# Proportional Sutro Weir Design Spreadsheet

## 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.  Equations that can be used for proportional sutro weir design are discussed in the next section.

## Equations for Proportional Sutro Weir Design

Equations for the base width and base height of a sutro weir are as follows:

• Wb  =  base width in ft (m for S.I. units)
• Hb  =  base height in ft (m for S.I. units)
• Hc  =  max height or curved portion of weir in ft (m for S.I. units)
• Qmax  =  design maximum flow over the weir in cfs (m3/s for S.I. units)
• Qmin  =  design minimum flow over the weir in cfs (m3/s for S.I. units)
• g = acceleration of gravity = 32.17 ft/s/s (9.81 m/s/s for S.I. units)

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 Wb .

## A Screenshot for a Proportional Sutro Weir Design Spreadsheet

For a proportional sutro weir design 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 proportional sutro weir design calculations, available  at our spreadsheet store in either U.S. or S.I. units at a very reasonable price.

Reference

Bengtson, Harlan H., Proportional Weir Design Equations,” an online blog article