Mach number =")
+
+disp("Entry Mach number =")
+disp(M1)
+
+disp("Exit Mach number =")
+disp(M2)
+
+disp("(c) Determine the pressure halfway along the pipe.")
+px=sqrt((p1^2+p2^2)/2);
+disp("Pressure =")
+disp(px)
+disp("N/m^2")
\ No newline at end of file diff --git a/1187/CH12/EX12.1/1.sce b/1187/CH12/EX12.1/1.sce new file mode 100755 index 000000000..67b062b21 --- /dev/null +++ b/1187/CH12/EX12.1/1.sce @@ -0,0 +1,15 @@ +clc
+
+Q=0.05; // m^3/s
+d=0.15; // m^2
+h=8; // m
+g=9.81; // m/s^2
+l=90; // m
+f=0.007;
+
+u1=Q/(%pi/4*d^2);
+
+t=-integrate('1/((h*g/l)+(2*f/d)*u^2)', 'u', u1, 0);
+disp("Time for which flow into the tank continues after the power failure = ")
+disp(t)
+disp("s")
\ No newline at end of file diff --git a/1187/CH12/EX12.4/4.sce b/1187/CH12/EX12.4/4.sce new file mode 100755 index 000000000..f28b8a37f --- /dev/null +++ b/1187/CH12/EX12.4/4.sce @@ -0,0 +1,41 @@ +clc
+
+disp("(b) Estimate the height of tank required")
+
+f=0.006;
+l=1400; // m
+g=9.81; // m/s^2
+d1=0.75; // m
+d2=3; // m
+Q=1.2; // m^3/s
+a=20; // m
+
+K=4*f*l/(2*g*d1);
+
+// 2*K*Y = l*a/(g*A) = 8.919 s^2
+
+// Y=2*K*Y/2*K
+
+Y=8.919/(2*K);
+// When t=0
+
+u0=Q/(%pi/4*d1^2);
+
+y0=K*u0^2;
+
+C=-Y/K/exp(y0/Y);
+
+// To determine the height of the surge tank, we consider the condition y = y_max when u = 0.
+
+// 0 = 1/K*(y_max+Y) + C*exp(y_max/Y)
+
+// From the above eqn we get
+
+y_max=-Y;
+
+H=a-y_max;
+disp("The minimum height of the surge tank =")
+disp(H)
+disp("m")
+
+disp("The actual design height should exceed the minimum required, say 23 m")
\ No newline at end of file diff --git a/1187/CH13/EX13.1/1.sce b/1187/CH13/EX13.1/1.sce new file mode 100755 index 000000000..cb461c034 --- /dev/null +++ b/1187/CH13/EX13.1/1.sce @@ -0,0 +1,51 @@ +clc
+
+// Maximum hydraulic efficiency occurs for minimum pressure loss, that is, when
+
+// dp1/dQ=2.38Q-1.43=0
+
+Q_opt=1.43/2.38;
+
+p1_min=1.19*Q_opt^2-1.43*Q_opt+0.47; // MPa
+
+rho=1000; // kg/m^3
+g=9.81; // m/s^2
+w=69.1; // rad/s
+P=200*10^3; // W
+Ohm_P=0.565; // rad
+d=0.5; // m
+h=0.06; // m
+
+p1=p1_min*10^6/(rho*g); // mH2O, coversion of units
+
+H=(w*P^(1/2)/(rho^(1/2)*Ohm_P))^(4/5)/g;
+
+Hydraulic_efficiency=(H-p1)/H;
+disp("Hydraulic Efficiency =")
+disp(Hydraulic_efficiency)
+
+Overall_efficiency=P/(Q_opt*rho*g*H);
+disp("Overall Efficiency =")
+disp(Overall_efficiency)
+
+H_Euler=H-p1;
+
+u1=w*0.25;
+v_w1=g*H_Euler/u1;
+A=%pi*d*h*0.95;
+v_r=Q_opt/A;
+
+alpha1=atand(v_r/v_w1);
+disp("Outlet angles of the guide vanes =")
+disp(alpha1)
+disp("degrees")
+
+beta1=atand(v_r/(v_w1-u1));
+disp("Rotor blade angle at inlet =")
+disp(beta1)
+disp("degrees")
+u2=w*0.325/2;
+beta2=atand(v_r/u2);
+disp("Rotor blade angle at outlet =")
+disp(beta2)
+disp("degrees")
diff --git a/1187/CH13/EX13.2/2.sce b/1187/CH13/EX13.2/2.sce new file mode 100755 index 000000000..a237355e1 --- /dev/null +++ b/1187/CH13/EX13.2/2.sce @@ -0,0 +1,39 @@ +clc
+
+w=6.25;
+D=0.75; // m
+gv_angle=15; // guide vane angle in degrees
+g=9.81; // m/s^2
+H=27.5; // m
+A1=0.2; // m^2
+rho=1000; // kg/m^3
+p_atm=101.3*10^3;
+p_min=35*10^3;
+
+u1=%pi*w*D;
+v1=u1*sind(105)/sind(60);
+v_r1=v1*sind(gv_angle);
+v_w1=v1*cosd(gv_angle);
+v_w2=0;
+
+n_hydraulic=u1*v_w1/g/H;
+
+n_overall=0.97*n_hydraulic;
+disp("Overall efficiency =")
+disp(n_overall)
+
+Q=A1*v_r1;
+
+P=n_overall*Q*rho*g*H;
+Ohm_P=w*2*%pi/(g*H)^(5/4)*(P/rho)^(1/2);
+
+// sigma > 0.119*(0.5)^(1.84) = 0.0331
+
+sigma=0.0331;
+
+//((p_atm-p_min)/(rho*g)-z0)/H > 0.0331
+
+z0=((p_atm-p_min)/(rho*g))-sigma*H;
+disp("Limiting value for the height of the draft tube above =")
+disp(z0)
+disp("m")
diff --git a/1187/CH13/EX13.3/3.sce b/1187/CH13/EX13.3/3.sce new file mode 100755 index 000000000..42a72e0fe --- /dev/null +++ b/1187/CH13/EX13.3/3.sce @@ -0,0 +1,42 @@ +clc
