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Thread: This could work
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01-22-2014, 07:49 AM #26Engineer-in-Training
- Join Date
- Oct 2013
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Well, I've just done a bunch of maths, and come to the conclusion that a syphon system won't work.
Code:V_outer = volume of water in the outer container V_outer,0 = initial volume of water in the outer container V_inner = volume of water in the inner container V_inner,0 = 0 (no water in there initially) A_outer,internal = area of the outer container, disregarding space occupied by the inner container A_inner,external = area of the inner container that it occupied in the outer container A_inner,internal = area of the inner container that can hold liquid (ie external area minus wall thickness) d = density of water M_inner,initial = mass of the inner container at the start (resin + container + weights) M_inner = mass of the inner container with whatever water it has in it. = M_inner,initial + V_inner*d h_outer = height of the water in the outer container, relative to the bottom of the outer container h_inner = height of the water in the inner container, relative to the bottom of the inner container = V_inner/A_inner,internal h_diff = difference in height between the water in the outer container and the inner container h_print = height of the printing surface (ie top of the water in the inner container) with respect to the bottom of the outer container h_sink = height of the bottom of the inner container with respect to the water in the outer container - how far the inner one sinks.
First up, how far down does the inner container sink in the outer one? Well, we know its mass, and we know the density of the water, and we know its external area. Therefore we can say:
Code:h_sink = M_inner / (d*A_inner,external) = (M_inner,initial + V_inner * d) / (d*A_inner,external)
Code:h_diff = h_sink - h_inner = (M_inner,initial + V_inner * d) / (d*A_inner,external) - V_inner/A_inner,internal
Code:h_outer = (V_outer + (h_sink * A_inner,external)) / A_outer
Code:h_print = h_outer - h_diff = (V_outer + (h_sink * A_inner,external)) / A_outer - (M_inner,initial + V_inner * d) / (d*A_inner,external) + V_inner/A_inner,internal = (V_outer,0 + M_inner,initial/d) / A_outer - (M_inner,initial/d + V_outer,0 - V_outer) / A_inner,external + (V_outer,0 - V_outer)/A_inner,internal = V_outer,0/A_outer + M_inner,initial/(d*A_outer) - M_inner,initial/(d*A_inner,external) - V_outer,0 / A_inner,external + V_outer/A_inner,external + V_outer,0/A_inner,internal + V_outer/A_inner,internal
Code:h_print = V_outer * (1/A_inner,internal + 1/A_inner,external) + <a whole bunch of constants>
Back to Mike's idea, which I think might work.
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