Measure Flow Rate Q Using the California Pipe Method

Nov 19

When you need to measure water flow rate “Q” using a partially filled horizontal pipe use the “California Pipe Method”

This method of Hydropower site flow measurement for Q. given in this post is derived from a technique often used to measure water flow rates in pipes for agricultural purposes such as irrigation. Hence the ‘California Pipe Method’ name. As you see, we’re back to our Blueberry ranch again, I digress…

Speaking of a Hydropower & Penstock pipeflow digression…
… Our friends over at have another penstock flow modeling software deal for us. 

This one is good until they say it’s gone!

… For more on this discount deal, See our Penstock Tools & Special Offers page too.

… Back to our Hydroelectric Site Survey methods;

This partial flow estimation method is used to measure the discharge from an open and a partially filled horizontal pipe. This pipe must discharge freely into the air. (Vanleer, 1922, 1924) There are times when this method is considered as a trajectory method, which was covered in a previous post on using a filled pipe. But this is really not a trajectory method, as can be seen by the requirement for horizontal pipe. The air gap in the pipeline over the water must flow for a length of at least six times the diameter of the pipe as measured from the exit opening. The discharge flow is at atmospheric pressure.

This flow measurement technique is based on measuring what’s called the waters “brink depth” at the end of the pipe; this depth is denoted as the height ‘a’ in the enclosed diagram. The inside diameter of the pipe is denoted as ‘D’. Both of these measurements for this calculation are given in feet. The resulting output is measured in cubic feet per second or CFS. You will need to convert into these units and back out if using metric. Sorry about that!

The figure given below illustrates how one pipe fitting arrangement will allow atmospheric pressure to exist above the water flow for a least six times the pipes diameter. Other configurations can be designed with the fundamental restriction that there must be air above the water for greater than six times the diameter of the tube and that the exit pipeline must be horizontal.

The only required measurement is the inside diameter of the pipe, (ID = ‘D’), and the distance from the inside surface of the pipe down to the flowing water’s surface at the exit point, (distance = ‘a’.) By simply obtaining these two distance measurements ‘D’ and ‘a’ in decimal feet. Then by using the following equation for Q., you can now compute Q. or the penstock potential flow rate in CFS.

Vanleer – Partial Pipe Flow Equation: Q = 8.69 (1 -a/D)^1.88 x D ^2.48

Measure Pipe Flow from a Partially Filled Pipe - California Pipe Method

Figure 1: Hydropower Penstock or pipe flow rate ‘Q’ measurement, with a partially filled pipe using the “California pipe method”


Where the key Partial Pipeflow Measurement Parameters are given as:

Q = Water discharge rate (ft3/s)

a = Distance measured in the plane of the end of the pipeline or penstock from the top of the inside surface of the pipe to the water surface (ft)

D = Internal diameter of the pipeline (ft)









Note: The following engineering flow measurement restrictions on using this technique to measure your hydropower water flow rate. Q.:

As much of this material was excerpted from the US Bureau of Reclamation site make sure you follow these limitations —


USBR Notes: 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 one-half 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 14-6. 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.
See: USBR Hydraulics Lab – Water Measurement Manual – Measurements in pressure conduits for more on water flow measurements.

Hydro Prospector Jess

Got SmallHydro?sidebar-pic
How may we help you Prospect for Small & Micro Hydropower Resources?