The Hartnell governor is a type of mechanical governor used to control the speed of an engine. It works by using centrifugal force to adjust the position of the governor balls, which in turn adjusts the fuel flow to the engine.


- Extreme radii of rotation of balls = 40mm, 60mm
- Corresponding speeds = 210rpm, 230rpm
- Mass of ball = 3kg
- Length of ball and sleeve arms are equal


To determine the internal compression and spring constant of the Hartnell governor, we need to use the following formulas:

- Centrifugal force = m * r * w^2
- Spring force = k * x

where,
- m = mass of ball (3kg)
- r = radius of rotation (40mm or 60mm)
- w = angular velocity (in radians/sec) = 2 * pi * n / 60 (where n is the speed in rpm)
- x = deflection of spring
- k = spring constant

From the given data, we can calculate the centrifugal force for both radii of rotation:

- For r = 40mm: Fc = 3 * 0.04 * (2 * pi * 210 / 60)^2 = 127.9 N
- For r = 60mm: Fc = 3 * 0.06 * (2 * pi * 230 / 60)^2 = 261.1 N

Now, we can find the deflection of the spring using the formula for spring force:

- For r = 40mm: Fs = k * x = 127.9 N
- For r = 60mm: Fs = k * x = 261.1 N

Since the length of the ball and sleeve arms are equal, the deflection of the spring for both cases will be the same. Therefore, we can use the above equations to solve for the spring constant:

- For r = 40mm: k = Fs / x = 127.9 N / x
- For r = 60mm: k = Fs / x = 261.1 N / x

We can now solve for x by equating the two equations:

127.9 N / x = 261.1 N / x

x = 0.49 mm

Substituting this value of x in either equation gives us the spring constant:

k = 127.9 N / 0.49 mm = 260.8 N/mm

Therefore, the internal compression and spring constant of the Hartnell governor are:

- Internal compression = 60mm - 40mm = 20mm
- Spring constant = 260.8 N/mm


The Hartnell governor is a mechanical governor used to control the speed of an engine. To determine the internal compression and spring constant of the governor, we used the formulas for centrifugal force and spring force. We found that the internal compression is 20mm and the spring constant is 260.8 N/mm.

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