GTU 3110006 Basic Mechanical Engineering (BME) Summer 2025 Solved Paper & Solutions

Global warming is the slow rise in the average temperature of the Earth. It is caused mainly by greenhouse gases, such as carbon dioxide (CO$_2$) and methane, which are released by the burning of coal, petrol and diesel. These gases trap the heat of the Sun. The effects are melting of ice, a rising sea level and climate change.

Solar energy is the energy of the Sun's rays. It is clean and renewable. It can be changed into electricity by solar cells (photovoltaic) or used for heating water by solar collectors. When solar energy replaces fossil fuels, less CO$_2$ is released, so it helps to reduce global warming.

The First Law of Thermodynamics says that energy can neither be created nor destroyed. It can only change from one form to another. For a closed system going through a process, its mathematical form is

or, for a very small change, $\delta Q = dU + \delta W$.

Meaning of the terms:

1. $Q$: the heat supplied to the system. It is positive when heat is added to the system and negative when heat is rejected.
2. $\Delta U$: the change in the internal energy of the system, $U_2 - U_1$. For a perfect gas, $\Delta U = mC_v(T_2 - T_1)$.
3. $W$: the work done by the system on the surroundings. It is positive when the system does work, and negative when work is done on the system.

All terms are in the same unit, kJ (or J). For a complete cycle, $\Delta U = 0$, so $\oint \delta Q = \oint \delta W$. The net heat supplied is equal to the net work done.

Characteristic gas equation: $PV = mRT$, where $P$ is the absolute pressure, $V$ is the volume, $m$ is the mass, $T$ is the absolute temperature and $R$ is the characteristic gas constant. It is obtained by combining two laws.

Boyle's law

At a constant temperature, the volume of a given mass of a gas is inversely proportional to its pressure.

Charles's law

At a constant pressure, the volume of a given mass of a gas is directly proportional to its absolute temperature.

Derivation

Let a gas change from the state 1 ($P_1$, $V_1$, $T_1$) to the state 2 ($P_2$, $V_2$, $T_2$). We take the gas through two steps, by way of an intermediate state ($P_2$, $V'$, $T_1$).

Equating the two values of $V'$:

For a gas of mass $m$, this constant is $mR$. So

For 1 kg of the gas, $Pv = RT$, where $v$ is the specific volume. The value of $R$ is different for each gas. For example, $R = 0.287$ kJ/kg K for air. $R = \dfrac{R_0}{M}$, where $R_0 = 8.314$ kJ/kmol K is the universal gas constant and $M$ is the molecular mass.

Example: for 1 kg of air at 300 K and 100 kPa, the specific volume is $v = \dfrac{RT}{P} = \dfrac{0.287 \times 300}{100} = 0.861$ m$^3$/kg.

A perfect gas is an imaginary gas that follows this equation at all pressures and temperatures. Real gases follow it closely at low pressure and high temperature.

Both are path functions, since their values depend on the path of the process. They are not properties of the system.

A prime mover is a machine that changes a natural source of energy into mechanical work. By the source of energy, the types are:

1. Heat energy of fuel (heat engines):

• External combustion engines: steam engine and steam turbine. The fuel is burnt outside the engine.
• Internal combustion engines: petrol engine, diesel engine and gas turbine. The fuel is burnt inside the engine.

2. Energy of water (hydraulic prime movers): water turbines such as Pelton, Francis and Kaplan turbines.
3. Energy of wind: windmills and wind turbines.
4. Nuclear energy: steam turbines run by the steam made in a nuclear reactor.
5. Solar energy: engines and turbines run by steam made in solar collectors.

In a domestic refrigerator, the vapour compression refrigeration cycle takes heat from the cold space (the freezer and the cabinet) and rejects it to the room. The refrigerant is usually R134a.

Layout

Processes of the cycle

1. Compression (1 to 2): the compressor draws the low pressure dry saturated vapour from the evaporator and compresses it. The pressure and temperature rise, so it becomes high pressure superheated vapour.
2. Condensation (2 to 3): the hot vapour flows through the condenser (the black grill at the back). It gives its heat to the surrounding air, and condenses into a high pressure liquid at constant pressure.
3. Expansion (3 to 4): the liquid passes through the capillary tube (the expansion device). Its pressure and temperature fall suddenly. It becomes a cold mixture of liquid and a little vapour. The enthalpy stays constant (throttling).
4. Evaporation (4 to 1): the cold mixture flows through the evaporator inside the refrigerator. It absorbs heat from the food and the air, and the liquid evaporates fully into vapour. The vapour goes back to the compressor.

Performance

The coefficient of performance is the refrigerating effect divided by the work of compression:

where $h$ is the enthalpy at each point.

Heat 1 kg of a perfect gas at constant pressure from $T_1$ to $T_2$. The heat supplied is

By the First Law, $Q = \Delta U + W$. The change in internal energy is $\Delta U = C_v\,(T_2 - T_1)$. The work done at constant pressure is $W = P\,(v_2 - v_1) = R\,(T_2 - T_1)$, using $Pv = RT$.

Cancelling $(T_2 - T_1)$:

This is true for a perfect gas, per kg of the gas. $C_p$ is more than $C_v$, since at constant pressure the heat also does the work of expansion.