+
+// Static head upstream = -11 mm H2O = -11*1000/1.2 mm air = -9.167 m air
+
+h=9.167; // m air
+g=9.81; // m/s^2
+d1=0.75; // m, tip diameters
+d2=0.4; // m, hub diameters
+d3=0.075; // m, diameter above atmospheric pressure
+d4=0.011; // m, diameter below atmospheric pressure
+P=6500; // W
+w=25;
+rho=1000; // kg/m^3
+
+v=sqrt(2*g*h); // Velocity upstream
+Q=%pi/4*d1^2*v; // Volume flow rate
+
+H=d3+d4; // Total head rise across fans
+p=rho*g*H;
+
+n_fan=Q*p/P;
+disp("Total efficiency =")
+disp(n_fan)
+
+p_ideal=p/n_fan;
+u=%pi*w*(d1+d2)/2;
+
+v_w2_A=p_ideal/(2*1.2*u);
+
+v1=Q/(%pi/4*(d1^2-d2^2 ));
+
+beta1_A=atand(v1/u);
+
+beta2_A=atand(v1/(u-v_w2_A));
+
+beta1_B=atand(v1/(u+v_w2_A));
+
+beta2_B=atand(v1/u);
+
+printf("Inlet angles for resp. fans %f & %f \n\n", beta1_A, beta1_B)
+
+printf("Outlet angles for resp. fans %f & %f", beta2_A, beta2_B)
diff --git a/1187/CH13/EX13.5/5.sce b/1187/CH13/EX13.5/5.sce new file mode 100755 index 000000000..60deebf50 --- /dev/null +++ b/1187/CH13/EX13.5/5.sce @@ -0,0 +1,39 @@ +clc
+
+Q=0.04; // m^3/s
+d=0.15; // m
+h=28; // m
+f=0.006;
+l=38; // m
+g=9.81;
+fre=50; // Hz
+n_manometer = 0.75;
+theta=30; // degrees
+
+v=Q/(%pi/4*d^2);
+h1=(3+4*f*l/d)*v^2/2/g; // Total head loss through pipes and valves
+
+h_m=h+h1; // Manometric head
+
+// w=2*%pi*50/n; where n = number of pairs of poles.
+// Ohm_s=w*Q^(1/2)/(g*H)^(3/4) = 0.876/n rad
+
+// If n = 2, Ohm_s = 0.438 rad, which suggests pump 1 or 2, and ω = 157 rad/s. Outlet flow area = %pi*D*D/10
+
+// v_r2=0.04/(%pi*D^2/10)
+// u2= ω*D/2 = 78.54 D
+
+// v_w2= g*h_m/(n_manometer*u2) = 5.06/D; // m^2/s
+
+// tan(theta) = v_r2/(u2-v_w2)
+
+// Solving above equation, we get
+// 78.54*D^3 - 5.06*D - 0.2205 = 0;
+
+// Solving above cubic equation we get
+
+D = 0.272; // m
+disp("D = ")
+disp(D)
+disp("m")
+disp("That is near enough. So we choose pump 1")
diff --git a/1187/CH13/EX13.6/6.sce b/1187/CH13/EX13.6/6.sce new file mode 100755 index 000000000..8ac30ca1a --- /dev/null +++ b/1187/CH13/EX13.6/6.sce @@ -0,0 +1,40 @@ +clc
+
+f=0.0085;
+l=21.1; // m
+d=0.09; // m
+g=9.81; // m/s^2
+rho=1000; // kg/m^3
+
+// h1=hf=(4*f*l/d)*(16*Q^2/(2*%pi^2*d^4*g)) = (100*Q)^2
+
+disp("(a)The head loss due to pipe friction in terms of flow rate Q is given as")
+disp("(100*Q)^2")
+
+// For Pump
+Q=[0:0.006:0.042 0.052];
+H=[15 16 16.5 16.5 15.5 13.5 10.5 7 0]
+plot(Q,H,"r")
+xlabel("Q(m^3/s)")
+ylabel("H(m)")
+
+// For Pipe System
+
+// H1 = 11.5 + (100*Q)^2;
+
+Q=[0:0.01:0.06];
+plot(Q,(11.5+10000*Q^2),"b")
+
+legend("pipe system", "pump")
+
+// From the plot of the pump and pipe characteristics, the intersection is at
+
+H=16; // m
+Q=0.021; // m^3/s
+n=0.74;
+
+P=rho*g*H*Q/n;
+
+disp("(b)Power required =")
+disp(P)
+disp("W")
diff --git a/1187/CH13/EX13.7/7.sce b/1187/CH13/EX13.7/7.sce new file mode 100755 index 000000000..dbf1abbde --- /dev/null +++ b/1187/CH13/EX13.7/7.sce @@ -0,0 +1,40 @@ +clc
+
+H=16.5; // m
+Q=0.015; // m^3/s
+n=0.63;
+H_s=11.5;
+rho=1000; // kg/m^3
+g=9.81; // m/s^2
+
+h_f=(100*Q)^2; // frictional head loss
+
+h_valve = H - H_s - h_f;
+
+P=rho*g*H*Q/n;
+disp("(i) the power consumption of the pump =")
+disp(P/1000)
+disp("kW")
+
+disp("(ii) The power dissipated in the pump =")
+P_d=P*(1-n)/1000;
+disp(P_d)
+disp("kW")
+
+disp("(iii) The power lost by pipe friction =")
+P_f=rho*g*h_f*Q;
+disp(P_f/1000)
+disp("kW")
+
+disp("(iv) The power lost in the valve =")
+P_valve=rho*g*h_valve*Q;
+disp(P_valve/1000)
+disp("kW")
+
+P_s=rho*g*H_s*Q;
+
+n_overall = P_s/P*100;
+
+disp("(b) Overall efficiency of the installation =")
+disp(n_overall)
+disp("%")
diff --git a/1187/CH2/EX2.1/1.sce b/1187/CH2/EX2.1/1.sce new file mode 100755 index 000000000..86f554e5d --- /dev/null +++ b/1187/CH2/EX2.1/1.sce @@ -0,0 +1,21 @@ +clc
