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Orifice Submerged in Liquid Discharge Rate Calculator and Equation
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Orifice Submerged in Liquid Discharge Rate Calculator and Equation
Submerged Orifice Operating under SteadyFlow Conditions
Preview Submerged Orifice Operating under SteadyFlow Conditions
Eq. 1
Q = A_{2} v_{2} = C_{d} C_{c} C_{v} C_{va} A [ 2 g (h_{1}  h_{2}) ]^{(1/2)}
The coefficient of contraction, C_{c}, accounts for the flow area reduction of the jet caused by the flow curving and springing from the orifice edges. The coefficient C_{va}accounts for the velocity distribution and friction loss. The product, C_{c} C_{va}, is sometimes called the coefficient of discharge, C_{d}. The coefficient C_{v} accounts for using the water head only and does not fully account for the velocity head of approach. The effective discharge coefficient, C_{d} , is the product C_{d} C_{c} C_{v} C_{va}, which has been determined experimentally to be 0.61 for rectangular irrigation weirs. The coefficient of contraction has the most influence on the effective coefficient discharge. Because C_{c} must approach unity as velocity approaches zero, its value will increase rapidly after reaching some low velocity. Thus, the equation should not be used for heads less than 0.2 ft even with very precise head measuring devices. The difference between upstream and downstream heads or water surface elevations is sometimes called the differential head, can be rewritten as:
Eq. 2
Q = C_{d} A [ 2 g (h_{1}  h_{2})^{(1/2)}
Q = C_{d} A [ 64.4 (h_{1}  h_{2})^{(1/2)}
where
v_{2} = velocity of fluid exiting orifice
Q = discharge (ft^{3}/s)
C_{d} = Discharge coefficient
C_{c}= coefficient of contraction (use 1.0 unless C_{d} specified)
C_{v}= coefficient of velocity caused by friction loss (use 1.0 unless C_{d} specified)
C_{va} = coefficient to account for exclusion of approach velocity head from the equation (use 1.0 unless C_{d} specified)
A = the area of the orifice (ft^{2})
g = acceleration caused by gravity (32.2 ft/s^{2})
h_{1} = upstream head (ft)
h_{1} = downstream head (ft)
Table 1 Variation in the Circular Orifice discharge coefficient, with relative distance from the orifice edge to the upstream and downstream concentric boundary (Adapted from Albertson et. al. 1960)
Boundary distance  C_{d} 
Increase in C_{d} (%) 
> 10 diameters  0.61 
 
1 diameter  0.62 
1% 
1/2 diameter  0.65 
6% 
1/4 diameter  0.68 
11% 
Table 2 Average discharge coefficients for furrow orifices measured by Rodinson (1959)
Orifice Diameter 
C_{d} Submerged Flow 
C_{d} Free flow 

mm 
(inches) 

19.1 
(3/4) 
0.57 
0.61 
26.4 
(1.0) 
0.58 
0.62 
34.9 
(13/8) 
0.61 
0.64 
44.5 
(13/4) 
0.61 
0.63 
50.8 
(2.00 ) 
0.61 
0.62 
63.5 
(21/2) 
0.60 
0.61 
76.2 
(3.00 ) 
0.60 
0.60 
88.9 
(31/2) 
0.60 
0.60 
101.6 
(4 ) 
0.60 
0.60 
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Source
 United States Department of the Interior Bureau of Reclamation
 Albertson, Maurice L., James R. Barton, and Daryl B. Simons. 1960.
 Fluid mechanics for engineers. Prentice Hall, Inc., Englewood Cliffs, NJ, pp 133 and 136.
 American Society of Mechanical Engineers (ASME). 1959. Fluid metersâ€”their theory and application. American Society of Mechanical Engineers 5th Edition. 19 West 39th St., New York, pp. 6977.
 Bos, M. G. 1976. Discharge measurement structures. Publication No. 20, International Institute for Land Reclamation and Improvement, Wageningen, The Netherlands.