h1. +Linear Flow Orifice Meter Sutro Weir Design Documentation+
h2. +Mathcad Code+
the mathcad code can be found [here|LFOM weir design documentation^Sutro Weir solution.xmcd]. You will need to have mathcad installed on your computer in order to open the file.
h2. Sutro Weir Design +Documentation+
*Note :* The values used in this documentation are not static andthe douser notcan correlatechange to actual design parametersthe inputs.
h3. Inputs
Inputs are the data that must be entereed by the user in order to design the sutro weir for the specific application. The mathcad inputs are shown below
!inputs.bmp!
{latex} $$ Q_{max} $$ {latex} = maximum flow through sutro wier, L/min
{latex} $$ H_{dmax} $$ {latex} = the set height of the curved portion of the wier, cm
{latex} $$ C_d $$ {latex} = proportionality constant, the average value is 0.62
{latex} $$ \Pi_{sutro} = {Q_{min} \over Q_{max}} $$ {latex} = fraction of Qmax that is equal to Qmin, accounts for the fact that the linear region doesn't include the rectangular base
{latex} $$ \Pi_{Qratio} $$ {latex} = {latex} $$ \Pi_{sutro} $$ {latex} = the use of two variables is just makes it easier to follow in the code.
h3. Linear Proportionality
!linear proportionality.bmp!
{latex} $$ C_{linear} $$ {latex} = linear proportionality, L/min/cm
h3. Rectangular Base Width
!rectangular base width.bmp!
W = rectangular base width, cm
g = gravity, 9.8 m/s^2
h3. Rectangular Base Height
!rectangular base height.bmp!
s = rectangular base height, cm
h3. Profile of curved portion of weir
!profile of curved portion.bmp!
y = the profile of the curved portion of the weir, cm
x = corresponds to the the vertical height of weir from \-s to
{latex} $$ H_{dmax} - {2 \over 3} s $$ {latex}
, cm
h3. Y-axis of the graph
!y- axis of the graph.bmp!
{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
h3. Sutro Weir Graph: Illustrates the shape of the weir.
!sutro weir graph.bmp!
Y-axis =
{latex} $$ H_d $$ {latex}
X-axis = y
h2. Linear Flow Orifice Meter Flow Rate Through Weir Documentation
h3. Inputs
Inputs are the data that must be entered by the user in order to design the sutro weir for the specific application. The mathcad inputs are shown below:
!flow inputs.bmp!
{latex} $$ C_d $$ {latex} = proportionality constant, the average value is 0.62
{latex} $$ Q_{max} $$ {latex} = maximum flow through sutro wier, L/min
{latex} $$ H_{dmax} $$ {latex} = the set height of the curved portion of the wier, cm
W = rectangular base width, cm
s = rectangular base height, cm
h3. The flow through the rectangular base
!flow through base.bmp!
{latex} $$ Q_{base} $$ {latex} = The flow through the rectangular base, L/min
h3. 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} $$ V_v = \sqrt {2g (x + s)} $$ {latex}
* velocity through the weir in the vena contracta (point in a fluid stream where the diameter of the stream is the least) {latex} $$ V_{vc} = \sqrt {2g (h - x)} $$ {latex}
* Effective area of a differential weir element as a function of height given the effect of the vena contracta {latex} $$ A = C_{d} 2 y $$ {latex} , y is the width of the cruved portion of the weir and it is dependent on {latex} $$ H_{dmax} $$ {latex} , {latex} $$ Q_{max} $$ {latex} and, x (the incremental height up the weir)
!momentum in.bmp!
{latex} $$ M_{in} $$ {latex} = momentum into the sutro weir, N
{latex} $$ \rho $$ {latex} = the density of water, 1,000 kg/m^3
g = gravity 9.81 m/s^2
h3. Exit Velocity of the Sutro Weir
!velocity out.bmp!
{latex} $$ V_{out} $$ {latex} = exit velocity of water from sutro weir, m/s
{latex} $$ \Pi_{sutrosafety} $$ {latex} = A safety factor, so there is no risk of flooding the pipe. Set equal to 2.
h3. Minimum Area of Riser Pipe
!min area.bmp!
{latex} $$ A_{pipemin} $$ {latex} = the minimum area of the riser pipe, m^2
h3. The Diameter of the Riser Pipe
!min diam.bmp!
{latex} $$ d_{pipemin} $$ {latex} = the minimum diameter of the riser pipe, m
h3. Graph of the Riser Pipe Diameter as a Function of Flow Rate
!min diam.bmp!
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