+d=1.5; // m
+m=1.2; // kg
+rate=0.0065; // K/m
+R=287; // J/(kg.K)
+T_0=288.15; // K
+p_0=101*10^3; // Pa
+g=9.81; // m/s^2
+
+rho=m/(%pi*d^3/6);
+rho_0=p_0/R/T_0;
+
+// log(rho/rho_0)=(g/R*rate - 1)*log((T_0-rate*z)/T_0)
+
+z=1/rate*(T_0-T_0*exp(log(rho/rho_0)/(g/R/rate-1)));
+
+disp("The height above sea level to which the ballon will rise = ")
+disp(z)
+disp("m")
+
+printf("The height above sea level to which the ballon will rise = %f m", z)
\ No newline at end of file diff --git a/1187/CH2/EX2.2/2.sce b/1187/CH2/EX2.2/2.sce new file mode 100755 index 000000000..b57396015 --- /dev/null +++ b/1187/CH2/EX2.2/2.sce @@ -0,0 +1,39 @@ +clc
+d=2; // m
+a=1; // radius in m
+rho=880; // density of oil in kg/m^3
+g=9.81; // m/s^2
+rho_w=1000; // density of water in kg/m^3
+
+C_0=4*a/3/%pi; // centroid of the upper semicircle
+h1=a-C_0; // distance of the centroid from the top
+
+P1=rho*g*h1; // Pressure of the oil at this point
+F1=P1*%pi*a^2/2; // Force exerted by the oil on the upper half of the wall
+
+cp1=a^4*(%pi/8-8/(9*%pi)); // (AK^2)_C
+
+cp2=cp1/(%pi*a^2/2*h1); // Centre of Pressure below the centroid
+
+cp0=cp2+h1; // Centre of Pressure below the top
+
+P_w=(rho*g*a)+(rho_w*g*C_0);
+F_w=P_w*%pi*a^2/2;
+
+h2=C_0+rho/rho_w;
+cp2_w=cp1/(%pi*a^2/2*h2);
+cp0_w=a+C_0+cp2_w; // below the top of cylinder
+
+F_total=F1+F_w;
+
+// F1*cp0 + F_w*cp0_w = F_total*x
+
+x=(F1*cp0 + F_w*cp0_w)/F_total;
+
+disp("Total force =")
+disp(F_total)
+disp("N")
+
+disp("Distance of line of action of total force from top of cylinder =")
+disp(x)
+disp("m")
\ No newline at end of file diff --git a/1187/CH2/EX2.3/3.sce b/1187/CH2/EX2.3/3.sce new file mode 100755 index 000000000..09d889c0b --- /dev/null +++ b/1187/CH2/EX2.3/3.sce @@ -0,0 +1,31 @@ +clc
+
+rho=1000; // kg/m^3
+g=9.81; // m/s^2
+r=4; // m
+h=2; // m
+l=5; // m
+theta=%pi/6;
+
+A=h*l;
+
+F_h=rho*g*h*A; // Horizontal force
+
+C0=(2^2/(12*2))+2; // distance of line of action below the free surface
+
+AB=4-4*cos(theta);
+
+F_v=rho*g*l*(AB*1+%pi*r^2*theta/(2*%pi)-1/2*h*r*cos(theta));
+BC=0.237; // m
+
+F_net=sqrt(F_h^2+F_v^2);
+
+phi=atand(F_v/F_h);
+
+disp("Net force =")
+disp(F_net)
+disp("N")
+
+disp("Angle between net force and horizontal =")
+disp(phi)
+disp("degrees")
\ No newline at end of file diff --git a/1187/CH2/EX2.4/4.sce b/1187/CH2/EX2.4/4.sce new file mode 100755 index 000000000..20be00e1e --- /dev/null +++ b/1187/CH2/EX2.4/4.sce @@ -0,0 +1,26 @@ +clc
+
+m=10; // kg
+M=80; // kg
+H=1.5; // m
+rho=1026; // kg/m^3
+g=9.81; // m/s^2
+d=1; // m
+
+// m*H + M*H/2 =(M+m)(OG)
+
+OG=(m*H + M*H/2)/(M+m);
+
+// For vertical equilibrium, buoyancy = weight
+h=(M+m)/(rho*%pi/4*d^2);
+
+BM=(%pi*d^4/64)/(%pi*d^2*h/4);
+OB=h/2;
+
+GM=OB+BM-OG;
+
+disp("GM =")
+disp(GM)
+disp("m")
+
+disp("Since this is negative (i.e. M is below G) buoy is unstable.")
\ No newline at end of file diff --git a/1187/CH2/EX2.5/5.sce b/1187/CH2/EX2.5/5.sce new file mode 100755 index 000000000..95c96b8bd --- /dev/null +++ b/1187/CH2/EX2.5/5.sce @@ -0,0 +1,22 @@ +clc
+m=10; // kg
+M=80; // kg
+OG=0.8333; // m
+rho=1026; // kg/m^3
+g=9.81; // m/s^2
+d=1; // m
+W=(m+M)*g;
+
+// W(OG) = (W + F)(OB + BM) = rho*g*%pi/4*d^2*h1*(h1/2+d^2/(16*h1))
+
+h1=sqrt(2*(W*OG/(rho*g*%pi/4*d^2) - d^2/16));
+
+F=rho*g*%pi/4*d^2*h1 - W;
+
+disp("Least vertical downward force =")
+disp(F)
+disp("N")
+
+disp("Depth of immersion =")
+disp(h1)
+disp("m")
diff --git a/1187/CH2/EX2.6/6.sce b/1187/CH2/EX2.6/6.sce new file mode 100755 index 000000000..7156c4856 --- /dev/null +++ b/1187/CH2/EX2.6/6.sce @@ -0,0 +1,27 @@ +clc
+
+a=5; // m/s^2
+s=0.5; // m
+phi=atand(1/4); // degrees
+g=9.81; // m/s^2
+rho=880; // kg/m^3
+