A throttling calorimeter is used to find the dryness fraction $x$ of wet steam. It uses the fact that during throttling (a sudden fall of pressure through a valve or an orifice) the enthalpy stays constant.

Sketch

Working

A small sample of the wet steam is taken from the main through a sampling tube, which has holes facing the flow. The steam is throttled to a low pressure (near atmospheric) in the calorimeter. After throttling it becomes dry or slightly superheated. The pressure $P_1$ (before the valve), the pressure $P_2$ and the temperature $T_2$ (after the valve) are noted.

Calculation. The enthalpy before and after the throttling is the same:

The values of $h_f$, $h_{fg}$ and $h_g$ are taken from the steam tables. The sampling tube has small holes facing the flow, so that it takes a fair sample. The pipes are insulated to reduce the heat loss. The pressure $P_2$ is kept low enough so that the steam after throttling is superheated, and its temperature can be read.

Advantages

• Simple in construction and cheap.
• Small and portable. It is easy to use and gives the result quickly.

Disadvantages

• It can be used only when the steam is nearly dry (about $x > 0.95$). For a wetter steam, the steam after throttling is still wet and the temperature does not give $x$.
• It is less accurate, since there is some heat loss from the calorimeter.
• The sample may not be a true sample of the steam in the main.

Classification of internal combustion engines:

1. By the cycle: Otto cycle (petrol), Diesel cycle and Dual cycle engines.
2. By the number of strokes: two stroke and four stroke engines.
3. By the fuel: petrol, diesel, gas (CNG, LPG) engines.
4. By the ignition: spark ignition (SI) and compression ignition (CI).
5. By the cooling: air cooled and water cooled.
6. By the arrangement of cylinders: inline, V type, radial and opposed cylinder.
7. By the use: automobile, marine, aircraft and stationary engines.

Applications of compressed air:

1. Pneumatic tools: drills, hammers, rivetting guns, wrenches and grinders.
2. Spray painting and spraying of insecticides.
3. Air brakes in trains, buses and trucks.
4. Cleaning and blowing of dust from machines and parts.
5. Starting of large IC engines and gas turbines.
6. Mining: drilling and running of machines where sparks are dangerous.
7. Inflating of tyres, and operating of air hoists, lifts and doors.
8. Sand blasting, pneumatic conveying of powders, and pneumatic control systems in industry.
9. Ventilation and air conditioning of mines and buildings, and the supply of air in diving.

The Cochran boiler is a vertical, multitubular, fire tube boiler with an internally fired furnace. It is a modified form of the simple vertical boiler. It occupies a small floor area, and it is used for small and medium steam demands.

Sketch

Main parts

1. Shell: the vertical cylindrical shell, with a hemispherical crown on top. The crown gives high strength, and a large space for the steam.
2. Furnace (firebox): the lower part is hemispherical. It has the grate on which the fuel burns. Below it is the ash pit.
3. Flue pipe (connecting pipe): it joins the furnace to the combustion chamber.
4. Combustion chamber: a lined space where the burning of the gases is completed. It has a fire brick lining, to protect the shell.
5. Fire tubes: many horizontal tubes through which the hot gases pass from the combustion chamber to the smoke box. They are surrounded by water.
6. Smoke box and chimney: the gases leave through the smoke box and the chimney.
7. Mountings: water level gauge, pressure gauge, safety valve, stop valve, feed check valve, fusible plug and man hole.

Working

The fuel is burnt on the grate in the furnace. The hot gases rise through the flue pipe into the combustion chamber. From there, they pass through the horizontal fire tubes, to the smoke box and the chimney. They give up their heat to the water through the walls of the furnace and the tubes. The steam collects in the space at the top and is taken out by the stop valve.

A single acting reciprocating pump has one cylinder with a piston moving back and forth. The liquid acts on one side of the piston only. The parts are the cylinder, piston, connecting rod and crank, the suction pipe with a suction valve, and the delivery pipe with a delivery valve.

Suction stroke: the piston moves back. A vacuum forms, the suction valve opens, and the liquid enters the cylinder. Delivery stroke: the piston moves forward. The suction valve closes, the delivery valve opens, and the liquid is pushed out. The liquid is delivered once in each revolution of the crank.

A single plate friction clutch connects the engine to the gearbox, and transmits the torque by friction between a plate and the flywheel. It is used in cars.

Parts: the flywheel (fixed to the engine shaft), the clutch plate (a disc with friction linings on both sides, on a splined gearbox shaft), the pressure plate, springs, and the release lever with the clutch pedal.

Engaged: the springs press the clutch plate between the flywheel and the pressure plate. The friction transmits the power to the gearbox shaft.

Disengaged: when the driver presses the pedal, the release lever moves the pressure plate away. The clutch plate is free, and the power is cut off. This allows a gear change.

A mechanical property shows how a material behaves when a load acts on it. The properties are:

Notes:

1. Elasticity is the basic property for all design. A material loaded within its elastic limit returns to its shape.
2. Ductility and malleability both describe plastic behaviour. A ductile material gives a long plastic strain before it breaks, so there is a warning before the failure.
3. Toughness is the energy absorbed up to the fracture, while resilience is the energy absorbed up to the elastic limit only. So resilience is a part of toughness.
4. Hardness is measured by tests such as Brinell, Rockwell and Vickers.