Linear Orifice Flow Meter Entrance Code Documentation and Drill size Determination

Intro

Research is being done to determine the optimal process for determining the diameter of the orifices on the LOFM. The drill size was previously determined using the assumption of 5 holes in the first row of orifices and then applying that drill size to the rest of the LFOM. the new method will calculate the optimal drill size based on the flow rates through the upper holes, currently all of the upper rows are being evaluated to determine the critical row.

Initial 5 orifices in the first row assumption.

The first row of orifies in the linear flow meter is approximating a rectangular base. Sutro altered the linear proportional weir, which has a base width that approaches infinity as the height approaches zero, by adding the rectangular base and a design restriction that the linear relationship only occurs above 1/3 the height of the rectangular base. Through trial and error a orifice number on the initial row was found to optimally be 5. The question explored here is why does the orifice value of 5 work and and does it really work for all values. The five orifices were chosen as optimal because when five orifices are used on the inital level then the subsequent rows don't encounter rounding errors, rounding errors can cause problems such as one row to contain zero orifices and the next row to contain two orifices. It is desirable to never have a subsequent row orifice number be greater then the row procedding it.

Current Research.

Currently we are looking at integrating over the row spacing starting at the top of the LFOM to determine the hole diameter that best approximates the row area. This will allow us to make sure that the height is appropriate at the most critical area, the top of the LFOM where normally only 1 hole is needed.

Model Optimization

I am currently working on evaluating the optimal way to determine diameter using a mathcad code. The Entrance Tank Code is available through the SourceForge repository, a storage system. To access the code follow these folders: design repository -> Automated Design -> Design -> EntranceTank. The code does not come with references at the top of the code, in order to run the file you need to add the following references: User Inputs, Math Functions, Pipe Database, Minor Loss Coefficients, Fluids Functions, Design Assumptions. All the references are available in the same folder as the Entrance Tank Code.

Model Optimization Code Documentation:

Step 1: Calculate the width of the rectangular portion of the weir

Step 2: Calculate the s value, the zero point of the sutro weir.

Step 3: Calculate the width of the entire weir, the curved portion and rectangular base.

Step 4: Create height arrays. The arrays will allow us to evaluate the flow rate occuring over one row.

Step 5: Calculate the area of each row and put that information into an array. Sample outputs for the height and area arrays are also show below.

Step 6: Determine the fewest number of holes by dividing the entire row area by the area of one hole with a diameter equal to the row spacing and rounding to an integer number of holes.

Step 7: Calculating the area of the optimal orifices for each row based on the rough number calculated in the previous step.

Step 8: Calculate the diameter of the orifices for each row based on the area of the orifices calculated above.

Step 9: Create the height arrays. The H_flowloc is an array of the height at which the flow rate is calculated (this is equal to 1/2*the row spacing above the row being evaluated). H_orificeloc is an array of the heights at which orifices will be made. The ramp funtion called herer is available in the math functions file.

Step 10: This creates the array of target flow rates based on the heights given by the H_flowloc array and assuming a perfectly linear realtionship.

Step 11: This is a function that calculates the actual flow rate through the LFOM for a given height of water. The program determines the flow through all orifices below the water level based on varying amounts of head (water elevation).

Step 12: This is a function that calculates the number of orifices necessary at each H_orificeloc based on a given diameter.

Step 13: This function calculates the error of the design based on the differences between the predicted flow rate and the actual flow rate through the LFOM.

Step 14: This funciton returns the maximum error, the absolute value of the errors is taken so that the positive and negative errors are accounted for.