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Linear

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Flow

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Orifice

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Meter

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Sutro

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Weir

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Design

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Documentation

Mathcad Code

the mathcad code can be found here. You will need to have mathcad installed on your computer in order to open the file.

Sutro Weir Design Documentation

This program creates a sutro weir design and is used to calulcate the optimal LFOM diameter.
Note : The values used in this documentation are not static the user can change the inputs.

Inputs

Inputs are the data that must be entereed by the user in order to design the sutro weir for the specific application.
Inputs

Symbol

Definition

Sample Value

Latex
 $$ Q_{max} $$

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maximum flow through sutro wier, L/min
400 L/min
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 Latex
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 $$ H_{dmax} $$ 
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the set height of the curved portion of the wier, cm
20 cm
 Latex
 $$ \Pi_{sutro} = {Q_{min} \over Q_{max}} $$ 
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the ratio of the minimum over the maximumflow given that the linear region doesn't include the rectabgular base
0.01
 Latex
 $$ C_d $$ 
proportionality constant
0.62
Linear Proportionality
Image Added
 Latex
 $$ C_{linear} $$ 
...
 = 
...
 linear 
...
 proportionality, 
...
 L/min/cm
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Rectangular 
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 Base 
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Width
Image Added
 W = rectangular base width, cm
 g = gravity, 9.8 m/s^2
Rectangular Base Height
Image Added
 s_base = rectangular base height, cm
Profile of curved portion of weir
Image Added
 y = the profile of the curved portion of the weir, cm
 x = corresponds to the the vertical height of weir from -s_base to 
 Latex
 $$ H_{dmax} - {2 \over 3} s_{base} $$ 
...
, 
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 cm
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Y-axis 
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 of 
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the graph
Image Added
 Latex
 $$ H_d $$ 
 = this is the vairable that corresponds to the height of the entire weir from the bottom of the rectangular base to the top of the curved portion of the weir, cm
Sutro Weir Graph: Illustrates the shape of the weir.
Image Added
 Y-axis = 
 Latex
 $$ H_d $$ 

 X-axis = y 
The height of the rectangular base
Image Added
 s_base = rectangular base height, cm
The flow through the rectangular base
Image Added
 Latex
 $$ Q_{
...
base} $$ 
 = The flow through the rectangular base, L/min
Initial Momemtum of Water Entering Riser Pipe
If the riser pipe diameter is too small for the flow rate then the water will back up in the bottom of the pipe and the water entering the weir won't experience free fall anymore. Balance of momentum in and out helps us achieve these values.Background for the development of the minimum cross sectional area equation are the equations below:
  • vertical velocity of the water from any height when it reaches the bottom of the weir 
     Latex
     $$ V_v = \sqrt {2g (x + s_{base})} $$ 
  • velocity through the weir in the vena contracta (point in a fluid stream where the diameter of the stream is the least) 
     Latex
     $$ V_{vc} = \sqrt {2g (h - x)} $$ 
  • Effective area of a differential weir element as a function of height given the effect of the vena contracta 
     Latex
     $$ A = C_{d} 2 y $$ 
     , y is the width of the cruved portion of the weir and it is dependent on 
     Latex
     $$ H_{dmax} $$ 
     , 
     Latex
     $$ Q_{max} $$ 
     and, x (the incremental height up the weir)
Image Added
 Latex
 $$ M_{in} $$ 
 = momentum into the sutro weir, N
 Latex
 $$ \rho $$ 
 = the density of water, 1,000 kg/m^3
 g = gravity 9.81 m/s^2
Exit Velocity of the Sutro Weir
Image Added
 Latex
 $$ V_{out} $$ 
 = exit velocity of water from sutro weir, m/s
 Latex
 $$ \Pi_{sutrosafety} $$ 
 = A safety factor, so there is no risk of flooding the pipe. Set equal to 2.
Minimum Area of Riser Pipe
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 Latex
 $$ A_{pipemin} $$ 
 = the minimum area of the riser pipe
The Diameter of the Riser Pipe
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 Latex
 $$ d_{pipemin} $$ 
 = the minimum diameter of the riser pipe
Graph of the Riser Pipe Diameter as a Function of Flow Rate
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