Measuring Streamflow Q. Using a Rectangular Slotted Weir

Dec 21

One method to accurately measure flow Q for small and medium-size streams is through the use of a slotted Weir.

Methods for Measuring Your Stream Flow…

Stream Flow x Fall = Hydro Power

Stream Flow x Head Pressure = Power

Stream levels will change through the seasons, so it is important to measure FLOW at various times of the year. We will need these varied flow measures to create an FDC or flow Duration curve, more on the FDC in a later post. If this seasonal variable flow measure is not possible, attempt to determine various annual flows by discussing the stream with a neighbor, or finding US geological survey flow data for your stream or a nearby larger stream. Also keep in mind that fish, birds, plants and other living things rely on your stream for survival. Especially during low water seasons, avoid using all the water for your hydro system. FLOW is typically expressed as volume per second or minute. This is also called a “FLOW rate” since it is a dynamic volume per time interval. Common examples of volume units are gallons or liters per second (or minute), and cubic feet or cubic meters per second (or minute):

A rectangular slotted Weir consists of a temporary dam structure with a rectangular slot are opening gate.

This slotted Weir gate has the following characteristics;

  1. All stream flow to be measured, Q. is constrained to go through the slotted gate.
  2. The bottom of the rectangular slotted Weir gate is leveled horizontally.
  3. A reference stake or pole is driven into the stream bed below the water line. So that it is exactly level with bottom of the Weir gate.
  4. The stake must be placed upstream at least four times the distance of the maximum Weir gate water depth.
  5. Water must be allowed to exit the Weir gate freely, such that there is an air gap beneath it as it flows over the Weir. A “sharp” 90 degree edge lip helps here.
  6. Water upstream of the Weir must move freely and not have major disturbances.
  7. Water will contract or shrink in width x depth, as it increases speed, when it approaches and flows through the opening.


Given both the width and depth of the water flowing over the Weir; it is a simple procedure to look up the value for the water flow using a Weir table.

Measure Stream Flow Q using a Rectangular Weir (contracted) Measure Stream Flow Q using a Rectangular Weir (contracted)

The following table is based on a reference Weir gate 1 inch wide.

An example of use is as follows:

Assume your Weir gate is 1 foot wide or 12 inches, you measure the water passing over it at 6 1/4 inches.

Using the table, you look up 6+1/4 and read 6.2 5 CFM per inch of width.

Multiply 6.25 CFM/in x 12 in = 75 CFM. That’s a pretty decent flow, if you have enough head you may be in business.

FYI – Metric Formula for a rectangular notched Weir is: Q = 2/3 x Cd x , 2g^1/2 x (L – 0.2h) x h^3/2, Where Cd is the coefficient of discharge.

Take Cd = 0.6 (normal case) then Q = 1.8 x (L – 0.2h) x h^3/2 in liters/sec

  +0/8 +1/8 +1/4 +3/8 +1/2 +5/8 +3/4 +7/8
0 0.00 0.01 0.05 0.09 0.14 0.19 0.26 0.32
1 0.40 0.47 0.55 0.64 0.73 0.82 0.92 1.02
2 1.13 1.23 1.35 1.46 1.58 1.70 1.82 1.95
3 2.07 2.21 2.34 2.48 2.61 2.76 2.90 3.05
4 3.20 3.35 3.50 3.66 3.81 3.97 4.14 4.30
5 4.47 4.64 4.81 4.98 5.15 5.33 5.51 5.69
6 5.87 6.06 6.25 6.44 6.62 6.82 7.01 7.21
7 7.40 7.60 7.80 8.01 8.21 8.42 8.63 8.83
8 9.05 9.26 9.47 9.69 9.91 10.13 10.35 10.57
9 10.80 11.02 11.25 11.48 11.71 11.94 12.17 12.41
10 12.64 12.88 13.12 13.36 13.6 13.85 14.09 14.34
11 14.59 14.84 15.09 15.34 15.59 15.85 16.11 16.36
12 16.62 16.88 17.15 17.41 17.67 17.94 18.21 18.47
13 18.74 19.01 19.29 19.56 19.84 20.11 20.39 20.67
14 20.95 21.23 21.51 21.80 22.08 22.37 22.65 22.94
15 23.23 23.52 23.82 24.11 24.40 24.70 25.00 25.30
16 25.60 25.90 26.20 26.50 26.80 27.11 27.42 27.72
17 28.03 28.34 28.65 28.97 29.28 29.59 29.91 30.22
18 30.54 30.86 31.18 31.50 31.82 32.15 32.47 32.80
19 33.12 33.45 33.78 34.11 34.44 34.77 35.10 35.44
20 35.77 36.11 36.45 36.78 37.12 37.46 37.80 38.15