+a_x=a*cosd(phi); // Horizontal component of acceleration
+a_z=a*sind(phi); // Vertical component of acceleration
+
+theta=atand(a_x/(a_z+g)); // b=tan(theta)
+
+d=(tand(phi)+tand(theta))/(1-tand(phi)*tand(theta));
+
+c=s*d;
+
+V=s*(s^2-s*c/2);
+
+disp("(a) Volume left in the tank =")
+disp(V*1000)
+disp("L")
+
+P=rho*g*s*cosd(phi);
+disp("(b)Pressure at the lowest corners of the tank =")
+disp(P)
+disp("Pa")
\ No newline at end of file diff --git a/1187/CH3/EX3.2/2.sce b/1187/CH3/EX3.2/2.sce new file mode 100755 index 000000000..e834f47b4 --- /dev/null +++ b/1187/CH3/EX3.2/2.sce @@ -0,0 +1,34 @@ +clc
+
+u_A=1.35; // m/s
+d_A=0.225; // m
+d_B=0.150; // m
+d_C=0.150; // m
+d=5.6; //m
+friction=2.5; // kW
+power_req=12.7; // kW
+
+rho=1000; // kg/m^3
+rho_m=13560; // kg/m^3
+
+g=9.81; // m/s^2
+
+pC=35000; // Pa
+pA=rho_m*g*(-d_B);
+
+Area_A=%pi*d_A^2/4;
+Area_B=%pi*d_B^2/4;
+Area_C=%pi*d_C^2/4;
+
+u_B=u_A*(Area_A/Area_B);
+u_C=u_A*(Area_A/Area_C);
+
+// Energy_added_by_pump/time = (Mass/time)*((pC-pA)/rho+(u_C^2-u_A^2)/2+g*(zC-zA))
+
+Energy_added = Area_A*u_A*(pC-pA+rho/2*(u_C^2-u_A^2)+rho*g*d)/1000+friction;
+
+Efficiency=Energy_added/power_req*100;
+
+disp("Overall efficiency of the pump =")
+disp(Efficiency)
+disp("%")
\ No newline at end of file diff --git a/1187/CH3/EX3.3/3.sce b/1187/CH3/EX3.3/3.sce new file mode 100755 index 000000000..fd0778a81 --- /dev/null +++ b/1187/CH3/EX3.3/3.sce @@ -0,0 +1,22 @@ +clc
+
+d_jet = 0.0086; // m
+d_orifice = 0.011; // m
+x = 2; // m
+y = 0.6; // m
+h = 1.75; // m
+g = 9.81; // m/s^2
+
+A2 = %pi/4*d_orifice^2;
+
+Cc = (d_jet/d_orifice)^2; // Coefficient of Contraction
+
+Cv = x/2/sqrt(y*h); // Coefficient of velocity
+
+Cd = Cv*Cc; // Coefficient of Discharge
+
+Q = Cd*A2*sqrt(2*g*h);
+
+disp("Rate of discharge = ")
+disp(Q)
+disp("m^3/s")
\ No newline at end of file diff --git a/1187/CH3/EX3.4/4.sce b/1187/CH3/EX3.4/4.sce new file mode 100755 index 000000000..be8d650b6 --- /dev/null +++ b/1187/CH3/EX3.4/4.sce @@ -0,0 +1,22 @@ +clc
+
+Cd=0.97;
+d1=0.28; // m
+d2=0.14; // m
+
+g=9.81; // m/s^2
+d=0.05; // difference in mercury level in metre
+rho=1000; // kg/m^3
+rho_m=13600; // kg/m^3
+
+A1=%pi/4*d1^2;
+A2=%pi/4*d2^2;
+
+p_diff=(rho_m-rho)*g*d;
+h=p_diff/rho/g;
+
+Q=Cd*A1*((2*g*h)/((A1/A2)^2-1))^(1/2);
+
+disp("Flow rate = ")
+disp(Q)
+disp("m^3/s")
diff --git a/1187/CH3/EX3.5/5.sce b/1187/CH3/EX3.5/5.sce new file mode 100755 index 000000000..65c95334b --- /dev/null +++ b/1187/CH3/EX3.5/5.sce @@ -0,0 +1,26 @@ +clc
+
+Cd=0.62;
+g=9.81; // m/s^2
+d=0.1; // m
+d0=0.06; // m
+d1=0.12; // m
+
+rho=1000; // kg/m^3
+rho_m=13600; // kg/m^3
+rho_f=0.86*10^3; //kg/m^3
+
+A0=%pi/4*d0^2;
+A1=%pi/4*d1^2;
+
+p_diff=(rho_m-rho_f)*g*d;
+
+h=p_diff/rho_f/g;
+
+Q=Cd*A0*((2*g*h)/(1-(A0/A1)^2))^(1/2);
+
+m=rho_f*Q;
+
+disp("Mass flow rate = ")
+disp(m)
+disp("kg/s")
\ No newline at end of file diff --git a/1187/CH3/EX3.6/6.sce b/1187/CH3/EX3.6/6.sce new file mode 100755 index 000000000..3f5f5f88d --- /dev/null +++ b/1187/CH3/EX3.6/6.sce @@ -0,0 +1,20 @@ +clc
+
+Cd=0.61;
+g=9.81; // m/s^2
+b=0.6; // m
+H=0.155; // mQ
+A=0.26; // m^2
+u1=0.254; // m/s
+
+Q=2/3*Cd*sqrt(2*g*b*(H)^3/2);
+
+velo=Q/A;
+
+H1=H+u1^2/(2*g);
+
+Q1=2/3*Cd*sqrt(2*g*b*(H1)^3/2);
+
+disp("Discharge =")
+disp(Q1)
+disp("m^3/s")
\ No newline at end of file diff --git a/1187/CH4/EX4.1/1.sce b/1187/CH4/EX4.1/1.sce new file mode 100755 index 000000000..9a49ced5d --- /dev/null +++ b/1187/CH4/EX4.1/1.sce @@ -0,0 +1,24 @@ +clc
+
+rho=1000; // kg/m^3
+u1=36; // m/s
+u2=30; // m/s
+d=0.05; // m
+theta=60; // degrees
+
+A=%pi/4*d^2;
+
+Q=A*u1;
+
+F_x=rho*Q*(u2*cosd(theta) - u1);
+F_y=rho*Q*u2*sind(theta);
+
+F=sqrt(F_x^2+F_y^2);
+phi=atand(F_y/F_x);
+
+disp("The Hydrodynamic force on the vane =")
+disp(F)
+disp("N")
