Custom Polynomial Weir Design and Hydraulics Consulting

What services are we providing at PolyWeir?

At PolyWeir we custom design the shape of high-order polynomial weirs to help achieve optimal head-discharge relationships at hydraulic outlets. Our services assist in designing new water infrastructure outlets, as well as upgrading existing water infrastructure outlets. The objective is to maximize hydraulic performance, such as flood control, and address effects of climate change.

What is a polynomial weir?

The polynomial weir introduced by Dr. Raouf E. Baddour [Baddour 2008] is a weir that has a versatile geometry that can be designed to achieve a wide range of head-discharge relationships. The designed weir geometries, which produce desirable head-discharge relationships, are provided to the clients as polynomial equations. Weir plates can then be precisely manufactured according to these equations and installed at the outlet of water infrastructures. You may contact us by email if interested in receiving a copy of the paper.

Note, most traditional weirs used in practice are also polynomial weirs, but of low-orders. For example, the rectangular weir is simply a polynomial weir of order zero (n=0). The triangular and trapezoidal weirs are also polynomial weirs of order one (n=1), and so on. More complex higher order weir geometries are, however, required to produce more desirable head-discharge relationships. Below is a direct comparison of head-discharge relationships of three weirs that have rectangular (n=0) , triangular (n=1) and higher order polynomial (n=5) geometries.

Although the three weirs shown below have the same peak discharge (1 m3/s) at the same maximum head (1 m), PolyWeir 5 releases much higher flows at low heads when compared to the rectangular and triangular weirs. This hydraulic behavior has a significant effect on storage volume requirement, and is the main idea behind our polynomial weir design.

Weir Geometry and Head Discharge Relationship

Why is a polynomial weir superior to control a flood than more traditional weirs?

Simply because the polynomial weir can be designed to release higher flow rates during the rising stage of a flood. As shown in the Figure to the right, the amount of storage required is the area between the inflow and outflow curves during the rising stage of the outflow. It can be seen by releasing more flow during the rising stage, the polynomial weir is reducing the amount of storage needed to achieve a maximum allowable outflow. This behavior is therefore capable of reducing the cost of a new storm-water detention facility. Also in the case of an existing water facility, an outlet retrofitted with a polynomial weir is capable of improving its capacity to handle more severe floods due to climate change.

Polyweir Graph

Why would you want to incorporate a polynomial weir in your design of a water infrastructure outlet?

The traditional weir geometries have restricted head-discharge relationships, which may not be the most efficient solution in many applications such as flood control. Our studies have shown that a high-order polynomial weir is capable of reducing significantly the size of water detention facilities.

In the example illustrated below, the size of the storm water detention pond equipped with a 5th order polynomial weir (PolyWeir 5) is 15% smaller than the pond equipped with a rectangular weir and 30% smaller than a pond equipped with a triangular weir.

Polyweir Model
Polyweir Model Results

Do you need more information?

We will be pleased to help out! Please use our Contact page to get in touch with us.