Here you will find informational articles on topics related to the Excel spreadsheets for civil and mechanical engineering calculations available from the DOWNLOADS page. This includes articles in the clickable categories below: pipe flow calculations, open channel flow, heat transfer/heat exchangers, storm water/hydrology, continuous beam analysis and design, open channel flow measurement, and pipe flow measurement topics. Scroll down on each category page to see all of the articles.
Similar blog articles are available at our companion site, www.EngineeringExcelSpreadsheets.com.
Scroll down for the following blog articles in this category:
Where to find a Parshall Flume Flow Rate Calculator Spreadsheet
For a Parshall flume flow rate calculator Excel spreadsheet to make open channel flow measurement calculations, click here to visit our spreadsheet store. Obtain a convenient, easy to use Parshall flume flow rate calculator spreadsheet at a reasonable price. Read on for information about Excel spreadsheets that can be used for Parshall flume/open channel flow measurement calculations.
Parshall flumes are used for a variety of open channel flow measurement. They are especially good for flows containing suspended solids, as for example the flow in wastewater treatment. As seen in the picture at the right, the plan view of a Parshall flume is similar to that of a venturi flume, with a converging section, a throat, and a diverging section. A Parshall flume, however, also has prescribed variations in the channel bottom slope as shown in the diagram in the next section. Flow rate through a Parshall flume can be calculated based on a measured head, using equations that will be discussed in a later section. A Parshall flume must be constructed with prescribed dimensions as shown in the next section.
Image Credit: City of Batavia, Illinois
Parshall Flume Configuration and Dimensions
The diagram at the left shows the general configuration of a Parshall flume with a plan and elevation view. The width of the throat is typically used to specify the size of a Parshall flume. The table at the right below, shows the standard dimensions for Parshall flumes with throat widths ranging from 1 ft to 8 ft. Similar information is available for throat widths down to 1 inch and up to 50 ft.
Such a range of sizes covers a very wide range of flow rates. A 1 inch flume will carry a flow of 0.03 cfs at 0.2 ft of head, while a 50 ft Parshall flume will carry 3,000 cfs at a head of 5.7 ft. For the range of throat widths in the table, the other dimensions in the diagram are constant at the following values:
E = 3'-0", F = 2'-0", G = 3'-0",
K = 3 inches, N = 9 inches,
X = 2 inches, Y = 3'
Free Flow and Submerged Flow in Parshall Flume Flow Rate Calculator
For "free flow" through a Parshall flume, the flow rate through the throat of the flume is unaffected by the downstream conditions. For free flow, a hydraulic jump will be visible in the throat of the Parshall flume. For flow situations where downstream conditions cause the flow to back up into the throat, the hydraulic jump isn't visible, and the flow is said to be "submerged flow" rather than "free flow."
The ratio between head measurements at the two locations, H_{a} and H_{b}, as shown in the diagram at the left above, can be used as a quantitative criterion to differentiate between free flow and submerged flow. The values of H_{b}/H_{a} for free flow and for submerged flow, for several ranges of throat width from 1" to 8' are as follows:
For 1” < W < 3” : free flow for H_{b}/H_{a} < 0.5; submerged flow for H_{b}/H_{a} > 0.5
For 6” < W < 9” : free flow for H_{b}/H_{a} < 0.6; submerged flow for H_{b}/H_{a} > 0.6
For 1’ < W < 8’ : free flow for H_{b}/H_{a} < 0.7; submerged flow for H_{b}/H_{a} > 0.7
For 8’ < W < 50’ : free flow for H_{b}/H_{a} < 0.8; submerged flow for H_{b}/H_{a} > 0.8
Excel Formulas for Free Flow Parshall Flume Flow Rate Calculator
The free flow equation for Parshall flume flow rate calculator is Q_{free} = C H_{a}^{n}, where
The tables below give the constants C and n in the equations for a free flow Parshall flume flow rate calculator for both U.S. units and for S.I. units.
The screenshot below shows a Parshall flume flow rate calculator spreadsheet that will calculate flow rate through the Parshall flume under free flow conditions in S.I. units for a selected throat width and a specified value for the measured head. This Excel spreadsheet and one for submerged flow calculation are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.
Excel Formulas for a Submerged Flow Parshall Flume Flow Rate Calculator
The submerged flow equations for a Parshall flume flow rate calculator, as used by the Excel formulas in the spreadsheet below, are summarized for U.S. units and for S.I. units in the diagrams below:
The primary submerged flow equation for a Parshall flume flow rate calculator is: Q_{subm} = Q_{free} - Q_{corr}, where
The screenshot of an Excel spreadsheet template shown at the left will serve as a submerged flow Parshall flume flow rate calculator in U.S. units for a selected throat width and a specified value for the measured heads, H_{a} and H_{b}. This Excel spreadsheet and one for free flow calculation are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.
