The apparatus should now be tested in regard to the quantity of liquid
which it will deliver under a given pressure in the piezometer. By means
of the stop-cock H the flow of water is so regulated that the outflow at
_c_ can be measured at a given height of the water in the piezometer.
Suppose that _a_ cubic centimeters of water flow in _t_ seconds, then
the quantity which would flow in one second is determined by the
formula, Q = a/t cubic centimeters. Since according to the law of
hydraulic outflow the quantities are proportional to the square root of
the height of the column it is easy to compute from any given height the
quantity which will flow from any other one desired. For the retardation
due to capillary attraction, it is sufficient, in general, to take it in
a constant quantity; if this constant quantity be represented by C, the
observed height of the water in the piezometer by _h_, and the quantity
of water flowing out by Q, the data required for any given velocity can
be calculated from the following proportion:
√(_h_₁ − C) : √(_h_₂ − C) = Q₁ : Q₂.
It is necessary to compute the magnitude of this constant C which is to
be subtracted. This is accomplished by measuring the quantity of water
which flows out at two different heights of the column in the
piezometer. From the foregoing proportion, the value of C is as follows:
C = (Q₁² _h_₂ − Q₂² _h_₁)/(Q₁²) − Q₂²) centimeters.
The value of C can be the more exactly determined as _h_₁ is greater and
_h_₂ smaller. It is best to choose the lowest height from which an exact
reading can be made; that is, by which the regular rise and fall of the
level of the water in the piezometer (in consequence of the formation of
drops) just begins to disappear. This usually takes place when _h_₂ =
1.5 centimeter to 1.7 centimeter. For the higher value _h_₁ it is best
to take about 100 centimeters. Suppose, for example, the following
results are obtained:
Height of
column to be
Observed height. Observed quantity of subtracted
outflow. due to
capillary
attraction.
_h₂_ _h₁_ Q₁ cubic Q₂ cubic
centimeters. centimeters. centimeters. centimeters. centimeters.
80 1.6 5.53 0.406 1.21
100 1.6 6.13 0.484 1.17
80 1.8 5.53 0.406 1.19
100 1.8 6.13 0.484 1.19
The same quantity of water which flows out in a unit of time passes also
at the same time over a cross section of the elutriating cylinder. The
diameter of this cylinder being D the equation is derived
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