In a Watt governor, the weight of the ball is 50 N and the friction at the sleeve is 10 N. The coefficient of detention would be:

Option 3 : 0.2

__Concept:__

**Coefficient of detention is given by:**

__\(\frac{{Friction\;force\;at\;sleeve}}{{Weight\;of\;ball}}= \frac{f}{{Mg}} \)__

__Calculation:__

**Given:**

Weight of the ball = 50 N, Friction force (f) = 10 N.

Coefficient of detention \(=\frac{{Friction\;force\;at\;sleeve}}{{Weight\;of\;ball}}= \frac{f}{{Mg}} \)

Coefficient of detention \(= \frac{{10}}{{50}}\)

**Coefficient of detention ****= 0.2**

Find the height of the watt governor, if the angular speed of the ball is 100 rad/sec.

Take g = 10 m/s^{2}.

Option 3 : 1 mm

__Concept:__

Watt Governor:

- It is a type of centrifugal governor.
- It is the simplest pendulum-type governor.
- It is unsuitable for high-speed Engine.

The above figure shows the simple watt governor,

Let, m = mass of each ball, h = height of the governor, w = weight of each ball, ω = angular velocity of the arm ball and sleeve, T = tension in the arm, r = radial distance of ball-centre from spindle axis

Assuming the link to be massless and neglecting the friction of the sleeve, the mass m at A is in static equilibrium under the action of.

- Weight w
- Centrifugal force mrω2
- Tension T in the upper link

The equilibrium of the ball provides

T × cos θ = mg

T × sin θ = mrω2

\(\tan \theta = \frac{{mr{ω ^2}}}{{mg}} = \frac{{r{ω ^2}}}{g} \Rightarrow \frac{r}{h} = \frac{{r{ω ^2}}}{g} = h = \frac{g}{{{ω ^2}}}\)

**Calculation:**

**Given:**

ω = 100 rad/sec, h = ?

\( h = \frac{g}{{{ω ^2}}}\)

\(h=\frac{10}{(100)^2}=1 ~mm\)

Option 1 : \(h\;=\frac{{g}}{{\omega^2}}\)

**Concept:**

**Governor:**

- It is a device which controls
**the mean speed of the engine over a long period due to load fluctuation.** - Governor has no influence over cyclic speed fluctuation

**Watt Governor:**

- It is a type of
**centrifugal governor.** - It is the simplest pendulum-type governor.
- It is
**unsuitable for high-speed Engine.**

The above figure shows the simple watt governor,

Let, m = mass of each ball, h = height of the governor, w = weight of each ball, ω = angular velocity of the arm ball and sleeve, T = tension in the arm, r = radial distance of ball-centre from spindle axis

Assuming the link to be massless and neglecting the friction of the sleeve, the mass m at A is in** static equilibrium** under the action of.

- Weight w
- Centrifugal force mrω
^{2} - Tension T in the upper link

The equilibrium of the ball provides

T × cos θ = mg

T × sin θ = mrω^{2}

\(\tan \theta = \frac{{mr{\omega ^2}}}{{mg}} = \frac{{r{\omega ^2}}}{g} \Rightarrow \frac{r}{h} = \frac{{r{\omega ^2}}}{g} = h = \frac{g}{{{\omega ^2}}}\)

Option 3 : Watt governor

**Explanation:**

**Governor:**

The **function of a governor is to regulate the mean speed of an engine when there are variations in the load.**

E.g. when the load on an engine increases, its speed decreases, therefore it becomes necessary to increase the supply of working fluid. On the other hand, when the load on the engine decreases, its speed increases and thus less working fluid is required.

- The
**governor automatically controls the supply of working fluid to the engine with the varying load conditions and keeps the mean speed within certain limits.** - When the load increases, the configuration of the governor changes and a valve is moved to increase the supply of the working fluid, conversely, when the load decreases, the engine speed increases and the governor decreases the supply of working fluid.

**Types of governor:**

**Governors are classified as**:

- Centrifugal Governor
- Inertia Governor

Centrifugal Governors are classified as:

- Dead Weight Governors:
- Porter governor
- Proell governor

Spring controlled governors:

- Hartnell governor
- Hartung governor
- Pickering governor

Watt Governors:

In this governor, the mass of the flyball is more than the mass of the sleeve.

Height of the governor is given by: \(h = \frac{{895}}{{{N^2}}}\)

Working:

When the load at the engine increases the angular velocity as well as the speed of the engine automatically decreases. At the uniform speed controlling force is equal to the centrifugal force which balances each other but when the centrifugal force on balls decreases, the balls and spindle start to move inward and downward direction respectively. These movements are responsible for the mechanism of the throttle valve and cause it opening widely which increases the fuel supply to maintain the speed.

At high speed, the sensitivity of watt governor is very less, hence it is not used nowadays.

Option 2 : Action of gravity

__Explanation:__

Governor:

The function of a governor is to regulate the mean speed of an engine when there are variations in the load.

E.g. when the load on an engine increases, its speed decreases, therefore it becomes necessary to increase the supply of working fluid. On the other hand, when the load on the engine decreases, its speed increases and thus less working fluid is required.

- The governor automatically controls the supply of working fluid to the engine with the varying load conditions and keeps the mean speed within certain limits.
- When the load increases, the configuration of the governor changes and a valve is moved to increase the supply of the working fluid, conversely, when the load decreases, the engine speed increases and the governor decreases the supply of working fluid.

Watt Governors:

- In this governor, the mass of the flyball is more than the mass of the sleeve.
- Gravity is the controlling force in Watt governor and spring force is the controlling force in Hartnell governor.
- Height of the governor is given by: \(h = \frac{{895}}{{{N^2}}}\)

Working:

When the load at the engine increases the angular velocity as well as the speed of the engine automatically decreases. At the uniform speed controlling force is equal to the centrifugal force which balances each other but when the centrifugal force on balls decreases, the balls and spindle start to move inward and downward direction respectively. These movements are responsible for the mechanism of the throttle valve and cause it to open widely which increases the fuel supply to maintain the speed.