References
1. U.S. EPA, Recommended Practice for the Use of Parshall Flume and Palmer Bowlus Flumes in Wastewater Treatment plants, EPA600/2-84-180, 1984
2. Wahl, Tony L., Equations for Computing Submerged Flow in Parshall Flumes, Bureau of Reclamation, Denver, Colorado, USA
3. U.S. Dept. of the Interior, Bureau of Reclamation, Water Measurement Manual, 2001 revised, 1997 third edition
4. Bengtson, Harlan H., "Parshall Flume Discharge Calculation - Open Channel Flow Measurement with Excel," an online blog article
Where to Find a Sharp Crested Rectangular Weir Equation Spreadsheet
For a sharp crested rectangular weir equation spreadsheet, click here to visit our spreadsheet store. Obtain a convenient, easy to use spreadsheet to use as a sharp crested rectangular weir equation spreadsheet at a reasonable price. Read on for information about Excel spreadsheets that can be used as contracted rectangular weir open channel flow calculators.
The following section, which gives background on sharp crested rectangular weirs in general, also appears in the companion article, "Suppressed Rectangular Weir Calculations with an Excel Spreadsheet"
Background on Sharp Crested Rectangular Weirs in General
The picture at the left shows a sharp crested rectangular weir measuring open channel flow rate in a natural channel. The diagram below right shows a longitudinal cross-section of a sharp crested weir, with some of the terminology and parameters often used for sharp crested weirs included on the diagram.
The weir crest is the top of the weir. For a rectangular weir it is the straight, levelbottom of the rectangular opening through which water flows over the weir. The term nappe is used for the sheet of water flowing over the weir. The equations for calculating flow rate over a weir in this article require free flow, which takes place when there is air under the nappe. The drawdown is shown in the diagram as the decrease in water level going over the weir due to the acceleration of the water. The head over the weir is shown as H in the diagram; the height of the weir crest is shown as P; and the open channel flow rate in the open channel (and over the weir) is shown as Q.
Image Credits: Rectangular, Sharp-Crested Weir: flowmeterdirectory.co.uk
Sharp Crested Weir Parameters: H. H. Bengtson, Ref #2
The Francis Equation as a Sharp Crested Rectangular Weir Equation
A contracted rectangular weir is one for which the weir extends across only part of the channel, so that the length of the weir, L, is different from as the width of the channel. The picture at the left shows a contracteded rectangular weir being used to measure the flow of water in a triangular open channel. The diagram below right shows some of the key parameters used in contracted rectangular weir flow rate calculations. Specifically, the height of the weir crest, P, the head over the weir, H, the weir length, L, and the channel width, B, are shown on the diagram of a contracted rectangular weir in a rectangular channel. The U.S. Bureau of Reclamation, in their Water Measurement Manual (Ref #1 below), recommend the use of the Francis equation (shown below) for completely contracted rectangular weirs, subject to the condition that H/L < 0.33, B - L > 4 H_{max}, and P > 2H_{max}.
For U.S. units: Q = 3.33(L - 0.2H)H^{3/2}, where
For S.I. units: Q = 1.84(L - 0.2H)H^{3/2}, where
Image Credits: Contracted Rectangular Weir picture: Food and Agricultural Organization of the United Nations.
Contracted Rectangular Weir Diagram – Bengtson, Harlan H.
The Kinsvater-Carter Formula as a Sharp Crested Rectangular Weir Flow Equation
If any of the three required conditions given in the previous section are not met, then the more general Kindsvater- Carter Equation, shown below should be used.
U.S. units: Q = C_{e}(2/3)[(2g)^{1/2}](L + k_{b})(H + 0.003)^{3/2}
S.I. units: Q = C_{e}(2/3)[(2g)^{1/2}](L + k_{b})(H + 0.001)^{3/2}
C_{e} is a function of L/B and H/P, while k_{b} is a function of L/B. There are graphs, tables and equations available for obtaining values for C_{e} and k_{b} for specified values of L/B and H/P. The equations given below were prepared from information in Reference #3 at the end of the article.
