Orifices

The purpose of an orifice generally is to divert excess stormwater from the stormwater system during dry weather periods and to restrict the entry of stormwater into the sanitary interceptors during periods of runoff. The orifice may divert the flow to another pipe, a pumping station or an off-line storage tank.

The Orifice Diversion dialog shows two typical diversions:

1. a dropout or sump orifice, and 
2. a side outlet orifice.

EXTRAN simulates both types of orifice by converting the orifice to an equivalent pipe. The conversion is made as follows. The standard orifice equation is:

Equation 35:  

where:

C_o = discharge coefficient (a function of the type of opening and the length of the orifice tube),

A_o = cross-sectional area of the orifice,

g = gravitational acceleration, and

h = the hydraulic head on the orifice.

Values of C_o and A_o are specified by the user. To convert the orifice to a pipe, the program equates the orifice discharge equation and the Manning pipe flow equation, i.e.,

Equation 36: 

where:

m = 1.486 for U.S. customary units and 1.0 for metric units, and S_o is the bed slope.

The orifice conduit is assumed to have the same diameter or depth, D, as the orifice and to be nearly flat, the invert on the discharge side being set 0.01 ft (3 mm) lower than the invert on the inlet side. In addition, for a sump orifice, the pipe invert is set by the program 0.96·D below the junction invert so that the orifice conduit is flowing full before any outflow from the junction occurs in any other pipe. For side outlet orifices, the user specifies the height of the orifice invert above the junction floor.

If the slope, S, is written as Hs/L where L is the pipe length, then Hs will be identically equal to h when the orifice is submerged. When it is not submerged, h will be the height of the water surface above the orifice centerline while Hs will be the distance of the water surface above critical depth (which will occur at the discharge end) for the pipe.

For practical purposes, it is assumed that Hs = h for this case also. Thus, letting S = h/L and substituting R = D/4 (where D is the orifice diameter) for circular conduits into equation 31 and simplifying gives,

Equation 37: 

The length of the equivalent pipe is computed as the maximum of the value entered in the "Simulation Tolerances" dialog in Job Control or

Equation 38: 

to ensure that the celerity (stability) criterion for the pipe is not violated. Manning’s n is then computed according to equation 35. This algorithm produces a solution to the orifice diversion that is not only as accurate as the orifice equation but also much more stable when the orifice junction is surcharged. A similar procedure is used for rectangular orifices with appropriate modifications to the hydraulic radius calculations.