+
+printf("This resultant force acts at angle of %f to the x-direction", phi)
+
\ No newline at end of file diff --git a/1187/CH4/EX4.2/2.sce b/1187/CH4/EX4.2/2.sce new file mode 100755 index 000000000..675778205 --- /dev/null +++ b/1187/CH4/EX4.2/2.sce @@ -0,0 +1,29 @@ +clc
+
+Q1=0.45; // m^3/s
+Q2=0.425; // m^3/s
+d1=0.6; // m
+d2=0.3; // m
+p1=1.4*10^5; // Pa
+rho=1000; // kg/m^3
+theta=45; // degrees
+
+A1=%pi/4*d1^2;
+A2=%pi/4*d2^2;
+
+u1=Q1/A1;
+u2=Q2/A2;
+
+p2=p1+rho/2*(u1^2-u2^2);
+
+F_x=rho*Q2*(u2*cosd(theta)-u1)-p1*A1+p2*A2*cosd(theta)
+F_y=rho*Q2*(u2*sind(theta)-0)+p2*A2*sind(theta);
+
+F=sqrt(F_x^2+F_y^2);
+phi=atand(F_y/F_x);
+
+disp("The net horizontal force exerted by the water onthe bend =")
+disp(F)
+disp("N")
+
+printf("This resultant force acts at angle of %f to the x-direction", phi)
\ No newline at end of file diff --git a/1187/CH4/EX4.3/3.sce b/1187/CH4/EX4.3/3.sce new file mode 100755 index 000000000..74a5449d2 --- /dev/null +++ b/1187/CH4/EX4.3/3.sce @@ -0,0 +1,18 @@ +clc
+
+rho=1.2; // kg/m^3
+d=12; // m
+u1=20; // m/s
+u4=8; // m/s
+
+A=%pi/4*d^2
+F=rho*A*(u1+u4)/2*(u1-u4);
+
+disp("(b) The thrust on the turbine = ")
+disp(F)
+disp("N")
+
+P=rho*A*(u1+u4)/2*(u1^2/2-u4^2/2);
+disp("Power generated by the turbine =")
+disp(P)
+disp("W")
\ No newline at end of file diff --git a/1187/CH5/EX5.3/3.sce b/1187/CH5/EX5.3/3.sce new file mode 100755 index 000000000..66edf88c5 --- /dev/null +++ b/1187/CH5/EX5.3/3.sce @@ -0,0 +1,36 @@ +clc
+
+u_p=10; // m/s
+scale=1/25; // l_m/l_p
+L=125; // m
+meu=1.235*10^(-6); // m^2/s
+meu_p=1.188*10^(-6); // m^2/s
+rho_p=1025; // kg/m^3
+rho_m=1000; // kg/m^3
+A=3500; // wetted surface in m^2
+
+u_m=u_p*sqrt(scale);
+
+d=L*scale;
+Re=d*u_m/meu; // Reynolds no.
+C_F=0.075/(log10(Re)-2)^2; // Skin friction coefficient
+
+res_skin=rho_m/2*u_m^2*(A*scale^2)*C_F;
+
+res_tot=54.2; // N
+
+F_resid_m=res_tot-res_skin;
+
+F_resid_p=F_resid_m*rho_p/rho_m/scale^3;
+
+Re_p=u_p*L/meu_p;
+
+C_F_p=0.075/(log10(Re_p)-2)^2+0.0004;
+C_F_pnew=1.45*C_F_p;
+
+res_friction=rho_p/2*u_p^2*A*C_F_pnew;
+
+Resistance=F_resid_p+res_friction;
+disp("The total resistance of the prototype =")
+disp(Resistance)
+disp("N")
diff --git a/1187/CH5/EX5.4/4.sce b/1187/CH5/EX5.4/4.sce new file mode 100755 index 000000000..200c571f7 --- /dev/null +++ b/1187/CH5/EX5.4/4.sce @@ -0,0 +1,11 @@ +clc
+
+A=0.88; // ratio of A2 and A1
+C_D=0.85; // ratio of C_D2 to C_D1
+P=1.20; // ratio of P2 to P1
+V1=11; // m/s
+
+V2=V1*(P/A/C_D)^(1/3);
+disp("Maximum speed of the redesigned torpedo =")
+disp(V2)
+disp("m/s")
\ No newline at end of file diff --git a/1187/CH6/EX6.1/1.sce b/1187/CH6/EX6.1/1.sce new file mode 100755 index 000000000..44cb37305 --- /dev/null +++ b/1187/CH6/EX6.1/1.sce @@ -0,0 +1,28 @@ +clc
+
+RD=0.83;
+rho_w=1000; // density of water in kg/m^3
+v=2.3; // m/s
+d=0.012; // m
+u=0.08; // dynamic viscocity in kg/m/s
+
+rho_oil=RD*rho_w;
+
+Re=rho_oil*v*d/u;
+disp("(a) Reynolds number =")
+disp(Re)
+
+v_max=2*v;
+disp("(b)Maximum velocity =")
+disp(v_max)
+disp("m/s")
+
+Q=%pi/4*d^2*v;
+disp("(c)Volumetric flow rate =")
+disp(Q)
+disp("m^3/s")
+
+p=-128*Q*u/%pi/d^4;
+disp("Pressure gradient along the pipe = ")
+disp(p)
+disp("Pa/m")
\ No newline at end of file diff --git a/1187/CH6/EX6.2/2.sce b/1187/CH6/EX6.2/2.sce new file mode 100755 index 000000000..82cee4e55 --- /dev/null +++ b/1187/CH6/EX6.2/2.sce @@ -0,0 +1,10 @@ +clc
+c=0.001; // m
+p1=15*10^3; // Pa
+u=0.6; // kg/m/s
+R=6; // ratio of R2/R1
+
+Q=%pi*c^3*p1/(6*u*log(R));
+disp("(b)Rate at which oil must be supplied =")
+disp(Q)
+disp("m^3/s")
\ No newline at end of file diff --git a/1187/CH6/EX6.3/3.sce b/1187/CH6/EX6.3/3.sce new file mode 100755 index 000000000..674f7f06e --- /dev/null +++ b/1187/CH6/EX6.3/3.sce @@ -0,0 +1,21 @@ +clc
