492 APPLIED MECHANICS a 
at their outer ends. A “bend” H leading from the tank K enters a 
short distance into the tube AB, and serves as a bearing for AB, — 
permitting the latter to rotate freely. A : 
footstep bearing is arranged at the lower 
end of AB, as shown. 
Water flows from the tank K through 
H into AB, and thence into the arms CD 
and EF. In CD and EF are orifices L 
and M, through which the water issues 
in jets perpendicular to the arms and 
horizontal, as shown. The reactions of 
the jets on the arms cause the latter to 
rotate, driving the central tube AB. The 
power developed may be taken off at the 
pulley N, which is secured to AB. Leak- 
age at the joint at the upper end of AB 
is prevented by a simple gland and 
stuffing-box, as shown. | 
In Whitelaw’s turbine, sometimes called 
the Scotch turbine, instead of the straight 
arms of the Barker’s mill, there are casings 
of a more or less spiral form leading the 
water to the orifices, the casings contract- Fia. 791. 
ing as they approach the orifices. 
Jet reaction wheels are not now in practical use, but they are 
interesting from the student’s point of view. 7 
The theory of the jet reaction wheel is as follows. Referring to . 
Fig. 791, let 
h=static head of water at orifices. 
7 = distance of orifices from axis of wheel. 
c=linear velocity of arms at radius 7. 
w= velocity of jets relative to arms. 
W = weight of water passing through wheel per second. 4 
The pressure exerted by the water in the neighbourhood of the — 
orifices is due to the static head / and to the centrifugal force of the 
revolving water in the arms. The head, due to the centrifugal pressure — 
2 
at the orifices, is 5: , and the total head at the orifices is therefore 
"a ——,; : 
h+ 29° Hence w= ,/2gh +c?, neglecting losses. 
The reaction of the jets on the arms at radius r is iC —c),and the — 
work imparted to the wheel per second is a (w —c)e. 
: . W (w—c)e 
The efficiency is — (w—c)c+ WA =S—_~ .. 
ve eae = 
2__ 92 . =. 
Tf w= /2gh+c?, then ha and the expression for the — 
: 2c 
efficiency becomes ——— . 
U+C 
