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h2. Introduction

*Definition of Weir* : A type of small overflow dam that can be used for flow measurement. The Linear Flow Orifice Meter is a mimic of a weir.
*Definition of Sutro Weir* : The dicharge (flow) through the weir is proportional to the head (water depth above a refernce plane located at one third of the depths of the crest of the base weir
*Development* : The linear-proportional weir was developed by Stout in 1897 and was theoretically based, the design stipulated the width at the base as infinite. In 1908 Sutro modified the design to create a practical linear-proportional weir, known as the sutro weir. The sutro wier has a rectangular base and the flow through the wier is proportional to the height of the water through the curved portion of the weir plus {latex} $$ 2\over 3 $$ {latex} of the height of the rectangular base.

h3. Source 1: Prof. B.S. Thandaveswara from the Indian Institute of Technology Madras [website|http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-MADRAS/Hydr/pdfs/Unit14/proportional-weir.pdf]

!Sutro Weir Picture.bmp||width=300,height=250!
Figure 1: Sutro weir with constraining equations.
* Note: The rectangular base is present in the design merely to simplify evaluation and analysis. Flow proportional to water height begins above the rectangular weir.

h5. Variables

W = base of rectangular weir
s = height of rectangular weir
h = wier hight above rectangular weir
c = constant of proportionality
{latex} $$ C_d $$ {latex} = coefficient of dicharge, ranges from 0.0597 to 0.619
{latex} $$ q_w $$ {latex} = Flow through rectangular weir
{latex} $$ q_u $$ {latex} = Flow through upper portion of weir, *Important Parameter*
Q = Total Discharge
{latex} $$ C_0 $$ {latex} = Proportionality constant, average value is 0.62
g = 9.81

h5. [Equations|LFOM Sutro Weir Equations]