This is sometimes quite improperly called the theoretical discharge
for any kind of orifice. Except for a well-formed conoidal orifice the
result is not approximate even, so that if it is supposed to be based
on a theory the theory is a false one.
_Use of the term Head in Hydraulics._--The term _head_ is an old
millwright's term, and meant primarily the height through which a mass
of water descended in actuating a hydraulic machine. Since the water
in fig. 14 descends through a height h to the orifice, we may say
there are h ft. of head above the orifice. Still more generally any
mass of liquid h ft. above a horizontal plane may be said to have h
ft. of elevation head relatively to that datum plane. Further, since
the pressure p at the orifice which produces outflow is connected with
h by the relation p/G = h, the quantity p/G may be termed the pressure
head at the orifice. Lastly, the velocity v is connected with h by the
relation v²/2g = h, so that v²/2g may be termed the head due to the
velocity v.
§ 17. _Coefficients of Velocity and Resistance._--As the actual
velocity of discharge differs from [root]2gh by a small quantity, let
the actual velocity
= v_a = c_v [root](2gh), (3)
where c_v is a coefficient to be determined by experiment, called the
_coefficient of velocity_. This coefficient is found to be tolerably
constant for different heads with well-formed simple orifices, and it
very often has the value 0.97.
The difference between the velocity of discharge and the velocity due
to the head may be reckoned in another way. The total height h causing
outflow consists of two parts--one part h_e expended effectively in
producing the velocity of outflow, another h_r in overcoming the
resistances due to viscosity and friction. Let
h_r = c_r h_e,
where c{r} is a coefficient determined by experiment, and called the
_coefficient of resistance_ of the orifice. It is tolerably constant
for different heads with well-formed orifices. Then
v_a = [root](2gh_e) = [root]{2gh/(1 + c_r)}. (4)