8. Orifice Relationships

Equations 2-9 and 2-13 can be used to develop a equation for flow through an orifice, which is a sharp-edged hole in the side or bottom of a container of water (figure 2-2a). To find the velocity of flow in the orifice, use equation 2-13, then multiply by area to get AV, or discharge, Q, resulting in:

eqn (2-14)

The subscript t denotes theoretical discharge through an orifice. This equation assumes that the water is frictionless and is an ideal fluid. A correction must be made because water is not an ideal fluid. Most of the approaching flow has to curve toward the orifice opening. The water, after passing through the orifice, continues to contract or curve from the sharp orifice edge. If the orifice edges are sharp, the jet will appear as shown on figure 2-2. The maximum jet contraction occurs at a distance of one-half the orifice diameter (d/2) downstream from the sharp edge. The cross-sectional area of the jet is about six-tenths of the area of the orifice. Thus, equation 2-14 must be corrected using a contraction coefficient, Cc, to produce the actual discharge of water being delivered. Thus, the actual discharge equation is written as:

eqn (2-15)

For a sharp-edged rectangular slot orifice where full contraction occurs, the contraction coefficient is about 0.61, and the equation becomes:

figure (2-16)

A nonstandard installation will require further calibration tests to establish the proper contraction coefficient because the coefficient actually varies with the proximity to the orifice edge with respect to the approach and exit boundaries and approach velocity.

Figure 2-2a -- Orifice flow.

Figure 2-2b -- Contraction at an orifice.