# Question:Integration error and graph

## Question:Integration error and graph

Maple 13

Dear sir,

I am unable to evaluate the mean pressure drop graph for different values of k , i will be thankful to you if any one solve my problem

here is my codes and mean pressure drop equation

restart:

with(DETools):

with(IntegrationTools):

eta:=1+k*x+epsilon*sin(2*Pi*x):

epsilon:=0.1:

R:=1.0:

A:=0.0628:

delta:=0.1:

k1:=k*delta:

alpha:=1.0:

A1:=(-exp(-alpha*x))/(2*eta^3):

A11:=diff(A1,x):

A2:=(3*exp(-alpha*x))/(2*eta):

A22:=diff(A2,x):

A3:=12*R*A1*diff(A1,x):

A4:=6*R*(A2*A11-A1*A22):

A5:=(1/2)*((k1+A*cos(2*Pi*x)))*((diff(A1,x)*eta+diff(A2,x)*(1/eta)))-(A3*eta^4/280)-(A4*eta^2/60):

A6:=(A3*eta^6/420)+(A4*eta^4/120)-(1/2)*((k1+A*cos(2*Pi*x)))*((diff(A1,x)*eta^3)+diff(A2,x)*eta):

psi0:= A1*y^3+A2*y:

psi1:= A3*y^7/840+A4*y^5/120+A5*y^3+A6*y:

psi:=psi0+delta*psi1:

V:=-diff(psi,x):

U:=diff(psi,y):

Ux:=diff(U,x):

Uy:=diff(U,y):

U2y:=diff(Uy,y):

g1:=delta*Ux:

g2:=int(U2y,x):

g22:=(1/delta)*g2:

g3:=U*Ux:

g33:=int(g3,x):

g4:=V*Uy:

g44:=int(g4,x):

P:=g1+g22-R*(g33+g44):

P1:=(1/eta)*int(P,y=0..eta):

Po:=subs(x=0,P1):

d1:=(Po-P1):

a0:=subs(k=0.0,d1):

a1:=subs(k=0.1,d1):

a2:=subs(k=0.5,d1):

plot([a0,a1, a2], x=0..1, title = "Mean Pressure Drop, alpha=1.0", legend = [k = 0, k= 0.1,k= 0.5], titlefont = ["ROMAN", 15], labels = ["x ", "Pd"], labeldirections = ["horizontal", "vertical"], labelfont = ["HELVETICA", 10], style = [POINT],symbol = [BOX,CROSS,CIRCLE],color = [black, black,black], axesfont = ["HELVETICA", "ROMAN", 8], legendstyle = [font = ["HELVETICA", 9], location = bottom],axes=boxed);

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