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 |
---|---|---|
Unable to find DVI conversion log file. | maximum flow through sutro wier, L/min |
400 L/min |
Unable to find DVI conversion log file. | the set height of the curved portion of the wier, cm |
20 cm |
Unable to find DVI conversion log file. | the ratio of the minimum over the maximumflow given that the linear region doesn't include the rectabgular base |
0.01 |
Unable to find DVI conversion log file. | proportionality constant |
0.62 |
Linear Proportionality
Unable to find DVI conversion log file. = 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 Unable to find DVI conversion log file., cm
Y-axis of the graph
Unable to find DVI conversion log file. = 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 = Unable to find DVI conversion log file.
X-axis = y
The height of the rectangular base
s_base = rectangular base height, cm
The flow through the rectangular base
Unable to find DVI conversion log file. = 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 Unable to find DVI conversion log file.
- velocity through the weir in the vena contracta (point in a fluid stream where the diameter of the stream is the least) Unable to find DVI conversion log file.
- Effective area of a differential weir element as a function of height given the effect of the vena contracta Unable to find DVI conversion log file. , y is the width of the cruved portion of the weir and it is dependent on Unable to find DVI conversion log file. , Unable to find DVI conversion log file. and, x (the incremental height up the weir)
Unable to find DVI conversion log file. = momentum into the sutro weir, N
Unable to find DVI conversion log file. = the density of water, 1,000 kg/m^3
g = gravity 9.81 m/s^2
Exit Velocity of the Sutro Weir
Unable to find DVI conversion log file. = exit velocity of water from sutro weir, m/s
Unable to find DVI conversion log file. = A safety factor, so there is no risk of flooding the pipe. Set equal to 2.
Minimum Area of Riser Pipe
Unable to find DVI conversion log file. = the minimum area of the riser pipe
The Diameter of the Riser Pipe
Unable to find DVI conversion log file. = the minimum diameter of the riser pipe
Graph of the Riser Pipe Diameter as a Function of Flow Rate