GTU BE01000081 Basic Mechanical Engineering Summer 2026 Solved Paper & Solutions

• Energy: the capacity to do work. It exists in many forms: mechanical (kinetic and potential), heat, electrical and chemical. Its SI unit is the joule (J). Energy can change from one form to another, but cannot be created or destroyed.
• Work: done when a force moves its point of application in the direction of the force. $W = F \times s$, in joules (1 J = 1 N·m). In thermodynamics, work is energy crossing the boundary of a system, other than heat.
• Power: the rate of doing work, $P = \dfrac{W}{t}$. Its unit is the watt (W), 1 W = 1 J/s. A 1 kW motor does 1000 J of work every second.

First law of thermodynamics: energy can neither be created nor destroyed; it can only change from one form to another. This is the law of conservation of energy applied to heat and work.

For a closed system undergoing a cycle, the net heat supplied equals the net work done:

For a closed system undergoing a process (change of state), the heat supplied is used partly to raise the internal energy and partly to do work:

Here $Q$ is the heat supplied to the system, $\Delta U$ is the change in internal energy, and $W$ is the work done by the system.

Explanation:

• If heat is supplied and no work is done, the internal energy rises (heating gas in a closed rigid tank).
• If the system is insulated ($Q = 0$), work done by it comes from its internal energy, so $W = -\Delta U$.
• A machine that produces work continuously without any energy input (PMM1) is impossible.

Example: 100 kJ of heat is given to a gas, and it does 40 kJ of work. Then $\Delta U = 100 - 40 = 60$ kJ.

Global warming

Global warming is the long-term rise in the average temperature of the Earth's surface and atmosphere.

Cause: the greenhouse effect. Sunlight passes through the atmosphere and warms the Earth. The warm Earth gives out infrared (heat) radiation. Greenhouse gases absorb this radiation and send part of it back, which keeps the Earth warm. Human activity has greatly increased these gases, so more heat is trapped.

Main greenhouse gases and sources:

Effects:

1. Melting of glaciers and polar ice, and rise in sea level.
2. More extreme weather: heat waves, floods, droughts and cyclones.
3. Changes in rainfall, which affect agriculture and water supply.
4. Loss of species and damage to coral reefs.
5. Spread of diseases and health problems.

Remedies: use renewable energy (solar, wind, hydro), improve energy efficiency, plant trees, use public transport and electric vehicles, and replace high global warming refrigerants. International agreements such as the Kyoto Protocol and the Paris Agreement set targets to cut emissions.

Ozone depletion

The ozone layer is a layer of ozone (O3) in the stratosphere, about 15 to 35 km above the Earth. It absorbs harmful ultraviolet (UV-B) radiation from the Sun.

Cause: CFCs (chlorofluorocarbons, used as refrigerants such as R-11 and R-12, and in aerosols and foams), halons (fire extinguishers) and some other chemicals rise to the stratosphere. UV light breaks them and frees chlorine atoms, which destroy ozone in a chain reaction:

One chlorine atom can destroy thousands of ozone molecules. An ozone hole forms over Antarctica every spring.

Effects:

1. More UV radiation reaches the Earth, causing skin cancer, cataracts and weaker immunity.
2. Damage to crops, plants and marine life (plankton).

Remedies: the Montreal Protocol (1987) phased out CFCs and halons. Refrigeration now uses ozone-friendly refrigerants such as R-134a, R-410A, R-290 (propane) and ammonia. The ozone layer is slowly recovering.

Charles's law: the volume of a given mass of a perfect gas is directly proportional to its absolute temperature, when the pressure is kept constant.

Explanation: when a gas is heated at constant pressure, its molecules move faster and push the walls harder, so the gas expands. Doubling the absolute temperature doubles the volume.

Example: a gas at $27^\circ$C (300 K) occupies 1 m³. At $327^\circ$C (600 K), at the same pressure, it occupies 2 m³. Temperatures must be in kelvin.

An adiabatic process is a process in which no heat is transferred between the system and the surroundings ($Q = 0$). All the change in energy is due to work.

From the first law, $Q = \Delta U + W$ with $Q = 0$:

• When a gas expands adiabatically, it does work using its internal energy, so its temperature falls.
• When a gas is compressed adiabatically, the work done on it raises its internal energy, so its temperature rises.

For a reversible adiabatic (isentropic) process of a perfect gas:

where $\gamma = C_p / C_v$ (1.4 for air).

Conditions: the system is perfectly insulated, or the process is so fast that there is no time for heat transfer.

Examples:

1. Compression and expansion strokes in IC engines.
2. Expansion of steam in a steam turbine and gas in a gas turbine.
3. Compression of air in an air compressor (nearly adiabatic when fast).
4. Rapid release of air from a tyre, which feels cold.

A throttling calorimeter is used to find the dryness fraction $x$ of wet steam. It is based on the fact that in throttling (a sudden fall in pressure through a small valve or orifice, with no work and no heat transfer), the enthalpy stays constant: $h_1 = h_2$.

