...
Linear
...
Flow
...
Orifice
...
Meter
...
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
Latex |
---|
$$ C_{linear} $$ |
...
...
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
Latex |
---|
$$ H_{dmax} - {2 \over 3} s_{base} $$ |
...
...
cm
...
Y-axis of the graph
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.
...
Y-axis
...
=
...
Latex |
---|
...
$$ H_d $$ |
...
X-axis
...
=
...
y
The height of the rectangular base
s_base = rectangular base height, cm
The flow through the rectangular base
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)
...
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
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of
...
the
...
Sutro
...
Weir
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
Latex |
---|
$$ A_{pipemin} $$ |
...
...
the
...
minimum
...
area
...
of
...
the
...
riser
...
pipe
The Diameter of the Riser Pipe
Latex |
---|
$$ d_{pipemin} $$ |
...
...
the
...
minimum
...
diameter
...
of
...
the
...
riser
...
pipe
Graph of the Riser Pipe Diameter as a Function of Flow Rate