CHAPTER 9 - SUBMERGED ORIFICES

5. Discharge Through a Submerged Rectangular
Orifice

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

(9-1b)

where:

*Q* = discharge (ft^{3}/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 (ft^{2})

*g* = acceleration caused by gravity (ft/s^{2)
}*h*_{1} = upstream head (ft)

*h*_{2} = 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*_{c}C_{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*_{c}C_{vf}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, and equation 9-1a can be rewritten as:

(9-1b)

where:

*h* = *h*_{1}
- *h*_{2}, 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 A9-2^{1}
was prepared for orifice areas from 0.25 to 2.0 ft^{2}.

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