+
+F=6*10^3; // Pa
+b=0.12; // m
+
+f=F*b;
+
+disp("(a) The load the pad will support =")
+disp(f)
+disp("N/m")
+
+dp=12*10^3; // N/m^2
+dx=0.12; // m
+c=0.00018; // m
+u=0.5; // kg/m/s
+V=5; // m/s
+
+q=(dp/dx)*c^3/12/u + V*c/2;
+disp("(b) The rate at which oil must be supplied =")
+disp(q)
+disp("m^2/s")
\ No newline at end of file diff --git a/1187/CH6/EX6.4/4.sce b/1187/CH6/EX6.4/4.sce new file mode 100755 index 000000000..ef1805894 --- /dev/null +++ b/1187/CH6/EX6.4/4.sce @@ -0,0 +1,18 @@ +clc
+
+d_p=0.05; // diameter of piston in m
+d_c=0.0504; // diameter of cylinder in m
+SG=0.87;
+rho_w=1000; // kg/m^3
+v=10^-4; // m^2/s
+dp=1.4*10^6; // Pa
+l=0.13; // m
+
+c=(d_c-d_p)/2; // clearance
+
+u=SG*rho_w*v; // Dynamice viscocity
+
+Vp=dp*c^3/(6*u*l*(d_p/2+c));
+disp("Velocity of the dashpot =")
+disp(Vp)
+disp("m/s")
\ No newline at end of file diff --git a/1187/CH6/EX6.5/5.sce b/1187/CH6/EX6.5/5.sce new file mode 100755 index 000000000..855726b1d --- /dev/null +++ b/1187/CH6/EX6.5/5.sce @@ -0,0 +1,32 @@ +clc
+
+disp("(a)the dynamic and kinematic viscosities of the oil")
+
+d=0.00475; // m
+g=9.81; // m/s^2
+rho_s=1151; // kg/m^3
+rho=880; // kg/m^3
+u=0.006; // m/s
+
+F=%pi/6*d^3*g*(rho_s-rho);
+
+rat_d=0.25; // ratio of d/D
+rat_F=1.8; // ratio of F/Fo
+
+dynamic=F/(1.8*3*%pi*u*d);
+
+kinematic=dynamic/rho;
+
+disp("Dynamic viscosity = ")
+disp(dynamic)
+disp("kg/m/s")
+
+disp("Kinematic viscosity =")
+disp(kinematic)
+disp("m^2/s")
+
+disp("(b) Reynolds number of sphere =")
+
+Re=rho*u*d/dynamic;
+disp("Reynolds number =")
+disp(Re)
diff --git a/1187/CH6/EX6.6/6.sce b/1187/CH6/EX6.6/6.sce new file mode 100755 index 000000000..2144a3761 --- /dev/null +++ b/1187/CH6/EX6.6/6.sce @@ -0,0 +1,16 @@ +clc
+
+D=0.120; // m
+h=0.08; // m
+c=0.001; // m
+t=0.01875; // m
+rev=65; // revolutions per min
+T=4*10^-3; // N.m
+
+K1=%pi*h/4/c;
+K2=%pi/32/t;
+
+u=T/(rev*2*%pi/60)/(K1*D^3+K2*D^4);
+disp("viscosity of the liquid =")
+disp(u)
+disp("Pa.s")
\ No newline at end of file diff --git a/1187/CH6/EX6.7/7.sce b/1187/CH6/EX6.7/7.sce new file mode 100755 index 000000000..34b9647d5 --- /dev/null +++ b/1187/CH6/EX6.7/7.sce @@ -0,0 +1,22 @@ +clc
+
+V=10; // m/s
+h1=0.0005; // m
+h2=0.00025; // m
+L=0.1; // m
+b=0.1; // m
+RD=0.87;
+u=2*10^-4; // m^2/s
+rho_w=1000; // kg/m^3
+
+H=h1/h2;
+
+Q=V/2*(1+H^2)/(1+H^3)*b*h1;
+disp("(b) Volumetric flow rate of oil =")
+disp(Q)
+disp("m^3/s")
+
+F=V/2*(1-(1+H^2)/(1+H^3))*12*RD*rho_w*u/h1^2*L^2/4*b;
+disp("The load supported by the bearing =")
+disp(F)
+disp("N")
\ No newline at end of file diff --git a/1187/CH7/EX7.1/1.sce b/1187/CH7/EX7.1/1.sce new file mode 100755 index 000000000..c38eaa830 --- /dev/null +++ b/1187/CH7/EX7.1/1.sce @@ -0,0 +1,22 @@ +clc
+
+Q=50*10^-3; // m^3/s
+d=0.15; // m
+l=300; // m
+v=1.14*10^-6; // m^2/s
+g=9.81; // m/s^2
+
+// For galvanised steel
+k=0.00015; // m
+t=0.001; // ratio of k to d ; (k/d)
+f=0.00515;
+
+A1=%pi/4*d^2;
+
+u=Q/A1;
+Re=u*d/v;
+
+h_f=4*f*l*u^2/d/(2*g);
+disp("Head lost to friction =")
+disp(h_f)
+disp("m")
\ No newline at end of file diff --git a/1187/CH7/EX7.2/2.sce b/1187/CH7/EX7.2/2.sce new file mode 100755 index 000000000..646b75200 --- /dev/null +++ b/1187/CH7/EX7.2/2.sce @@ -0,0 +1,18 @@ +clc
+
+k=0.00025; // m
+d=0.1; // m
+l=120; // m
+h_f=5; // m
+g=9.81; // m/s^2
+v=10^-5; // m^2/s
+
+f=0.0079042;
+
+u=sqrt(h_f*d*(2*g)/(4*f*l));
+Re=u*d/v;
+
+Q=u*%pi/4*d^2;
+disp("Rate =")
+disp(Q)
+disp("m^3/s")
\ No newline at end of file diff --git a/1187/CH7/EX7.3/3.sce b/1187/CH7/EX7.3/3.sce new file mode 100755 index 000000000..3f372de27 --- /dev/null +++ b/1187/CH7/EX7.3/3.sce @@ -0,0 +1,16 @@ +clc
+
+h_f=9; // m
+l=180; // m
+Q=85*10^-3; // m^3/s
+f=0.00475;
