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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 |
|---|---|---|
|
...
maximum |
...
flow |
...
through |
...
sutro |
...
wier, |
...
L/min |
...
400 |
...
L/min |
...
|
...
the |
...
set |
...
height |
...
of |
...
the |
...
curved |
...
portion |
...
of |
...
the |
...
wier, |
...
cm |
...
20 |
...
cm | ||
|
...
the |
...
ratio |
...
of |
...
the |
...
minimum |
...
over |
...
the |
...
maximumflow |
...
given |
...
that |
...
the |
...
linear |
...
region |
...
doesn't |
...
include |
...
the |
...
rectabgular |
...
base |
...
0.01 |
...
|
...
proportionality |
...
constant |
...
0.62 |
...
Linear Proportionality
| Wiki Markup |
|---|
{latex} $$ C_{linear} $$ {latex} |
...
...
linear
...
proportionality,
...
L/min/cm
...
Rectangular
...
Base
...
Width
W = rectangular base width, cm
g = gravity, 9.8 m/s^2
Rectangular Base Height
s_base = rectangular base height, cm
Profile of curved portion of weir
y = the profile of the curved portion of the weir, cm
x = corresponds to the the vertical height of weir from -s_base to
| Wiki Markup |
|---|
{latex} $$ H_{dmax} - {2 \over 3} s_{base} $$ {latex} |
...
cm
...
Y-axis
...
of
...
the
...
graph
| Wiki Markup |
|---|
{latex} $$ H_d $$ {latex} |
...
...
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.
...
Y-axis
...
=
| Wiki Markup |
|---|
{latex} $$ H_d $$ {latex} |
...
X-axis
...
=
...
y
The height of the rectangular base
s_base
...
=
...
rectangular
...
base
...
height,
...
cm
...
The
...
flow
...
through
...
the
...
rectangular
...
base
| Wiki Markup |
|---|
{latex} $$ Q_{base} $$ {latex} |
...
...
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
Wiki Markup {latex} $$ V_v = \sqrt {2g (x + s_{base})} $$ {latex}
...
- velocity
...
- through
...
- the
...
- weir
...
- in
...
- the
...
- vena
...
- contracta
...
- (point
...
- in
...
- a
...
- fluid
...
- stream
...
- where
...
- the
...
- diameter
...
- of
...
- the
...
- stream
...
- is
...
- the
...
- least)
...
Wiki Markup {latex} $$ V_{vc} = \sqrt {2g (h - x)} $$ {latex}
...
- Effective
...
- area
...
- of
...
- a
...
- differential
...
- weir
...
- element
...
- as
...
- a
...
- function
...
- of
...
- height
...
- given
...
- the
...
- effect
...
- of
...
- the
...
- vena
...
- contracta
Wiki Markup {latex} $$ A = C_{d} 2 y $$ {latex}
...
,
...
- y
...
- is
...
- the
...
- width
...
- of
...
- the
...
- cruved
...
- portion
...
- of
...
- the
...
- weir
...
- and
...
- it
...
- is
...
- dependent
...
- on
Wiki Markup {latex} $$ H_{dmax} $$ {latex}
...
,Wiki Markup {latex} $$ Q_{max} $$ {latex}
...
and,
...
- x
...
- (the
...
- incremental
...
- height
...
- up
...
- the
...
- weir)
| Wiki Markup |
|---|
{latex} $$ M_{in} $$ {latex} |
...
...
momentum
...
into
...
the
...
sutro
...
weir,
...
N
| Wiki Markup |
|---|
{latex} $$ \rho $$ {latex} |
...
...
the
...
density
...
of
...
water,
...
1,000
...
kg/m^3
...
g
...
=
...
gravity
...
9.81
...
m/s^2
...
Exit
...
Velocity
...
of
...
the
...
Sutro
...
Weir
| Wiki Markup |
|---|
{latex} $$ V_{out} $$ {latex} |
...
...
exit
...
velocity
...
of
...
water
...
from
...
sutro
...
weir,
...
m/s
...
| Wiki Markup |
|---|
{latex} $$ \Pi_{sutrosafety} $$ {latex} |
...
...
A
...
safety
...
factor,
...
so
...
there
...
is
...
no
...
risk
...
of
...
flooding
...
the
...
pipe.
...
Set
...
equal
...
to
...
2.
...
Minimum
...
Area
...
of
...
Riser
...
Pipe
| Wiki Markup |
|---|
{latex} $$ A_{pipemin} $$ {latex} |
...
...
the
...
minimum
...
area
...
of
...
the
...
riser
...
pipe
...
The
...
Diameter
...
of
...
the
...
Riser
...
Pipe
| Wiki Markup |
|---|
{latex} $$ d_{pipemin} $$ {latex} |
...
...
the
...
minimum
...
diameter
...
of
...
the
...
riser
...
pipe
...
Graph
...
of
...
the
...
Riser
...
Pipe
...
Diameter
...
as
...
a
...
Function
...
of
...
Flow
...
Rate