CHAPTER 9 - SUBMERGED ORIFICES

5. Discharge Through a Submerged Rectangular Orifice

The equation for computing the discharge of the standard submerged rectangular orifice is:

where:

Q = discharge (ft³/s)
C_c = coefficient of contraction
C_vf = coefficient of velocity caused by friction loss
C_va = coefficient to account for exclusion of approach velocity head from the equation
A = the area of the orifice (ft²)
g = acceleration caused by gravity (ft/s²⁾
h₁ = upstream head (ft)
h₂ = downstream head (ft)

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_vf accounts for the velocity distribution and friction loss. The product, C_cC_vf, is sometimes called the coefficient of discharge, C_d. The coefficient C_va accounts for using the water head only and does not fully account for the velocity head of approach. This coefficient is near unity if all the requirements of section 4 are met. The effective discharge coefficient, C_d, is the product C_cC_vfC_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, and equation 9-1a can be rewritten as:

where:

h = h₁ - h₂, differential head
C_d = 0.61, as determined experimentally.

The discharge, when velocity of approach is negligible, may be computed using equation 9-1b. Table A9-2¹ was prepared for orifice areas from 0.25 to 2.0 ft².

¹ The prefix "A" denotes tables that are located in the appendix.