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...

Linear

...

Flow

...

Orifice

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Meter

...

Sutro

...

Weir

...

Design

...

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
 $$ Q_{max} $$

...

maximum flow through sutro wier, L/min
400 L/min
...
 Latex
...
 $$ H_{dmax} $$ 
...
the set height of the curved portion of the wier, cm
20 cm
 Latex
 $$ \Pi_{sutro} = {Q_{min} \over Q_{max}} $$ 
...
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
...
Rectangular 
...
 Base 
...
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
 $$ H_{dmax} - {2 \over 3} s_{base} $$ 
...
, 
...
 cm
...
Y-axis of 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
Image Added
 Latex
 $$ A_{pipemin} $$ 
...
 = 
...
 the 
...
 minimum 
...
 area 
...
 of 
...
 the 
...
 riser 
...
pipe
The Diameter of the Riser Pipe
Image Added
 Latex
 $$ d_{pipemin} $$ 
...
 = 
...
 the 
...
 minimum 
...
 diameter 
...
 of 
...
 the 
...
 riser 
...
pipe
Graph of the Riser Pipe Diameter as a Function of Flow Rate
Image Added