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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. 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. Archimedes formula for the calculation of buoyancy can be seen below
FORMULAAAAAA Buoyancy
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.
Formula....for mass balance around float
Form (Can you detail this moment balance? A diagram perhaps and the equations and the result of these equations.) This is to ensure that a change in head in the entrance tank will cause a similar change in the relative height of the float. (Can you make the previous sentence a little clearer? What ensures a change in head in the entrance tank will cause a similar change in the relative height of the float?) We first determined the weight and location of each components of the lever arm with respect to the pivot. (How? You don't show or give a method here.) We then identified all the moments for each of those components. (What were all of the components?) We then specified a float diameter and specified and solved for the weight of the float with the specification that at equilibrium the float will be halfway submerged in the water. (Okay...isn't this inherent in what we assume with bouyancy? Where are you using bouyancy principles in these calculations?)
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?)
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