A Weir is especially effective for measuring FLOW during different times of the year. Once the Weir is in place, it is easy to quickly measure the depth of the water and chart FLOW at various points in time. Design Flow Even though your Flow may be very high after exceptionally rainy periods, it probably won’t be cost effective to design your turbine system to handle all that water for just a few days of the year. Instead, it makes sense to build a system that uses Flow you can count on for much of the year. This is called Design Flow, and it is the maximum Flow your hydro system is designed to accommodate. Design Flow, along with Net Head, determines everything about your hydro system, from pipeline size to power output.  For more on measuring stream flow you may want to visit Canyon Hydro – Measuring Flow, or British Hydro – Flow Measuring.

Estimation of Water Flow Rate Q Using Average Cross-section

Dec 16

Equation of interest: Area x Average speed x 80% Friction Factor = Q,  
the estimated average stream flow rate.


By measuring the rate of travel for a floating object traveling down the main flow of a stream and then multiplying by the average cross-sectional area. One can determine the average volume flow rate or Q directly. Please note that this method is only an estimation, and will have inaccuracies due to anomalies in the channel and issues surrounding the float chosen, etc. The main difficulty in carrying out this measurement has to do with the care and problems in accurate measurement of the streams cross-sectional profile between the points B-B’.



  1. Pick a fairly regular part of the stream with about the same cross section and curvature for a 100 foot distance.
  2. Measure a 50 to 100 foot section or race course of your stream bed. The length between point A and B. will be used to measure the velocity of the float.
  3. Select a float that will be somewhat neutrally buoyant, such as an orange. Plus it’s biodegradable :-)
  4. The goal is to have it float just at or under the surface down through the race course between point A and B.
  5. Use a stopwatch to time, several runs, tossing your float in upstream from section A while starting the watch as the float crosses section A and stopping the watch just as the float crosses section B.  Repeat this sequence 5 or 10 times and average the measured times. The average is obtained by adding the times up and dividing by the number of times that you measured the elapsed time. Throw out any times that are grossly apart from each other.
  6. Now measure the cross sectional area of the creek by measuring the distance from the surface to the bottom of the creek (Use a level reference line see diagram in this post.) Each distance must be taken using the same horizontal interval, say 1 foot. Now add up the depth measurements and divide by the number of measurements. This is your average cross sectional depth. Multiply by the interval width and you have average area.
  7. Multiply average stream velocity x average cross section area x friction correction factor of 0.8. Due to friction, bottom irregularities, etc. this is the least accurate measurement. It is likely only about 15-20% accurate at best. Concrete channels are best and rough streambeds the worst cases for using this method. Still, it will be better at stream flow estimation than a rough estimate or wild guess.

Diagram: Stream Flow Measurement Using a Float, Stopwatch and average cross sectional area estimate.

Stream Flow Estimation By Direct Measurement of Speed x Cross section Area

Stream Flow Estimation By Direct Measurement of Speed x Cross section Area

For more on this method visit this US EPA Water Flow Rates document.

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.

Measuring the flow rate Q from an open pipe

Oct 02

How to Measure your Water Flow Rate Q from an Open Pipe:

There are times when it’s necessary to estimate the flow rate from a stream constrained to flow in a water jet flowing from an open pipe. This flow measurement method doesn’t require us to have precision fluid flow measurement instrumentation, other than a straight edge and plumb bob. Flow meters or weirs would likely be more accurate, but sometimes all you have is a filled pipe with a jet of water streaming out. If that’s the case, then try this method.

