§ 54. If the water to be measured is passed through a known orifice
under an arrangement by which the constancy of the head is ensured,
the amount which passes in a given time can be ascertained by the
formulae already given. It will obviously be best to make the orifices
of the forms for which the coefficients are most accurately
determined; hence sharp-edged orifices or notches are most commonly
used.
_Water Inch._--For measuring small quantities of water circular
sharp-edged orifices have been used. The discharge from a circular
orifice one French inch in diameter, with a head of one line above the
top edge, was termed by the older hydraulic writers a water-inch. A
common estimate of its value was 14 pints per minute, or 677 English
cub. ft. in 24 hours. An experiment by C. Bossut gave 634 cub. ft. in
24 hours (see Navier's edition of _Belidor's Arch. Hydr._, p. 212).
L. J. Weisbach points out that measurements of this kind would be made
more accurately with a greater head over the orifice, and he proposes
that the head should be equal to the diameter of the orifice. Several
equal orifices may be used for larger discharges.
[Illustration: FIG. 65.]
_Pin Ferrules or Measuring Cocks._--To give a tolerably definite
supply of water to houses, without the expense of a meter, a ferrule
with an orifice of a definite size, or a cock, is introduced in the
service-pipe. If the head in the water main is constant, then a
definite quantity of water would be delivered in a given time. The
arrangement is not a very satisfactory one, and acts chiefly as a
check on extravagant use of water. It is interesting here chiefly as
an example of regulation of discharge by means of an orifice. Fig. 65
shows a cock of this kind used at Zurich. It consists of three cocks,
the middle one having the orifice of the predetermined size in a small
circular plate, protected by wire gauze from stoppage by impurities in
the water. The cock on the right hand can be used by the consumer for
emptying the pipes. The one on the left and the measuring cock are
connected by a key which can be locked by a padlock, which is under
the control of the water company.
§ 55. _Measurement of the Flow in Streams._--To determine the quantity
of water flowing off the ground in small streams, which is available
for water supply or for obtaining water power, small temporary weirs
are often used. These may be formed of planks supported by piles and
puddled to prevent leakage. The measurement of the head may be made by
a thin-edged scale at a short distance behind the weir, where the
water surface has not begun to slope down to the weir and where the
velocity of approach is not high. The measurements are conveniently
made from a short pile driven into the bed of the river, accurately
level with the crest of the weir (fig. 66). Then if at any moment the
head is h, the discharge is, for a rectangular notch of breadth b,