(^596) A Textbook of Engineering Mechanics
The downward movement of fly balls will push down the sleeve. It will change the position of
throttle valve, in such a way, that it increases the supply of fuel, which will increase the engine speed.
Similarly, if load on the engine decreases, it will increase the speed of the engine shaft. The increase
in the speed of engine shaft will increase the speed of centrifugal governor, as a result of which the
flyballs will go up due to increased centrifugal force. The upward movement of the flyballs will pull
up the sleeve. It will change the position of the throttle valve, in such a way, that it decreases the
supply of fuel which will decrease the engine speed.
29·11. WATT GOVERNOR
The simplest form of a centrifugal governor is a Watt
governor. It is basically a conical pendulum with links connecting
flyballs and sleeve of negligible mass. Now consider a Watt
governor as shown in Fig. 29·8.
Let m = Mass of a flyball
ω = Angular velocity of the flyball.
r = Radius of the path of rotation
of the flyball,
h = *Height of the governor, and
T = Tension in the arm.
We know that centrifugal force acting on the ball,
Pc = mω^2 r
Taking moments of centrifugal force (mω^2 r), weight of flyball (m.g) and tension in arm (T)
about the pivot O and equating the same,
mω^2 r × h = (mg) r ...(Moment of T about O is zero)
∴ 2
g
h=
ω
Example 29·6. A centrifugal governor is fitted with two balls each of mass 2·5 kg. Find the
height of the governor, when it is running at 75 r.p.m. Also find the speed of the governor, when the
balls (i) rise by 20 mm and (ii) fall by 20 mm. Neglect friction of the governor.
Solution. Given : †Mass of flyballs (m) = 2·5 kg and angular frequency (N) = 75 r.p.m.
Height of the governor
We know that angular velocity of the governor,
2275
2·5 rad/s
60 60
ππ×N
ω= = = π
and height of governor, (^22)
9·8
0·159 m 159 mm
(2·5 )
g
h== = =
ωπ
Ans.
(i) Speed of the governor when the balls rise by 20 mm
In this case height of governor, h 1 = 159 – 20 = 139 mm = 0·139 m
∴^2
1
9·8
70·5
0·139
g
h
ω= = =
- It is the vertical distance between the centres of flyballs and pivot of the governor.
† Superfluous data
Fig. 29.8. Watt governor