+k=0.00015; // m
+v=1.14*10^-6; // m^2/s
+g=9.81; // m/s^2
+
+d=(4*f*l*Q^2/h_f/(%pi/4)^2/(2*g))^(1/5);
+Re=(Q/(%pi*d^2/4))*d/v;
+
+disp("The size of galvanized steel pipe = ")
+disp(d)
+disp("m")
diff --git a/1187/CH7/EX7.4/4.sce b/1187/CH7/EX7.4/4.sce new file mode 100755 index 000000000..d588264b9 --- /dev/null +++ b/1187/CH7/EX7.4/4.sce @@ -0,0 +1,15 @@ +clc
+
+// D1=(5*b1/3/a)^(1/8)
+// D2=(5*b1/3/a)^(1/8)
+
+// But b2=2.5*b1
+// Therefore D2=(2.5)^(1/8)*D1
+
+D1=600; // mm
+
+D2=(2.5)^(1/8)*D1;
+
+disp("Revised estimate of the optimum pipe diameter =")
+disp(D2)
+disp("mm")
\ No newline at end of file diff --git a/1187/CH7/EX7.5/5.sce b/1187/CH7/EX7.5/5.sce new file mode 100755 index 000000000..f15ef340c --- /dev/null +++ b/1187/CH7/EX7.5/5.sce @@ -0,0 +1,28 @@ +clc
+
+disp("(a) Feed is at the end of the main")
+Q0=4.5*10^-3; // m^3/s
+d=0.1; // m
+l=4.5*10^3; // m
+g=9.81; // m/s^2
+f=0.006;
+rho=1000; // kg/m^3
+
+u0=Q0/(%pi/4*d^2);
+h_f=4*f*u0^2*l/3/(d*2*g);
+
+dp=h_f*rho*g;
+disp("Pressure difference =")
+disp(dp)
+disp("N/m^2")
+
+disp("(b) Feed is at the centre of the main")
+
+Q0_b=Q0/2;
+u0_b=u0/2;
+l_b=l/2;
+
+dp_b=(u0_b/u0)^2*(l_b/l)*dp;
+disp("Pressure difference =")
+disp(dp_b)
+disp("N/m^2")
\ No newline at end of file diff --git a/1187/CH7/EX7.6/6.sce b/1187/CH7/EX7.6/6.sce new file mode 100755 index 000000000..bf3137e46 --- /dev/null +++ b/1187/CH7/EX7.6/6.sce @@ -0,0 +1,29 @@ +clc
+
+d1=3; // m
+d2=2; // m
+f=0.007;
+l=75; // m
+d=0.05; // m
+g=9.81; // m/s^2
+h1=1.8; // m
+
+A1=%pi/4*d1^2;
+A2=%pi/4*d2^2;
+
+// dh/dt=dz1/dr*(1+A1/A2)
+// Q=-A1*dz1/dt = -4/13*A1*dh/dt
+
+// u=(Q/2)^2/(%pi/4*d^2)
+// h=(4*f*l/d + 1.5)*u^2/2g = 1.438*10^5*Q^2
+
+// t=integrate('-1/(1+A1/A2)*A1*(1.438*10^5/h)^(1/2)','h',h1,H)
+
+// By integrating, we get
+H=(h1^(1/2)-(900/2/824.7))^2;
+h=h1-H;
+dz1=1/(1+A1/A2)*h;
+
+disp("The change in the level in larger tank =")
+disp(dz1)
+disp("m")
\ No newline at end of file diff --git a/1187/CH8/EX8.1/1.sce b/1187/CH8/EX8.1/1.sce new file mode 100755 index 000000000..170e55343 --- /dev/null +++ b/1187/CH8/EX8.1/1.sce @@ -0,0 +1,15 @@ +clc
+
+delta=0.6; // mm
+
+delta1=delta/3;
+
+theta=2/15*delta;
+
+disp("Displacement thickness =")
+disp(delta1)
+disp("mm")
+
+disp("Momentum thickness =")
+disp(theta)
+disp("mm")
\ No newline at end of file diff --git a/1187/CH8/EX8.3/3.sce b/1187/CH8/EX8.3/3.sce new file mode 100755 index 000000000..9fa95ddaa --- /dev/null +++ b/1187/CH8/EX8.3/3.sce @@ -0,0 +1,40 @@ +clc
+
+disp("(a) To determine the values of a1 & a2")
+
+// To determine the values of a1 & a2 following conditions must be satisfied
+
+// Condition I - When n=0, u/um=0
+// Condition II - When n=1, u/um=a1+a2=1
+// Condition III - When n=1, d(u/um)/dn = a1+2a2=0
+
+// By satisfying these conditions, we have
+// a1+a2=1;
+// a1+2a2=0;
+
+A=[1,1;1,2];
+B=[1;0];
+X=inv(A)*B;
+
+a1=X(1);
+a2=X(2);
+
+disp("a1=")
+disp(a1)
+disp("a2=")
+disp(a2)
+
+disp("(b)Evaluate the constants A and B")
+
+// A = integrate('(1-f(n))*f(n)','n',0,1)
+
+A=integrate('(1-(2*n-n^2))*(2*n-n^2)','n',0,1)
+disp("A =")
+disp(A)
+
+// B = differentiation of (2*n-n^2) at n=0, we get
+B=2;
+
+disp("B =")
+disp(B)
+
diff --git a/1187/CH8/EX8.4/4.sce b/1187/CH8/EX8.4/4.sce new file mode 100755 index 000000000..8eb24280e --- /dev/null +++ b/1187/CH8/EX8.4/4.sce @@ -0,0 +1,22 @@ +clc
+
+v=1.5*10^(-5); // m^2/s
+Re_t=5*10^5;
+x_t=1.2; // m
+rho=1.21; // kg/m^3
+
+u_m=v*Re_t/x_t;
+
+disp("(a) the velocity of the airstream =")
+disp(u_m)
+disp("m/s")
+
+theta=0.646*x_t/sqrt(Re_t);
+
+F=rho*u_m^2*theta;
+
+D_F=2*F*x_t;
+
+disp("(b) the frictional drag of the plate, D_F =")
+disp(D_F)
+disp("N")
diff --git a/1187/CH8/EX8.5/5.sce b/1187/CH8/EX8.5/5.sce new file mode 100755 index 000000000..23330c8c5 --- /dev/null +++ b/1187/CH8/EX8.5/5.sce @@ -0,0 +1,28 @@ +clc