C_{e} is dimensionless, so the equation for C_{e} is as a function of L/B and H/P is the same for both S.I. and U.S. units and is as follows:
C_{e} = α(H/P) + β, where β = 0.58382 + 0.016218(L/B), and
α = [-0.0015931 + 0.010283(L/B)]/[1 - 1.76542(L/B) + 0.870017(L/B)^{2}]
The equation for k_{b} as a function of L/B has different constants for S.I. and U.S. units. The two versions of the equation for k_{b} are as follows:
U.S. units: for 0 < L/B < 0.35: k_{b} = 0.007539 + 0.001575(L/B) - (k_{b} is in ft)
for 0.35 < L/B < 1.0: k_{b} = -0.34806(L/B)^{4} + 0.63057(L/B)^{3} - 0.37457(L/B)^{2} + 0.09246(L/B) - 0.000197 - (k_{b} is in ft)
S.I. units: for 0 < L/B < 0.35: k_{b} = 0.002298 + 0.00048(L/B) - (k_{b} is in m)
for 0.35 < L/B < 1.0: k_{b} = -0.10609(L/B)^{4} + 0.1922(L/B)^{3} - 0.11417(L/B)^{2} + 0.028182(L/B) - 0.00006 - (k_{b} is in m)
Note that if H/L < 0.33, B - L > 4 H_{max}, and P > 2H_{max}, then the Francis Equation and the Kindsvater-Carter Equation will give nearly the same value for Q. As conditions diverge more and more from the requirements, the calculations from the two equations will diverge more and more. In these cases the value calculated by the Kindsvater-Carter formula should be used.
A Sharp Crested Rectangular Weir Equation Spreadsheet
The Excel spreadsheet template shown below can be used as a sharp crested rectangular weir equation calculator, using both the Francis equation and the Kindsvater-Carter equation. Only four input values are needed. They are the height of the weir crest above the channel invert, P; the width of the channel, B; the weir length L; and the measured head over the weir, H. With these four input values, the Excel formulas will calculate the parameters needed and check on whether the conditions required for use of the Francis equation are met. If the conditions are all met, then the value of Q calculated with the Francis equation can be used. If any of the conditions aren’t met, then the value of Q calculated with the Kindsvater-Carter formula should be chosen. This Excel spreadsheet and others for suppressed and contracted rectangular weir calculations are available in either U.S. or S.I. units at a very low cost in our spreadsheet store.
1. U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997, 3rd ed, Water Measurement Manual
2. Bengtson, H. H., Sharp-Crested Weirs for Open Channel Flow Measurement, An online continuing education course for PDH credit for Professional Engineers.
3. Bengtson, H.H., Open Channel Flow Measurement - Weirs and Flumes, An online continuing education course for PDH credit for Professional Engineers
4. Merkley, Gary P., Weirs for Flow Measurement Open Course Ware, Utah State University.
5. Bengtson, Harlan H., "An Excel Spreadsheet as a Rectangular Weir Flow Calculator", an online blog article
Where to get Spreadsheets with Proportional Weir Design Equations
To find spreadsheets for proportional weir design equations and calculations in either U.S. or S.I. units, click here to visit our spreadsheet store. Obtain convenient, easy to use spreadsheets with proportional weir design equations and calculations at reasonable prices. Read on for information about the use of Excel spreadsheets for sutro weir design.
Principles of Proportional Sutro Weir Design
For the commonly used rectangular weir or V-notch weir, the flow rate over the weir increases as the head over the weir increases, but the flow rate increases at a faster rate than the head over the weir. For some applications, it is desirable for the flow rate over a weir to be proportional to the head over the weir. The sutro weir, also known as a proportional weir accomplishes this by having the width of the opening above the weir crest decrease with increasing head over the weir crest as shown in the diagram of a sutro weir at the right. Proportional weir design eauations are discussed in the next section.
Proportional Weir Design Equations
Equations for the base width and base height of a sutro weir are as follows:
The equation for the curved portion of a proportional sutro weir is:
X and Z are position parameters as shown in the diagram above. They will have the same units as W_{b} .
A Spreadsheet with Proportional Weir Design Equations
For using proportional weir design equations in a spreadsheet with calculations in S.I. or U.S. units, or for other spreadsheets for open channel flow measurement calculations, see: www.engineeringexceltemplates.com
The Excel spreadsheet screenshot below shows part of a spreadsheet for calculations with proportional weir design equations, available at our spreadsheet store in either U.S. or S.I. units at a very reasonable price.
Bengtson, Harlan H., "Proportional Sutro Weir Design Spreadsheets", an online blog article
Introduction to the Rectangular Sharp Crested Weir
If you want to obtain an Excel spreadsheet for rectangular weir flow measurement calculations, click here to visit our download page. Read on for information about Excel spreadsheets that can be used as suppressed rectangular weir open channel flow calculators.
