Gas Laws

Gas Laws explain the behavior of an ideal gas in terms of Temperature, Pressure, Volume. The following are some of the important gas laws are

• Boyle’s Law
• Charles Law
• Gay-Lussac’s Law
• Avogadro’s law
• Universal Gas Law

Boyle’s Law:

Boyle’s law states that the volume of a given mass of gas (V) is inversely proportional to its absolute pressure (P), provided the temperature of the gas (T) remains constant.
Boyle’s law formula

Charles Law:

According to Charles law, the volume of a given mass of gas (V) is directly proportional to its absolute temperature (T), when its pressure remains constant.
Charles law formula

Gay-Lussac’s Law:

Gay-Lussac's Law is also know as Amontons’ law. It states that if the volume of a given mass of a gas (V) is kept constant, then the pressure of the gas (P) is directly proportional to its absolute temperature (T).
Gay-Lussac's Law Formula

Avogadro’s Law:

Avogadro's law states that equal volumes of different perfect gases, at the same temperature (T) and pressure (P), contain equal number of molecules (n).
Avogadro’s law equation

Universal Gas Law:

Combined Gas law is derived from the three gas laws Boyles law, Charles law and Gay-Lussacs law.

Universal Gas Law Formula

Laws of Friction

The sliding of a solid body in contact with another solid body is always opposed by  force of friction. Friction acts in the direction opposite to that of relative motion and it is tangential to the surface of two bodies at the point of contact.

Friction is a necessary in every machine because it involves wearing of machine component and consumes energy that transfers into heat. In come cases friction is desirable in case for functioning of a machine, such as belt drives, friction clutches.

The Five Laws of Friction:

1. When a body is moving, the friction is directly proportional to normal force and frictional force direction is perpendicular to the normal force.
2. Friction doesn't depend on the area of contact so long as there is an area of contact.
3. The coefficient of static friction is slightly higher the value than the coefficient of kinetic friction.
4. Kinetic friction is independent of velocity of the body.
5. Friction depends upon the type of the surfaces in contact.

Manometer Types

A manometer is a device used for measure the pressure of a fluid by balancing it with against a column of a liquid. Five different types of manometers are shown with pictures below.

U-Tube Manometer :

It consist a U – shaped bend whose one end is attached to the gauge point ‘A’ and other end is open to the atmosphere. It can measure both positive and negative (suction) pressures. It contains liquid of specific gravity greater than that of a liquid of which the pressure is to be measured.

where 'γ' is Specific weight, 'P' is Pressure at A.

Pressure at A is P = γ₂h₂ – γ₁h₁

Differential Manometer :

A U-Tube manometric liquid heavier than the liquid for which the pressure difference is to be measured and is not immiscible with it.

Pressure difference between A and B is given by equation

P_A – P_B = γ₂h₂ – γ₃h₃ – γ₁h₁

Inverted U-Tube Manometer :

Inverted U-Tube manometer consists of an inverted U - Tube containing a light liquid. This is used to measure the differences of low pressures between two points where where better accuracy is required. It generally consists of an air cock at top of manometric fluid type.

Pressure difference can be calculated from equation

P₁ - ρ₁*g*H₁ – ρ_m*g(H₂– H₁) = P₂ – ρ₂*gH₂

Micro Manometer :

Micro Manometer is is the modified form of a simple manometer whose one limb is made of larger cross sectional area. It measures very small pressure differences with high precision.

Let 'a' = area of the tube,

A = area of the reservoir,

h_{3 =} Falling liquid level reservoir,

h_{2 =} Rise of the liquid in the tube,

By conversation of mass we get A*h₃ = a*h₂

_{Equating pressure heads at datum we get} 

P₁ = (ρ_m – ρ₁)*gh₃ + ρ_m*gh₂ - ρ₁*gh₁

Inclined Manometer :

Inclined manometer is used for the measurement of small pressures and is to measure more accurately than the vertical tube type manometer. Due to inclination the distance moved by the fluid in manometer is more.

Pressure difference between A and B is give by equation

Governor types - Centrifugal Governor and Inertia Governor

Governor is a device used to maintain the speed of an engine within specified limits when the engine works in varying of different loads.

Based on the source of controlling force, the governors can be classified into two types. They are centrifugal governors and inertia governors.

Centrifugal Governors :

In centrifugal governors, multiple masses know as governor balls, are responsible to revolve about the axis of a shaft, which is driven through suitable gearing from the engine crankshaft. Each ball is acted upon by a force which acts in the radially inward direction and is provided by dead weight, a spring or a combination of two. This force is commonly called as the controlling force and it will increase as the distance of the ball from the axis of rotation increases. The inward or outward movement of the ball is transmitted by the governor mechanism to the valve which controls the amount of energy supplied to the engine.

Image Source : flickr.com

Inertia Governor :

In inertia governors, the balls are arranged in manner that the inertia forces caused by angular acceleration or retardation of the governor shaft tend to change their position. The obvious advantage of inertia governor lies in its rapid response to the effect of a change of load. This advantage is small, however by the practical difficulty of arranging for the complete balance of the revolving parts of the governor. For this reason Centrifugal governors are preferred over the inertia governors.