**Note:**

At high speed, the sensitivity of watt governor is very less, hence it is not used nowadays.

__Additional Information__

Types of governor:

Governors are classified as:

- Centrifugal Governor
- Inertia Governor

Centrifugal Governors are classified as:

- Dead Weight Governors:
- Porter governor
- Proell governor

Spring controlled governors:

- Hartnell governor
- Hartung governor
- Pickering governor

In a Watt governor, the weight of the ball is 50 N and the friction at the sleeve is 10 N. The coefficient of detention would be:

Option 3 : 0.2

__Concept:__

**Coefficient of detention is given by:**

__\(\frac{{Friction\;force\;at\;sleeve}}{{Weight\;of\;ball}}= \frac{f}{{Mg}} \)__

__Calculation:__

**Given:**

Weight of the ball = 50 N, Friction force (f) = 10 N.

Coefficient of detention \(=\frac{{Friction\;force\;at\;sleeve}}{{Weight\;of\;ball}}= \frac{f}{{Mg}} \)

Coefficient of detention \(= \frac{{10}}{{50}}\)

**Coefficient of detention ****= 0.2**

Find the height of the watt governor, if the angular speed of the ball is 100 rad/sec.

Take g = 10 m/s^{2}.

Option 3 : 1 mm

__Concept:__

Watt Governor:

- It is a type of centrifugal governor.
- It is the simplest pendulum-type governor.
- It is unsuitable for high-speed Engine.

The above figure shows the simple watt governor,

Let, m = mass of each ball, h = height of the governor, w = weight of each ball, ω = angular velocity of the arm ball and sleeve, T = tension in the arm, r = radial distance of ball-centre from spindle axis

Assuming the link to be massless and neglecting the friction of the sleeve, the mass m at A is in static equilibrium under the action of.

- Weight w
- Centrifugal force mrω2
- Tension T in the upper link

The equilibrium of the ball provides

T × cos θ = mg

T × sin θ = mrω2

\(\tan \theta = \frac{{mr{ω ^2}}}{{mg}} = \frac{{r{ω ^2}}}{g} \Rightarrow \frac{r}{h} = \frac{{r{ω ^2}}}{g} = h = \frac{g}{{{ω ^2}}}\)

**Calculation:**

**Given:**

ω = 100 rad/sec, h = ?

\( h = \frac{g}{{{ω ^2}}}\)

\(h=\frac{10}{(100)^2}=1 ~mm\)

Option 1 : \(h\;=\frac{{g}}{{\omega^2}}\)

**Concept:**

**Governor:**

- It is a device which controls
**the mean speed of the engine over a long period due to load fluctuation.** - Governor has no influence over cyclic speed fluctuation

**Watt Governor:**

- It is a type of
**centrifugal governor.** - It is the simplest pendulum-type governor.
- It is
**unsuitable for high-speed Engine.**

The above figure shows the simple watt governor,

** static equilibrium** under the action of.

- Weight w
- Centrifugal force mrω
^{2} - Tension T in the upper link

The equilibrium of the ball provides

T × cos θ = mg

T × sin θ = mrω^{2}

\(\tan \theta = \frac{{mr{\omega ^2}}}{{mg}} = \frac{{r{\omega ^2}}}{g} \Rightarrow \frac{r}{h} = \frac{{r{\omega ^2}}}{g} = h = \frac{g}{{{\omega ^2}}}\)

Option 3 : Watt governor

**Explanation:**

**Governor:**

The **function of a governor is to regulate the mean speed of an engine when there are variations in the load.**

E.g. when the load on an engine increases, its speed decreases, therefore it becomes necessary to increase the supply of working fluid. On the other hand, when the load on the engine decreases, its speed increases and thus less working fluid is required.

- The
**governor automatically controls the supply of working fluid to the engine with the varying load conditions and keeps the mean speed within certain limits.** - When the load increases, the configuration of the governor changes and a valve is moved to increase the supply of the working fluid, conversely, when the load decreases, the engine speed increases and the governor decreases the supply of working fluid.

**Types of governor:**

**Governors are classified as**:

- Centrifugal Governor
- Inertia Governor

Centrifugal Governors are classified as:

- Dead Weight Governors:
- Porter governor
- Proell governor

Spring controlled governors:

- Hartnell governor
- Hartung governor
- Pickering governor

Watt Governors:

In this governor, the mass of the flyball is more than the mass of the sleeve.

Height of the governor is given by: \(h = \frac{{895}}{{{N^2}}}\)

Working:

When the load at the engine increases the angular velocity as well as the speed of the engine automatically decreases. At the uniform speed controlling force is equal to the centrifugal force which balances each other but when the centrifugal force on balls decreases, the balls and spindle start to move inward and downward direction respectively. These movements are responsible for the mechanism of the throttle valve and cause it opening widely which increases the fuel supply to maintain the speed.

At high speed, the sensitivity of watt governor is very less, hence it is not used nowadays.

A simple watt governor rotates at 75 rpm. Find the magnitude of change in vertical height (in mm) when its speed increases to 80 rpm.

__Concept:__

For watt governor

\(h = \frac{{895}}{{{N^2}}}\;metres\)

__Calculation:__

\({h_1} - {h_2} = 895\left( {\frac{1}{{N_1^2}} - \frac{1}{{N_2^2}}} \right) = 895\left( {\frac{1}{{{{75}^2}}} - \frac{1}{{{{80}^2}}}} \right)\)

H_{1} – h_{2} = 19.27 mm