V Notch Weir Calculator for Open Channel Flow Measurement
Posted on Sunday, April 17, 2011 at 2:25 PM

 Introduction to V Notch Weirs

If you want to obtain an Excel spreadsheet for v notch weir flow measurement calculations, click here for the downloads page.  Read on for information about Excel spreadsheets that can be used as V notch weir open channel flow calculators.

As shown in the diagrams and picture below, v-notch weir is a descriptive name for this open channel flow measument device.  It is basically a v shaped notch in a plate place perpendicular to the flow in an open channel.  The water must flow through the v notch and thus create a measureable head over the weir that can be measured and used to calculate the open channel flow rate.

Sharp Crested Weir Background

 There are several commonly used types of sharp crested weirs, including the rectangular, cipolleti, and v notch weirs.  The diagram at the left shows several commonly used sharp crested weir parameters on a longitudinal cross-sectional view.  The picture at the right below shows a v notch weir as used to measure open channel flow rate.  

The terms illustrated on the diagram include the weir crest, which is the point of the "v notch," for a v notch weir; the nappe, which is the sheet of water flowing over the weir; and the drawdown, which is thedecrease in water level going over the weir.  The drawdown is caused by the acceleration of the water as it goes over the weir.  The v notch weir equations that will be discussed require free flow over the weir.  In order to have free flow, there must be air under the nappe, as shown in the diagram.

The head over the weir is the measurement shown as H in the diagram; P is the height of the weir crest above the bottom of the channel; and Q is shown as the open channel flow rate, which must also be the flow over the weir.

Picture Credit:  U.S. Forest Service

V-Notch Weir Equations for a 90 Degree Notch Angle

The equation recommended by the U.S. Department of the Interior, Bureau of Reclamation in their Water Measurement Manual (ref #1 below) for fully contracted, 90 degree v notch weirs, for free flow conditions and 0.2 ft  <  H  <  1.25 ft, is as follows:

Q = 2.49H2.48, for U.S. units, where Q and H are as shown in the diagram above, that is: Q = flow rate over the weir in cfs and H = head over the weir in ft.

In S.I. units:  Q = 1.36H2.48, where Q = flow rate over the weir m3/s and H = head over the weir in m.

The conditions required for a v notch weir to be fully contracted are:  P > 2Hmax and S > 2Hmax.

The diagram above shows the parameters, H, P, θ and S for a v notch weir, as used in the equations and conditions given above for open channel flow measurement.

The screenshot to the right shows an Excel spreadsheet that can be used as a  90o, v notch weir flow calculator.  Input values for H, P, S, and Hmax, the spreadsheet checks on whether the conditions required for use of the above equations are met.  It also calculates the flow rate Q, based on the specified value of the head over the weir, H.  Check out the downloads page for this spreadsheet in either U.S. or S.I. units at very low cost.

 

 

 

V notch Weir Equations for Notch Angles Other Than 90 Degrees

 The Kindsvater-Carter equation is recommended in the Water Measurement Manual (Ref #1) for v notch weirs having a notch angle other than 90 degrees.  The general form of the Kindvater-Carter equation is:

Q =(8/15)(2g)1/2 Ce Tan(θ/2)(H + k)5/2, where the effective discharge coefficient, Ce, and the head correction factor, k, are both functions of the notch angle, θ.  The equation can be written for either U.S. or S.I. units as follows:

U.S. units:  Q = 4.28 Ce Tan(θ/2)(H + k)5/2, with H in ft and Q in cfs,  and

k = 0.0144902648 – (0.00033955535)θ + (3.29819003 x 10-6)θ2 – (1.06215442 x 10-8)θ3ft

S.I. units:  Q = 2.36 Ce Tan(θ/2)(H + k)5/2, with H in m and Q in m3/s, and

k = 0.3048[0.0144902648 - (0.00033955535)θ + (3.29819003 x 10-6)θ2 - (1.06215442 x 10-8)θ3]  m

For either U.S. or S.I. units:

Ce = 0.607165052 – (0.000874466963)θ + (6.10393334 x 10-6)θ2

NOTE: The angle, θ, in the above equations for Ce and k must be in degrees, not radians.

The Excel spreadsheet formulas in the spreadsheet template at the left will calculate Ce, k, and Q  (S.I. units) for a given head over a V notch weir with a notch angle other than 90o. Values for P, S, and Hmax are needed, because the same conditions given in the previous section must also be met in order to reliably use these equations. This spreadsheet template is similar to the one in the previous section, except it also provides for input of the notch angle, θ, and calculation of Ce and k.  This Excel spreadsheet and others for v notch weir calculations are available from the download page at a very low cost .

References:

1. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual, available for online use or download at: http://www.usbr.gov/pmts/hydraulics_lab/pubs/wmm/index.htm.

2. Bengtson, Harlan H., Open Channel Flow III – Sharp Crested Weirs, an online continuing education course for PDH credit, http://www.online-pdh.com/engcourses/course/view.php?id=87

3. Munson, B. R., Young, D. F., & Okiishi, T. H., Fundamentals of Fluid Mechanics, 4th Ed., New York: John Wiley and Sons, Inc, 2002.

4. Bengtson, Harlan H., "Sharp Crested Weirs for Open Channel Flow Measurement," an Amazon Kindle ebook