Weirs are commonly used to measure flow at small creeks and other flow systems. We have developed a simple Python function to calculate the discharge from a weir “discharge_weir(C,L,H,n)”. We will check our results using two formulas -Addition formula and Francis formula.
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def discharge_weir(C,L,H,n):
#Weirs allow hydrologists and engineers a simple method of measuring
#the volumetric flow rate in small to medium-sized streams
# Function for the discharge equation by Addition in 1949, for TRAPEZOIDAL WEIR
'''
Q is flow rate
C is a constant for structure, when flow in cfs, C=3.37
L is the width of the crest in FEET
H is the height of head of water over the crest in FEET
n varies with structure (e.g. 3/2 for horizontal weir, 5/2 for v-notch weir)
'''
return round(C*L*(H**n),2), 'is the flow in CFS using Addition (1949) formula'
'''
for RECTANGULAR WEIRS:
The flow rate measurement in a rectangular weir is based on the Bernoulli Equation
principles and can be expressed as:
Q = 2/3 C L (2 g)1/2 H^(3/2)
where
Q = flow rate (m3/s)
H = head on the weir (m)
L = width of the weir (m)
g = 9.81 (m/s2) - gravity
C= discharge constant for the weir - must be determined
'''
#The Francis Formula - Imperial Units
def discharge_weir_Francis(C,L,H,n):
'''Flow through a rectangular weir can be expressed in imperial units with the Francis formula
Q = 3.33 (L - 0.2 H) H^(3/2)
where
Q = flow rate (ft3/s)
H = head on the weir (ft)
L = width of the weir (ft)
C=3.33
n=3/2=1.5
'''
return round(C*(L-0.2*H)*(H**n),2), 'is the flow in CFS using Francis formula'
print discharge_weir(3.37,3.0,2.0,1.5)
print discharge_weir_Francis(3.33,3.0,2.0,1.5)
Output
(28.6, 'is the flow in CFS using Addition (1949) formula') (24.49, 'is the flow in CFS using Francis formula'
Run the program online by calling the Python Function:
http://www.codeskulptor.org/#user20_ONn0eFrNzO_2.py