462 APPLIED MECHANICS 
jecting horizontally into the tank from an iron pipe EF at one 
Water flows from the tank through the glass tube and thence through 
the iron pipe. The iron pipe descends 
vertically to about 7 feet below the ~ = 
tank, and at its lower end it is pro- | Cas===—=—===— 
vided with a cock, by means of which | K ‘C 
the rate of flow through the glass tube 
CD may be regulated. Fia. 759. 
A glass tube HK communicates 
with a reservoir containing deeply-coloured water and terminates at i 
lower end in a pipette, the axis of which coincides with the axis of he 
tube CD. A jet of coloured water may thus be sent into the gle 
tube CD to flow with the water going through that tube. 
At velocities below a certain velocity, called the critical velocity, 
jet of coloured water travels in a straight unbroken stream along the axis — 
of CD, but when the critical velocity is exceeded the coloured stream 
breaks up within CD, and when photographed with an electric spark it is 
seen that the coloured water is whirling and eddying, showing that the 
motion of the water within the tube is no longer steady and in parallel 
stream lines, but sinuous or turbulent. o 
In the experiments described above, the water is still before ente: 
the experimental tube. Professor Osborne Reynolds experimented cn 
other apparatus, in which he caused turbulent water to flow through a 
long smooth pipe, and he found that below a certain critical velocity the — 
turbulent motion became non-sinuous, but this critical velocity was much 
lower than the critical velocity first referred to. The first critical velocr 
is called the higher critical velocity, and the second is called the loin 4 
critical velocity. For example, in a smooth pipe 1 inch in diameter, with — 
the water at 0° C., the higher critical velocity is about 3 feet per second, “4 
while the lower critical velocity is only about 4 foot per second, 
The critical velocities vary inversely as the diameter of the pipe, and — 
they are lowered by raising the temperature of the water. 
‘For further particulars of Osborne Reynolds’ researches see the q 
Transactions of the Royal Society, 1884, or Dunkerley’s Hydraulics, — 
vol. i. chap. vii. 4 
404. Loss of Energy or Head due to Friction in a Pipe. —At : 
velocities below the critical velocity, the motion being non-sinuous, ws 9 
experiments of Osborne Reynolds showed that the loss of energy 
directly proportional to the velocity, directly proportional to the length of — 
the pipe, and inversely proportional to the square of the diameter of the — 
ne 
pipe, or h’ es where h’ is the loss of head, » the velocity of the water, — 
Z the length, and d the diameter of the pipe. But when the er 
velocity was exceeded, the motion being then sinuous or turbulent, the 
loss of energy was proportional to the 1:72 power, or nearly as ; 
square, of the velocity, directly proportional to the length, and faverely : 
yi? 
proportional to the diameter of the pipe, or h’ = e - 
In practical cases the velocity is greater than the critical velocity, and 
the pipes in use have varying and uncertain degrees of roughness, so that 
