_v_ = Q(4)/(πD²) centimeters.
Since the velocity in the elutriating cylinder v is directly as the
quantity of water overflowing so is
_v_ : _v_ₙ = √(_h_ − C) : √(_h_ₙ − C);
then _v_ₙ = √(_h_ₙ − C) (_v_)/(√(h − C))
and _h_ₙ = _v_ₙ²((_h_ − C)/(_v_²) + C. The constant (_h_ − C)/(_v_²)
is obtained from the means of a number of estimations; for example as
illustrated in the following data:
Observed Corresponding velocity
quantity of in elutriating cylinder Constant.
Observed height, outflow, cubic of 4.489 centimeters (_h_ −
centimeters. centimeters. diameter, millimeters. C)/(2)
1.6 0.406 0.0257 621
1.8 0.484 0.0306 652
80.0 5.530 0.3490 647
100.0 6.130 0.3870 660
———
Mean 645
Then are obtained the following values of _h_ₙ and _v_ₙ:
_h_ₙ = 645(Vₙ²) + 1.19 centimeters.
and _v_ₙ = √(_h_ₙ − 1.19) × 0.0394 centimeters.
In order to be able easily and rapidly to judge under what pressure the
outflow has taken place in any particular instance, a larger number of
values are computed with the help of the formula given and placed
together in tabular form. As an example the following table may serve
which was computed for one of the apparatus used. Usually it will be
sufficient to test the apparatus for four different heights and then to
interpolate the values for all the others. The numbers marked with a
star in the table are those which were determined by experiment; the
others were calculated.
Public-domain text, read in full here on John Shaqi.
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