Sketch

Construction

• Sampling tube: a perforated tube in the steam main, with holes facing the flow, so a fair sample of steam is taken.
• Throttle valve: a small valve or orifice that throttles the steam.
• Calorimeter chamber: an insulated chamber after the valve, with a thermometer (T2) and a pressure gauge or manometer (P2).
• Pressure gauge (P1) before the valve.

Working

1. Wet steam from the main enters the sampling tube.
2. It is throttled through the valve to a low pressure $P_2$ (near atmospheric).
3. After throttling, the steam becomes dry and slightly superheated, because its enthalpy stays the same while the pressure falls.
4. The pressure $P_1$, the pressure $P_2$ and the temperature $T_2$ are noted.

Calculation

Since $h_1 = h_2$:

$h_{f1}$ and $h_{fg1}$ are read at $P_1$, and $h_{g2}$ and $T_{s2}$ (saturation temperature) at $P_2$ from the steam tables. $C_{ps}$ is the specific heat of superheated steam (about 2.1 kJ/kg·K).

Advantages and limitations

• Advantages: simple, cheap, small and quick.
• Limitation: it works only for steam that is nearly dry ($x$ above about 0.95). Wetter steam stays wet after throttling, and its temperature cannot give $x$. For wetter steam, a separating and throttling calorimeter is used.
• Some error from heat loss and from the sample not being truly representative.

A heat engine is a device that converts heat into mechanical work, working in a cycle.

It takes heat $Q_1$ from a high temperature source (burning fuel), converts part of it into work $W$, and rejects the rest $Q_2$ to a low temperature sink (atmosphere).

No heat engine can be 100% efficient. Examples: petrol and diesel engines (internal combustion), steam engines and turbines (external combustion).

The Rankine cycle is the ideal cycle of a steam power plant.

Processes:

1. 4 to 1, boiler: water is heated at constant pressure to steam (dry or superheated). Heat supplied $Q_1 = h_1 - h_4$.
2. 1 to 2, turbine: steam expands isentropically and does work $W_T = h_1 - h_2$.
3. 2 to 3, condenser: exhaust steam is condensed at constant pressure to water. Heat rejected $Q_2 = h_2 - h_3$.
4. 3 to 4, pump: water is pumped isentropically back to boiler pressure. Pump work $W_P = h_4 - h_3$ (small).

Efficiency:

Neglecting the pump work, $\eta \approx \dfrac{h_1 - h_2}{h_1 - h_{f2}}$.

It is better than the Carnot cycle in practice because only liquid water is pumped, which needs little work. Its efficiency rises with a higher boiler pressure and steam temperature and a lower condenser pressure.

The Babcock and Wilcox boiler is a water tube boiler: water flows inside the tubes, and hot flue gases flow outside them. It is used in power plants and large industries.

Sketch

Construction

1. Steam and water drum: a long horizontal drum at the top, half filled with water. It carries the steam stop valve, safety valve, water level indicator and pressure gauge.
2. Water tubes: many tubes, inclined at about 15 degrees to the horizontal, connecting the down-take header (at the rear) and the up-take header (at the front).
3. Headers: vertical boxes joining the tubes to the drum. The down-take header is connected to the rear of the drum, and the up-take header to the front.
4. Mud box: at the bottom of the down-take header, to collect sediment, removed by a blow-off cock.
5. Furnace and grate: below the front (higher) end of the tubes. Coal is burnt on a chain grate stoker.
6. Baffles: fire brick walls that make the flue gases pass across the tubes three times (up, down and up again).
7. Superheater: tubes placed between the water tubes and the drum, to superheat the steam.
8. Chimney and damper: to remove the flue gases and control the draught.

Working

1. Fuel burns on the grate. The hot flue gases rise and, guided by the baffles, flow across the water tubes three times, and then leave through the chimney.
2. The water in the tubes above the furnace (front, hotter side) gets heated, becomes lighter and rises through the up-take header into the drum.
3. Cooler, heavier water from the drum flows down through the down-take header into the tubes.
4. This sets up a continuous natural circulation of water.
5. The steam separates from the water in the drum, collects at the top, passes through the superheater and leaves through the stop valve.

Features

• Pressure: up to about 40 bar. Capacity: up to about 40,000 kg of steam per hour.
• Advantages: large heating surface, quick steam raising, fast circulation, easy cleaning and replacement of tubes, safer than fire tube boilers (a tube burst causes less damage).
• Disadvantages: needs pure feed water to avoid scale in tubes, higher first cost.

An air compressor is a machine that takes in air at atmospheric pressure, compresses it and delivers it at a higher pressure. It uses mechanical work from an electric motor or engine.

Functions and uses of compressed air:

• Running pneumatic tools (drills, hammers, riveters) and spray painting.
• Air brakes in buses, trucks and trains.
• Starting large diesel engines, and supplying air to gas turbines.
• Filling tyres, cleaning, and pneumatic conveying.
• Refrigeration and air conditioning, and blast furnaces.

