Linear Flow Orifice 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 |
---|---|---|
Unknown macro: {latex} $$ Q_ Unknown macro: {max}
$$ |
maximum flow through sutro wier, L/min |
400 L/min |
Unknown macro: {latex} $$ H_ Unknown macro: {dmax}
$$ |
the set height of the curved portion of the wier, cm |
20 cm |
Unknown macro: {latex} $$ \Pi_ Unknown macro: {sutro}
= {Q_ Unknown macro: {min}
\over Q_{max}} $$ |
the ratio of the minimum over the maximumflow given that the linear region doesn't include the rectabgular base |
0.01 |
Unknown macro: {latex} $$ C_d $$ |
proportionality constant |
0.62 |
Linear Proportionality
$$ C_
$$
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
$$ H_
-
s_
$$
Y-axis of the graph
Sutro Weir Graph: Illustrates the shape of the weir.
Y-axis =
X-axis = y
The height of the rectangular base
s_base = rectangular base height, cm
The flow through the rectangular base
$$ Q_
$$
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 Unknown macro: {latex}
$$ V_v = \sqrt {2g (x + s_
Unknown macro: {base})} $$
- velocity through the weir in the vena contracta (point in a fluid stream where the diameter of the stream is the least) Unknown macro: {latex}
$$ V_
Unknown macro: {vc}= \sqrt
Unknown macro: {2g (h - x)}$$
- Effective area of a differential weir element as a function of height given the effect of the vena contracta Unknown macro: {latex}, y is the width of the cruved portion of the weir and it is dependent on
$$ A = C_
Unknown macro: {d}2 y $$
Unknown macro: {latex},$$ H_
Unknown macro: {dmax}$$
Unknown macro: {latex}and, x (the incremental height up the weir)$$ Q_
Unknown macro: {max}$$
$$ M_
$$
g = gravity 9.81 m/s^2
Exit Velocity of the Sutro Weir
$$ V_
$$
$$ \Pi_
$$
Minimum Area of Riser Pipe
$$ A_
$$
The Diameter of the Riser Pipe
$$ d_
$$
Graph of the Riser Pipe Diameter as a Function of Flow Rate