# Chapter 4: Principles of Fluid Flow¶

## Example 4.1 , Page no:172¶

In [1]:
import math
from __future__ import division

#Variable declaration
L = 3 ; #Length
D = 0.01 ; #ID
V = 0.2 ; #Average Velocity
rho =999.7 ; #kg /m^ 3

#calculations
v =1.306 * 10** -6 ; #m^2/ s
ReD =0.2*0.01/(1.306*10** -6) ;
f = 16/ ReD ;
deltap = 4*f*(L/D)*( rho*V **2) /2;
Vmax = 2*V;

#result
print"Pressure drop is",round(deltap,4),"Pa";
print"Maximum velocity is",round(Vmax,3),"m/s";

Pressure drop is 250.6768 Pa
Maximum velocity is 0.4 m/s


## Example 4.2(a) , Page no:180¶

In [2]:
import math
from __future__ import division

#Variable declaration
L = 3 ; #m
D = 0.01 ; #m
V = 0.2 ;#m/ s
rho = 971.8 ; #kg /m^ 3

#calculations
v = 0.365 * 10** -6 ; #m^2/ s
ReD = D*V/v;
f =0.079*( ReD )**( -0.25) ;
deltap = (4*f*L* rho *V**2) /(D *2) ;
x = ((f/2) **0.5) *V ;
yplus = 0.005* x /(0.365*10** -6) ;
Vmax = x *(2.5* math.log ( yplus ) + 5.5) ;
ratio = Vmax /V;

#result
print"(a) If the temperature of water is increased to 80 degree C";
print"Pressure drop is",round(deltap,4),"Pa";
print"Vmax =",round(Vmax,4),"m/s";
print"Vmax/Vbar =",round(ratio,4);

(a) If the temperature of water is increased to 80 degree C
Pressure drop is 214.1563 Pa
Vmax = 0.2515 m/s
Vmax/Vbar = 1.2575


## Example 4.2(b) , Page no:180¶

In [3]:
import math
from __future__ import division

#Variable declaration
L = 3 ; #m
D = 0.01 ; #m
V = 0.2 ; #m/s
V1 =0.7;
v1 = 1.306 * 10** -6 ; #m^2/ s
V1 =0.7; #m/ s

#calculations
ReD1 =V1*D /(1.306*10** -6) ;
f1 = 0.079*( ReD1 )**( -0.25) ;
deltap1 = (4* f1*L *999.7*0.7**2) /(0.01*2) ;
x1 = (( f1 /2)**0.5) *V1 ;
y1plus = 0.005* x1 /( v1);
Vmax1 = x1 *(2.5* math.log ( y1plus ) + 5.5) ;
ratio1 = Vmax1 /V1;

#result
print"(b) If the velocity is increased to 0.7 ";
print"Reynolds no is",round(ReD1,4);
print"Pressure drop is",round(deltap1,4),"pa";
print"y+ at centre line =",round(y1plus,4);
print"Vmax is",round(Vmax1,4),"pa";
print"Vmax/Vbar =",round(ratio1,4);

(b) If the velocity is increased to 0.7
Reynolds no is 5359.8775
Pressure drop is 2713.6598 pa
y+ at centre line = 182.087
Vmax is 0.8804 pa
Vmax/Vbar = 1.2577


## Example 4.3 , Page no:181¶

In [4]:
import math
from __future__ import division

#Variable declaration
P = 80 * 10**3 ; #Pa
L = 10 ; #m
Vbar = 1.9 ; #m/s
l = 0.25 ; #m
b = 0.15 ; #m
rho = 1.185 ; #kg /m^ 3

#calculations
mew = 18.35 * 10** -6 ; #kg /m s
rho1 = rho *(80/101.3) ; #kg /m^ 3
r = b/l;
De = (4* l/2*b /2) /(l/2 + b /2) ;
Dl = (2/3 + 11/24*0.6*(2 -0.6)) * De ;
Re = rho1 * Dl * Vbar / mew ;
f = 0.079*( Re ** -0.25) ;
deltaP = 4*f*(L/ Dl )*( rho1 *( Vbar **2) /2) ;
power = deltaP *( Vbar *l*b)

#result
print"Reynolds no =",round(Re,4);
print"f =",round(f,4);
print"Pressure drop =",round(deltaP,4),"Pa";
print"Power required =",round(power,4),"W";

Reynolds no = 19107.1453
f = 0.0067
Pressure drop = 2.3024 Pa
Power required = 0.164 W


## Example 4.4 , Page no:189¶

In [5]:
import math
from __future__ import division

#Variable declaration
l = 2 ; #m
b = 1 ; #m
V = 1 ; #m/s
rho = 1.060 ; #kg /m^ 3
x = 1.5 ; #m^2/s

#calculations
v = 18.97 * 10** -6 ;
Re = V*x/v; #Reynolds number
d = 5*x/( Re **(1/2) ) *1000 ;
Rel = V*l/v;
cf = 1.328* Rel** -(1/2) ; #drag coefficient
Fd = 0.00409*(1/2) *rho *(2* l*b) *1**2;

#result
print"Thickness of Boundary layer at x =1.5 is ",round(d,4),"mm"
print"Drag Coefficient cf =",round(cf,5);
print"Drag Force FD =",round(Fd,6),"N";

Thickness of Boundary layer at x =1.5 is  26.6716 mm
Drag Coefficient cf = 0.00409
Drag Force FD = 0.008671 N


## Example 4.5 , Page no:195¶

In [6]:
import math
from __future__ import division

#Variable declaration
l = 2 ; #m
v = 4 ; #m/s

#calculations
mew = 18.1*10** -6; #N s /m^ 2
rho = 1.205*1.5; #kg /m^ 3
Rel = rho*v*l/ mew ;
Cf = 0.074*(7.989*10**5) **( -0.2) - 1050/ Rel ;
Df = Cf *1/2* rho*l*v **2;
x = 3*10**5 * (18.1*10** -6) /(1.808*4) ;

#result
print"Drag coefficieent is",round(Cf,6);
print"Drag force per meter width =",round(Df,6),"N";
print"Value of xc is",round(x,6),"m";

Drag coefficieent is 0.003569
Drag force per meter width = 0.103221 N
Value of xc is 0.75083 m