Question

A centrifugal Watt governor is fitted with two balls, each of mass 2.5 kg. Find the sped of the governor, when the balls rise by 20 mm.

(a) 80.2 r.p.m.

(b) 90.2 r.p.m.

(c) 100.2 r.p.m.

(d) 110.2 r.p.m.

I had been asked this question in a national level competition.

My question is taken from Wilson-Hartnell and Pickering Governor in section Governors of Machine Dynamics

Answer 1

Correct option is (a) 80.2 r.p.m.

Easiest explanation: Mass of flyballs(m) = 2.5 kg and N speed of governor = 75 r.p.m.

So the angular velocity of the governor ω = 2пN/60 = 2п75/60 = 2.5п rad/s

Height of the governor, h = g/ω^2 = 9.81/2.5п^2 = 0.159m = 159 mm

Speed of the governor when balls rise by 20 mm

The height of the governor h reduces to h1 = 159 – 20 = 139 mm = 0.139 m

Hence, the angular velocity ω1 corresponding to height h1,

ω1^2 = g/h1= 9.81/0.139 = 70.5

ω1 = 8.4 rad/s

Speed in r.p.m., N1 = 60ω1/2п = 60 x 8.4/2п = 80.2 r.p.m.