Pipe Flow Direct Q Measurement Diagram A

Pipe Flow Q Direct Measure Diagram A

There are two basic pipe flow measurement methods used to make this estimation. The first pipe flow measurement method involves pipes that are completely filled; that is they have no air in  the water pipe above the fluid exiting the pipe, the other method used is a partially filled pipe. The completely filled pipe flow case will be fairly easy to measure utilizing the table enclosed below. The other method we will cover in another blog post.

Meanwhile let’s examine how to measure the pipe flow rate Q from a water jet squirting from a full pipe:

What is needed to measure the completely filled pipe flow case is a simple straight edge ruler and a plumb bob marked off at an appropriate pre defined distance, in this case we use 13 inches. To utilize this method one simply measures out an appropriate extra distance parallel to the initial pipe exit flow direction up to an intercept point with the plumb bob line that is 13 inches below that point. See  flow measurement diagrams A, B & C.

You will move the ruler parallel to the pipeline until the plumb bob just touches the outer edge of the falling stream of water. By measuring this intercept distance X. for the given 13 inch plumb bob Y. value, you then simply use the table below with your pipe diameter and X value to look up the flow in gallons per minute or GPM.  You can convert these values to your desired standard units of measurement as well.

This water flow estimation technique is used in agriculture to measure irrigation flow from an open pipe. This method can also be used for smaller flows,  if a stream can be constrained temporarily to completely fill the inside of a pipe and flow out the end above the ground or stream tail water enough to not interfere with the plumb bob.

Keep in mind that if the pipe is small enough, direct measurement can be made by filling the bucket and timing the amount of time it takes to fill it, we’ll discuss this in another Small Hydro power stream flow measurement post and link to it later.

So, Let’s take a look at the measurement technique, see pipe flow measurement procedures, and diagrams A., B. and C. :

Tools needed to measure your hydropower system pipe flow rate Q:

  1. Straight edge ruler marked in inches
  2. Plumb bob or thinweight and string at least 2 feet long
  3. A pipe completely filled with the water flow jet about 18-24 inchs up in the air above any interference.


Procedure to measure potential hydropower system flow Q from a full flowing pipe:

  1. Tie plumb bob so it dangles 13 inches below the bottom of staight edge ruler
  2. Place straight edge ruler along top edge of pipe parallel to exit flow
  3. Shift ruler until plumb bob  just touches outer surface of the flow at 13 inches below the attachment to ruler.
  4. Measure X distance betwee pipe tip and bob string attachmet point.
  5. Measure inside diameter of pipe
  6. Use ‘X’ and Diameter with edges of table to read off flow rate in GallonsPer Minute (GPM)


Note: Keep ruler parallel to pipe at all times.

Pipe Flow Q Direct Measure Diagrams Full & Partial flow D-E

Pipe Flow Q Direct Measure Diagrams Full & Partial flow D-E

















Some more views of the same measurement, it works the same regardless of pipe angle. Of course bigger errors can happen at steeper angles.


Pipe Flow Q Direct Measure Diagrams B & C















The following table can be used to look up the corresponding flow rate in gallons per minute or GPM when given your measured X. value.  See the reference equation given below for how this was computed. Also see the OSU irrigation and hydrology site for more information on these irrigation and other water flow measurement methods.  Click the water flow table picture below to get a closer view of the table or to print it  out.


Equation for computing Full Pipe Flow Rate in GPM

Equation for Full Pipe Flow Rate in GPM

Note  Disclaimer

- This is a pipe flow estimation table calculated for 13 inches of  ‘Y’ fall. For other ‘Y’ distances use the formula given.  Accuracy is not guaranteed, so check your work to make sure the results are adequate for your application.



Pipe Flow Direct Measure Flow - Q Chart

Pipe Flow Direct Measure Flow - Q Chart

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