

In [3]:

    
from IPython.display import Image
Image("https://raw.githubusercontent.com/albinengqvist/headloss/master/Wapro.png", width = 500)









    Out[3]:

Flow Headlosses

Definintion.
Factors affecting Head Loss.
Testing and interpretation of test results.

Definition

$h_L = \left(\frac{fL}{D} + \sum{K_L}\right)\frac{V^2}{2g}$

$ \Delta p_{f,minor_L} = \frac{K_L \rho V^2}{2} = \rho g h_{L,minor} \Rightarrow K_L \frac{V^2}{2g} $

f: Frictionfactor [-]
L: Length [m]
D: Diameter [m]
V: Velocity [m/s]
K_L: Loss coefficient [-]
g: Gravitational constant [m/s^2]



In [27]:

    
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
import itertools
sns.set_style("darkgrid")
 

ls=np.array([110, 220, 330, 440, 550, 660, 770, 880, 990, 1100])
hloa=np.array([275.6082551, 337.6957121, 419.7588915, 521.7977934, 643.8124176, 785.8027643, 947.7688333, 1129.710625, 1331.628139, 1553.521375])
hlsm=np.array([97.33285084, 129.2994326, 182.0637356, 255.6257598, 349.9855051, 465.1429717, 601.0981594, 757.8510684, 935.4016985, 1133.75005])
v = (ls/1000)/(3.14*.3**2)
hlp = v**2/(2*9.81)*1000
dpoints = np.prod(ls.shape)

kl=[]
for i in range(0,dpoints):
    kl.append((hlsm[i]/1000*2*9.81)/(v[i]))

label=[]
for i in range(0,dpoints):
    label.append("%s \n\n%s" %(ls[i], round(v[i],1)))
palette = itertools.cycle(sns.color_palette())
ax = plt.gca()

plt.xlabel("Volume $[l/s]$ \nVelocity $[m/s]$")
plt.ylabel("Headloss $[mmH_2O]$")
plt.title("Headloss WaStop DN600")
ax.xaxis.set_label_coords(-0.02, -0.025)
plt.plot(ls,hloa, label="Open air")
plt.plot(ls,hlsm, label="Submerged")
plt.plot(ls,hlp,'--', label="Pipe outlet")

sns.despine()
plt.legend(loc='upper left')
plt.xticks(ls, label)
plt.savefig('hlws590.png', bbox_inches='tight')
plt.show()



In [29]:

    
vs = np.array([[0.360579339, 13.11494829], [0.630707975, 6.327570779],[0.827308733, 4.475241236],[1.156346006, 3.291538182],[1.796251721, 3.351837723],[2.685729428,2.308585886],[3.361514288, 1.973324374],[3.751193792, 1.756208531],[3.983929796, 1.643932524],[2.38443832, 2.35984761],[ 
1.744985423, 2.911150525]])
vs= vs[np.argsort(vs[:,0])]
plt.scatter(vs[:,0],vs[:,1], marker = 'o', color=next(palette))
plt.axhline(y=2, xmin=0.5, color=next(palette), linestyle='--')
plt.axhline(y=1, color=next(palette), linestyle='--')
plt.xlabel("Velocity $[m/s]$")
plt.ylabel("Minor Loss Coeff. $K_L$")
plt.text(1.8,1.8, '$K_L = 2$')
plt.text(0.2,1.3, '$K_L = 1$')
plt.text(3,8, '$H_L = K_L(V^2/2g)$')
plt.savefig('klws590sm.png', bbox_inches='tight')
plt.show()