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Float Calculation

Figure 1: Free Body Diagram of Lever Arm

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 doser lever arm.
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.

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).

Figure 2: Lever arm/float orientation

Figure 2 shows the orientation the doser arm experiences through min/max plant flow rate and how the float level changes accordingly. 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

FORMULAAAAAA Buoyancy

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.)

Bibliography

Deliverables

  • Final Float Design Parameters and Calculations
  • Float protype for March 2010 EPA Competition
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