CHAPTER 14  MEASUREMENTS IN PRESSURE CONDUITS
This method measures the discharge from the open end of partially filled horizontal pipes discharging freely into the air (Vanleer, 1922; 1924). This method is sometimes considered a trajectory method. However, the measurement is really based on the brink depth at the end of the pipe. This method can be adapted to the measurement of discharge in small open channels where the discharge can be diverted through a horizontal pipe flowing partially full and discharging freely into the air.
Figure 1411 illustrates one pipe fitting arrangement to accommodate the California pipe discharge measurement. Other arrangements may be possible. With such an arrangement, the only measurements necessary are the inside diameter of the pipe and the vertical distance from the upper inside surface of the pipe to the surface of the flowing water at the outlet end of the pipe. With this information, the discharge may be computed by:
Q = 8.69 (1 a/d)^{1.88} d^{2.48} (146)
where:
Q = discharge (ft^{3}/s)
a = distance measured in the plane of the end of the pipe from the top of the inside surface of the pipe to the water surface (ft)
d = internal diameter of the pipe (ft)

This equation, developed from experimental data for pipes 3 to 10 in in diameter, gives reasonably accurate values of discharge for that range of sizes under certain flow conditions. However, tests by the Natural Resources Conservation Service (formerly U.S. Soil Conservation Service) (Rohwer, 1943) showed that for depths greater than about onehalf the diameter of the pipe or a/d less than about 0.5, the discharge does not follow the Vanleer equation. Bos (1989) shows that brink depth must be less than 0.55d, or a/d must be greater than 0.45. Care should therefore be taken in using equation 146. The discharge uncertainty of this method is expected to be about +/10 percent, assuming careful brink depth and pipe diameter measurements.
Some additional requirements for proper use and for attaining potential accuracy of the California pipe measurement method are:
(1) The discharge pipe must be level.
(2) The pipe must be partially full with a/d greater than 0.45.
(3) The flow must discharge freely into the air.