46 PHYSICS. 
D. Dywamics or Liaurips; Hypropynamics; Hyprautics. 
a. Velocity of Efflux. 
Hydrodynamics exhibits the laws of motion of liquid bodies; and at the 
head of this part of natural philosophy stands the law of Torricelli, that when 
an aperture is made in the side or bottom of a vessel filled with liquid, this 
liquid escapes with a velocity equal to that which would be attained by a 
body falling freely from the surface of the liquid to the orifice of discharge. 
According to this, the velocity of efflux is entirely independent of the nature 
and specific gravity of the liquid; it is in connexion, however, with the 
depth of the orifice below the surface, and is as the square root of the height 
of pressure. A convenient form of apparatus for experiments upon the 
efflux of liquids is represented in pl. 17, figs. 32, 33. The main part con- 
sists of a cylindrical] tin vessel, communicating with a glass tube, in which 
the liquid stands at the same height as in the vessel itself; this height is 
measured by a scale attached to the tube. In the side of the vessel are two 
apertures, b and c, one above the other; there is a third opening in the 
bottom of the vessel, on which account the small table supporting it must 
have a hole pierced through it; a fourth orifice is to be found at a, in a 
short horizontal tube. This latter part is represented on a larger scale in 
jig. 33. Through the wall of the vessel, aa, passes a tube, d, which ends 
in a shoulder. In this tube is a second smaller one, capable of rotation — 
about its axis, within the first. In the side of this smaller tube is a thin 
plate of brass, with the efflux aperture screwed in it, and by turning the 
tube this aperture may be directed vertically up or down, sideways or ob- 
liquely. By means of the valve, c, the access of water to the aperture, }, 
can be regulated at pleasure, the other apertures having also valves raised 
by strings when the water is to flow out through them. 
_ To prove the Torricellian law by experiment, suppose the water to pour 
out of the point a, in fig. 32, with the same velocity as if it had fallen from 
the surface of the water to the depth a, then the stream of water must again 
attain the same height. This, however, is by no means the case, as the 
water falling from the highest point of the column retards the ascent of that 
following after it, as is shown by the fact that the stream ascends consider- 
ably higher when its direction is so inclined as to prevent this interference. 
Under favorable circumstances an altitude can be obtained equal to nine 
tenths of the depth of fall; the rema‘ning tenth is accounted for by the resist- 
ance of the atmosphere and the friction of the sides of the tube. Allow the 
water to pass out from b or ¢ ( fig. 32), and the stream will be as represented 
in fig. 31: it will form a parabola whose shape depends upon the velocity of 
efflux. The theoretical parabola will, however, differ from the actual, in the 
ordinate being less than that of calculation, the reason lying in the retardations 
of atmospheric pressure and of friction. 
The stream of water, immediately after leaving the orifice, contracts to two 
thirds of its diameter. this contraction continuing, although in an insensible 
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