+
+u_m = 50; // m/s or 180 km/h
+v=1.5*10^(-5); // m^2/s
+l=100; // m
+rho=1.2; // kg/m^3
+b=8.3; // m
+
+delta = 0.37*(v/u_m)^(1/5)*l^(4/5);
+
+disp("(a) the boundary layer thickness at the rear of the train =")
+disp(delta)
+disp("m")
+
+Re_l = u_m*l/v;
+C_F=0.074*(Re_l)^(-1/5);
+F=0.037*rho*u_m^2*l*Re_l^(-1/5);
+
+D_F = F*b;
+
+disp("(b) the frictional drag acting on the train, D_F =")
+disp(D_F)
+disp("N")
+
+P=D_F*u_m;
+disp("(c) the power required to overcome the frictional drag =")
+disp(P/1000)
+disp("kW")
diff --git a/1187/CH8/EX8.6/6.sce b/1187/CH8/EX8.6/6.sce new file mode 100755 index 000000000..e64653a84 --- /dev/null +++ b/1187/CH8/EX8.6/6.sce @@ -0,0 +1,17 @@ +clc
+
+Re_t=5*10^5;
+Re_l=5*10^6;
+
+r1=Re_t/Re_l; // r1=x_t/l
+r2=1-36.9*(1/Re_t)^(3/8); // r2=x_0/x_t
+
+r=r1*r2; // r=x_0/l;
+
+disp("(a) the proportion of the plate occupied by the laminar boundary layer =")
+disp(r*100)
+disp("%")
+
+C_F = 0.074/Re_l^(1/5)*(1-r)^(4/5);
+disp("(b) the skin friction coefficient CF evaluated at the trailing edge =")
+disp(C_F)
diff --git a/1187/CH9/EX9.2/2.sce b/1187/CH9/EX9.2/2.sce new file mode 100755 index 000000000..821fd2317 --- /dev/null +++ b/1187/CH9/EX9.2/2.sce @@ -0,0 +1,18 @@ +clc
+
+// p_a-p_b=-1/2*rho*C^2*(1/R_A^2-1/R_B^2)
+
+rho_w=1000; // kg/m^3
+g=9.81; // m/s^2
+h=0.0115; // m
+rho=1.22; // kg/m^3
+R_A=0.4; // m
+R_B=0.2; // m
+
+C=sqrt(rho_w*g*h*2/(rho*(1/R_B^2-1/R_A^2)));
+
+m=rho*C*R_B*integrate('1/R','R', R_B, R_A);
+
+disp("Mass flow rate =")
+disp(m)
+disp("kg/s")
diff --git a/1187/CH9/EX9.3/3.sce b/1187/CH9/EX9.3/3.sce new file mode 100755 index 000000000..a22fcfd41 --- /dev/null +++ b/1187/CH9/EX9.3/3.sce @@ -0,0 +1,25 @@ +clc
+
+// p=1/2*rho*w^2*R^2 + C
+
+
+// At z=0
+rho=900; // kg/m^3
+g=9.81; // m/s^2
+h=0.6; // m
+
+C=rho*g*h;
+
+// p = -rho*K^2/(2*R^2)+D
+// From this we get, D = 9*w^2 + C
+
+// At z = 0
+// p = D - rho*K^2/2/R^2;
+p_max=150000; // Pa
+
+// From the above equation we obtain,
+w=135.6; // rad/s
+
+disp("The maximum speed at which the paddles may rotate about their vertical axis =")
+disp(w)
+disp("rad/s")
diff --git a/1187/CH9/EX9.4/4.sce b/1187/CH9/EX9.4/4.sce new file mode 100755 index 000000000..9eef6a109 --- /dev/null +++ b/1187/CH9/EX9.4/4.sce @@ -0,0 +1,27 @@ +clc
+
+U=40; // m/s
+h=0.01; // m
+
+m=2*U*h;
+disp("(a) the strength of the line source =")
+disp(m)
+disp("m^2/s")
+
+s = m/(2*%pi*U);
+disp("(b) the distance s the line source is located behind the leading edge of the step =")
+disp(s*1000)
+disp("mm")
+
+x=0; // m
+y=0.005; // m
+
+u=U + m/(2*%pi)*(x/(x^2+y^2));
+v=m/(2*%pi)*(y/(x^2+y^2));
+disp("Horizontal component =")
+disp(u)
+disp("m/s")
+
+disp("Vertical Component =")
+disp(v)
+disp("m/s")
diff --git a/1187/CH9/EX9.5/5.sce b/1187/CH9/EX9.5/5.sce new file mode 100755 index 000000000..8d46a31a9 --- /dev/null +++ b/1187/CH9/EX9.5/5.sce @@ -0,0 +1,13 @@ +clc
+
+b=0.0375; // m
+t=0.0625; // m
+U=5; // m/s
+
+m=2*%pi*U*t/atan(2*b*t/(t^2-b^2));
+
+L=2*b*(1+m/(%pi*U*b))^(1/2);
+
+disp("L =")
+disp(L)
+disp("m")
diff --git a/1187/CH9/EX9.7/7.sce b/1187/CH9/EX9.7/7.sce new file mode 100755 index 000000000..1b3faec04 --- /dev/null +++ b/1187/CH9/EX9.7/7.sce @@ -0,0 +1,34 @@ +clc
+
+l1=10; // m
+r1=2; // m
+C_D1=0.0588;
+theta1=6.5; // degrees
+
+AR1=l1/r1; // Aspect ratio
+
+C_L=0.914;
+
+C_D2=C_L^2/(%pi*AR1);
+theta2=atand(C_L/(%pi*AR1))
+
+C_D3=C_D1-C_D2;
+theta3=theta1-theta2;
+
+AR2=8;
+
+C_Di=C_L^2/(%pi*AR2);
+C_D=C_Di+C_D3;
+
+theta4=atand(C_L/(%pi*AR2));
+theta=theta4+theta3;
+
+disp("Lift coefficient =")
+disp(C_L)
+
+disp("Drag coefficient =")
+disp(C_D)
+
+disp("Effective angle of attack =")
+disp(theta)
+disp("degrees")
|