h1. Float Calculation
h2.
!doser arm.JPG|align=right!
h5. Figure 1: Free Body Diagram of Lever Arm
h3. Abstract
In the fall semester of 2009, the Non-linear Chemical Doser team developed a Mathcad file to help plant operators choose a float given a non-linear dosing system.
For our prototype, we calculated that our float needs to weigh 4.95 lbs with a diameter of 6 inches and 4 inches of thickness. The calculations for these numbers will be enumerated below.
h3. Method
The float design parameters can be determined using a moment balance around the pivot of the lever arm. As seen in Figure 1 above, the major forces acting on the lever arm are the center of masses of the lever arm on either side of the pivot, the weight of the dosing slide, the alum dosing tube, and the components of the float. A moment balance was performed in order to determine what mass of float would be required in order to balance the lever arm at the lever arm angle corresponding to maximum plant flow. The forces due to the masses of the lever arm to the left and right of the lever arm cancel out. All that remains then acting on the lever arm is the force due to the alum tube, the weight of the sliding scale, and the tension caused by the float. The weight for the float is then changed until the moment about the pivot point becomes zero. The weight found makes the lever arm perfectly balanced at a maximum dosing rate of 100 mg/l at the maximum angle the doser arm will experience (max flow rate).
!dosertank.JPG|align=right!
Figure 2 shows the orientation the doser arm experiences through min/max plant flow rate and how the float level changes accordingly.
h5. Figure 2: Lever arm/float orientation
The formula for the moment balance can be seen below.
sum(M)=0, Tension*L/2=alum tube*arm+scale*arm
The force Archimedes formula for the calculation of buoyancy can be seen below
{latex}
\large
$$
F_b = \gamma V
$$
{latex}
Where:
Fb = The force of buoyancy [Newtons]
\gamma = Unit weight of water [1000 Kg/m^3]
V = Volume of displaced water
h3. Possible sources of Error
An assumption was made here which may cause some error in our calculation; in order to calculate the tension force for the line connecting the lever arm and the float, we had to make an assumption for the amount of displaced water caused by the float.
It was assumed that the float was positioned halfway up in the water. This assumption for the position of the float allowed for the force of buoyancy and thus the tension force to be calculated, the relationship is seen below.
Form
Results/Discussion
The scale portion of the lever where the dual scale and the slider and the doser tube are connected is heavy enough that there will always be tension on the float. As water level in the entrance tank rises, the buoyant force +of water will push up the float pushing up one side of the lever arm+ -will increase- until the lever arm +(on the other side of the pivot)+ -on the scale- drops releasing the necessary alum flow rate while maintaining the tension on the float. +(Maintaining tension is a very important point. Can you show the calculations that illustrate your point?)+
Conclusion and Future Work
We require a float with a weight of 4.95 lbs, diameter of 6 inches and 4 inches of thickness +(maybe I missed it, but where did you come up with 4 inches of thickness?)+ for our prototype lever arm.
Once we build the lever arm, we would further specify the float parameters by utilizing a makeshift float that we can adjust prior to ordering the final float for the design competition. +(Sounds like a good plan to me.)+
h2. Bibliography
* CEE4540 Flow Control Measurement Notes at https://confluence.cornell.edu/display/cee4540/Syllabus
h2. Deliverables
* Final Float Design Parameters and Calculations
* Float protype for March 2010 EPA Competition
| 