# Chapter 14: Steady Incompressible Flow in Pipe and Duct System¶

## Example 14.1, Page 468¶

In [1]:
from __future__ import division
import math

#Initializing  the  variables
L1  =  5;
L2  =  10;
d  =  0.1;
f  =  0.08;
Za_Zc  =  4;                                                 #difference  in  height  between  A  and  C
g  =  9.81  ;
Pa  =  0;
Va  =  0;
Za_Zb  =  -1.5;
V  =  1.26;
rho  =  1000;

#Calculations
D  =  1.5  +  4*f*(L1+L2)/d  ;                               #  Denominator  in  case  of  v**2
v  =  (2*g*Za_Zc/D)**0.5;
Pb  =  rho*g*Za_Zb  -  rho*V**2/2*(1.5+4*f*L1/d);
print "Pressure in the pipe at B (kN/m2):",round(Pb/1000,2)
print "Mean Velocity at C    (m/s)      :",round(v,2)

Pressure in the pipe at B (kN/m2): -28.61
Mean Velocity at C    (m/s)      : 1.26


## Example 14.3, Page 473¶

In [1]:
from __future__ import division
import math
from sympy import symbols,solve
import sympy

#Initializing  the  variables
Za_Zb  =  10;
f  =  0.008;
L  =  100;
d1  =  0.05;
g  =  9.81;
d2  =  0.1;

#Calculations

def  flowRate(d):
D = 1.5 + 4*f*L/d ;                                     #  Denominator  in  case  of  v1**2
A  =  math.pi*d**2/4;
v  =  (2*g*Za_Zb/D)**0.5;
z  =  A*v;
return z
Q1  =  flowRate(d1);
Q2  =  flowRate(d2);
Q=round(Q1+Q2,4)

D=symbols('D')
roots=solve(241212*D**5  -3.2, D)
dia=roots[0]

print "Rate flow for pipe 1            (m^3/s) :",round(Q1,4)
print "Rate flow for pipe 2            (m^3/s) :",round(Q2,4)
print "Combined Rate flow              (m^3/s) :",round(Q,4)
print "Diameter of single equivalent pipe (mm) :",round(dia,3)*1000

Rate flow for pipe 1            (m^3/s) : 0.0034
Rate flow for pipe 2            (m^3/s) : 0.019
Combined Rate flow              (m^3/s) : 0.0224
Diameter of single equivalent pipe (mm) : 106.0


## Example 14.4, Page 476¶

In [2]:
from __future__ import division
import math
import sympy
from sympy import solve,symbols

#Initializing  the  variables
Za_Zb  =  16;
Za_Zc  =  24;
f  =  0.01;
l1  =  120;
l2  =  60;
l3  =  40;
d1  =  0.12;
d2  =  0.075;
d3  =  0.060;
g  =  9.81;
#Calculations

v1=symbols('v1')
ash=solve(v1-0.3906*(g-1.25*v1**2)**0.5-0.25*(17.657-1.5*v1**2)**0.5,v1)
v1=round(abs(ash[0]),2)
Q1=math.pi/4*d1**2*v1

v2=(g-1.25*v1**2)**0.5
Q2=math.pi/4*d2**2*v2

v3=(17.657-1.5*v1**2)**0.5
Q3=math.pi/4*d3**2*v3

print "Flow rate in pipe 1 (m^3/s):",round(Q1,4)
print "Flow rate in pipe 2 (m^3/s):",round(Q2,4)
print "Flow rate in pipe 3 (m^3/s):",round(Q3,4)
print "continuity condition satisfied as Q1=Q2+Q3"

Flow rate in pipe 1 (m^3/s): 0.0206
Flow rate in pipe 2 (m^3/s): 0.0105
Flow rate in pipe 3 (m^3/s): 0.0101
continuity condition satisfied as Q1=Q2+Q3


## Example 14.5, Page 480¶

In [6]:
from __future__ import division
import math

#Initializing  the  variables
D  =  0.3;
Q  =  0.8;
rho  =  1.2;
f  =  0.008;
L_entry  =  10;
L_exit  =  30;
Lt  =  20*D                              #Transition  may  be  represented  by  a  separation  loss  equivalent  length  of  20  *  the  approach  duct  diameter
K_entry  =  4;
K_exit  =  10
l  =  0.4;                               #  length  of  cross  section
b  =  0.2;                               #  width  of  cross  section

#Calculations
A  =  math.pi*D**2/4;
Dp1  =  0.5*rho*Q**2/A**2*(K_entry  +  4*f*(L_entry+Lt)/D);
area  =  l*b;
perimeter  =2*(l+b);
m  =  area/perimeter;
Dp2  =  0.5*rho*Q**2/area**2*(K_exit  +  f*L_exit/m);
Dfan  =    Dp1+Dp2;

print "fan Pressure input (N/m2) :",round(Dfan,1)

fan Pressure input (N/m2) : 1254.6


## Example 14.6, Page 482¶

In [7]:
from __future__ import division
import math

#Initializing  the  variables
D  =  [0.15 , 0.3];
rho  =  1.2;
f  =  0.008;
L_entry  =  10;
L_exit  =  20;
Lt  =  20*D[1]
K  =  4;
Q1  =  0.2;

#Calculations
Q2  =  4*Q1;
A=[0.0,0.0]
A[0]  =  math.pi*D[0]**2/4;
A[1]  =  math.pi*D[1]**2/4;
Dp1  =  0.5*rho*Q1**2/A[0]**2*(K  +  4*f*L_entry/D[0]);
Dp2  =  0.5*rho*Q2**2/A[1]**2*(4*f*(L_exit  +  Lt)/D[1]);
Dfan  =    Dp1+Dp2;

print "fan Pressure input (N/m2) :",round(Dfan,2)

fan Pressure input (N/m2) : 684.51


## Example 14.7, Page 487¶

In [8]:
from __future__ import division
import math
from scipy.optimize import fsolve

#Initializing  the  variables
d  =  [0.1 , 0.125,  0.15,  0.1,  0.1  ];                    #  Corrosponding  to  AA1B  AA2B  BC  CD  CF
l  =  [30 , 30 , 60,  15,  30];                                      #  Corrosponding  to  AA1B  AA2B  BC  CD  CF
rho   =  1.2;
f     =  0.006;
Ha    =  100;
Hf    =  60;
He    =  40;
K = [0.0, 0.0, 0.0, 0.0, 0.0]
#Calculations
for i in range(0,len(l)):
K[i]  =  f*l[i]/(3*d[i]**5);

K_ab  =  K[0]*K[1]/((K[0])**0.5+(K[1])**0.5)**2;
K_ac  =  K_ab  +  K[2];
Hc  =  (K_ac*Hf  +K[4]*Ha/4)/(K_ac+K[4]/4);
Q  =  ((Ha  -  Hc)/K_ac)**0.5;

def  f(n):
z  =  He  -  Hc  +  (0.5*Q)**2  *(K[3]+(4000/n)**2);
return z

n  =  fsolve(f,1);

print "total Volume flow rate (m3/s):",round(Q, 4)
print "Head at C (m)                :",round(Hc,2)
print "Percentage valve opening (%) :",round(n,2)

total Volume flow rate (m3/s): 0.1016
Head at C (m)                : 75.48
Percentage valve opening (%) : 38.58