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 fall by 20 mm.

(a) 60 r.p.m.

(b) 70 r.p.m.

(c) 70.2 r.p.m.

(d) 80 r.p.m.

This question was posed to me at a job interview.

My doubt stems from Wilson-Hartnell and Pickering Governor in portion Governors of Machine Dynamics

Answer 1

Right option is (c) 70.2 r.p.m.

The explanation is: 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 fall by 20 mm

The height of the governor h increases to h2 = 159 + 20 = 179 mm = 0.179 m

Hence, the angular velocity ω2 corresponding to height h2,

ω2^2 = g/h2= 9.81/0.179 = 54.7

ω2 = 7.4 rad/s

Speed in r.p.m., N2 = 60ω2/2п = 60 x 7.4/2п = 70.7 r.p.m.