As shown in the diagrams and pictures below, the rectangular refers the the shape of the water cross-section as it goes over a sharp crested rectangular weir, which consists of a plate placed in an open channel so that the water is forced to flow through the rectangular open in the weir plate. It can be used for open channel flow rate measurement, by measuring the height of water above the weir crest (the straight, level top of the weir opening), which can then be used to calculate the water flow rate over the weir.
The picture at the left shows a rectangular weir measuring open channel flow rate in a natural channel. The diagram below right shows a longitudinal cross-section of a sharp crested weir, with some of the terminology and parameters often used for sharp crested weirs included on the diagram.
The Francis Equation for Suppressed Rectangular Weir Flow Calculations
A suppressed rectangular weir is one for which the weir extends across the entire channel, so that the length of the weir, L, is the same as the width of the channel, B. The picture at the left shows a suppressed rectangular weir being used to measure the flow of water in an open channel. The diagram below right shows some of the key parameters used in suppressed rectangular weir flow rate calculations. Specifically, theheight of the weir crest, P, the head over the weir, H, and the weir length, L (equal to channel width, B) are shown on the diagram. The U.S. Bureau of Reclamation, in their Water Measurement Manual (Ref #1 below), recommend the use of the Francis equation (shown below) for suppressed rectangular weirs, subject to the condition that H/P < 0.33 and H/B < 0.33:
For U.S. units: Q = 3.33 B H^{3/2}, where
For S.I. units: Q = 1.84 B H^{3/2}, where
The same condition for H/P and H/B apply.
Image Credits: Suppressed Rectangular Weir Picture - U.S. Dept. of the Interior, Bureau of Reclamation, 2001 revised, 1997 third edition, Water Measurement Manual.
Suppressed Rectangular Weir Diagram - Bengtson, Harlan H.
The Kindsvater-Carter Formula for Suppressed Rectangular Weirs
If either of the requirements in the previous section (H/P < 0.33 and H/B < 0.33) are not met the the more general Kindsvater- Carter Equation, shown below should be used.
U.S. units: Q = [0.075(H/P) + 0.602](2/3)[(2g)^{1/2}](L - 0.003)(H + 0.003)^{3/2}
S.I. units: Q = [0.075(H/P) + 0.602](2/3)[(2g)^{1/2}](L - 0.001)(H + 0.001)^{3/2}
Note that if H/P < 0.33 and H/B < 0.33, then the Francis Equation and the Kindsvater-Carter Equation will give nearly the same value for Q. As H/P and/or H/B increase more and more above the 0.33 limit the calculations from the two equations will diverge more and more. In these cases the value calculated by the Kindsvater-Carter formula should be used.
An Excel Spreadsheet as a Suppressed Rectangular Weir Flow Calculator
The Excel spreadsheet template shown below can be used to calculate the water flow rate over a suppressed rectangular weir, using both the Francis equation and the Kindsvater-Carter equation. Only three input values are needed. They are the height of the weir crest above the channel invert, P; the width of the channel, B (which equals the weir length L); and the measured head over the weir, H. With these three input values, the Excel formulas will calculate H/P and H/B. If both of these are less than 0.33, then the value of Q calculated with the Francis equation can be used. If either of the conditions aren't met, then the value of Q calculated with the Kindsvater-Carter formula should be chosen. This Excel spreadsheet and others for suppressed and contracted rectangular weir calculations are available in either U.S. or S.I. units at a very low cost from our download page.
2. Bengtson, H. H., Sharp-Crested Weirs for Open Channel Flow Measurement, An online course for PDH credit for Professional Engineers.
3. Merkley, Gary P., Weirs for Flow Measurement Open Course Ware, Utah State University.
4. Bengtson, Harlan H., "Sharp Crested Weirs for Open Channel Flow Measurement," an Amazon Kindle ebook.
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 = 2.49H^{2.48}, 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 = 1.36H^{2.48}, where Q = flow rate over the weir m^{3}/s and H = head over the weir in m.
The conditions required for a v notch weir to be fully contracted are: P > 2H_{max} and S > 2H_{max.}
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 90^{o}, v notch weir flow calculator. Input values for H, P, S, and H_{max}, 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})θ^{2} – (1.06215442 x 10^{-8})θ^{3}ft
S.I. units: Q = 2.36^{ }Ce Tan(θ/2)(H + k)^{5/2}, with H in m and Q in m^{3}/s, and
k = 0.3048[0.0144902648 - (0.00033955535)θ + (3.29819003 x 10^{-6})θ^{2} - (1.06215442 x 10^{-8})θ^{3}] m
For either U.S. or S.I. units:
Ce = 0.607165052 – (0.000874466963)θ + (6.10393334 x 10^{-6})θ^{2}
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 90^{o}. Values for P, S, and H_{max} 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