Types: reciprocating, rotary (screw, vane) and centrifugal compressors.

Priming is the process of filling the suction pipe, the casing and the impeller of a centrifugal pump completely with the liquid to be pumped, so that all air is removed, before the pump is started.

Why it is needed: the pressure an impeller produces depends on the density of the fluid. Air is about 800 times lighter than water, so an impeller running in air cannot lift water up the suction pipe. The pump runs dry, delivers nothing, and may damage its seals.

Methods of priming:

1. Manual priming: water is poured into the casing through a funnel, with the air vent open, until water comes out of the vent.
2. Priming with a vacuum pump: air is sucked out of the casing and suction pipe, so water rises into the pump.
3. Foot valve: a non-return valve at the bottom of the suction pipe keeps the pipe full of water after the pump stops, so priming is needed only the first time.
4. Self-priming pumps: designed to retain water in the casing and remove air themselves.

Reciprocating pumps do not need priming, because they are positive displacement pumps.

A reciprocating pump is a positive displacement pump. A piston (or plunger) moving to and fro in a cylinder sucks liquid in and pushes it out, using two non-return valves.

Sketch (single-acting)

Construction

1. Cylinder: in which the piston moves.
2. Piston and piston rod: moved to and fro by a crank and connecting rod, driven by a motor or engine.
3. Suction pipe with a suction valve: connects the cylinder to the sump. The valve opens only towards the cylinder.
4. Delivery pipe with a delivery valve: connects the cylinder to the tank. The valve opens only away from the cylinder.
5. Air vessels (optional) on the suction and delivery pipes, to smooth the flow.

Working

Suction stroke: the crank turns, and the piston moves outward (away from the valves). The volume in the cylinder increases and the pressure falls below atmospheric (partial vacuum). The suction valve opens, the delivery valve stays closed, and water from the sump is pushed into the cylinder by atmospheric pressure.

Delivery stroke: the piston moves inward. The water in the cylinder is compressed, and its pressure rises. The suction valve closes, the delivery valve opens, and water is forced up the delivery pipe to the tank.

The cycle repeats. In a single-acting pump, water is delivered once per revolution. In a double-acting pump, both sides of the piston work, so water is delivered twice per revolution and the flow is smoother.

Discharge

where $A$ is the piston area, $L$ the stroke and $N$ the speed in rpm. The actual discharge is a little less because of leakage (slip).

Features and uses

• Gives high pressure with small discharge; no priming needed.
• Flow is pulsating; many moving parts need maintenance.
• Used for boiler feed, hydraulic presses, oil drilling, car washing and small water supply.

Oldham coupling connects two parallel shafts whose axes are slightly offset (not in line), and transmits power at the same speed.

Construction: two flanges, one on each shaft, each with a slot (groove) across its face. A middle floating disc has a tongue on each face, at 90 degrees to each other. Each tongue fits the slot of one flange.

Working: when shaft 1 turns, the disc turns with it and slides in the slots, taking up the offset. Shaft 2 turns at the same speed. Used where shafts are slightly misaligned.

A centrifugal clutch engages automatically when the speed of the driving shaft rises, using centrifugal force. It is used in mopeds, scooters, chain saws and small machines.

Construction:

• A hub (spider) is fixed on the driving shaft (engine).
• Shoes with friction lining are placed in guides on the hub. They can move outward.
• Springs hold the shoes inward, away from the drum.
• A drum is fixed on the driven shaft and surrounds the shoes.

Working:

1. At low speed, the spring force is greater than the centrifugal force, so the shoes stay inward. The clutch is disengaged, and the engine idles without moving the vehicle.
2. As the speed rises, the centrifugal force on the shoes increases. When it exceeds the spring force, the shoes move outward and press against the drum.
3. Friction between the shoes and the drum drives the drum, and power is transmitted.
4. When the speed falls, the springs pull the shoes back, and the clutch disengages.

No clutch pedal is needed, so it gives smooth, automatic starting.

A brake absorbs the kinetic energy of a moving body by friction, to slow it down or stop it. In a shoe brake, a block (shoe) is pressed against a rotating wheel or drum.

Types

1. Single block (shoe) brake
2. Double block (shoe) brake
3. Internal expanding shoe brake (used in vehicles)

Single block brake

• A lever is pivoted at a fulcrum. A shoe with a friction lining is fixed to the lever.
• When a force P is applied at the end of the lever, the shoe presses on the drum with a normal force $R_N$.
• The friction force $F = \mu R_N$ acts on the drum and slows it.
• Braking torque: $T_B = \mu R_N r$, where $r$ is the drum radius.
• It puts a side load on the shaft bearing, so it is used only for small torques.

Double block brake

• Two shoes press on opposite sides of the drum, using a spring and a release mechanism (often an electromagnet).
• The side forces cancel, so there is no bending load on the shaft.
• Braking torque is about double: $T_B = (F_1 + F_2)\,r$.
• Used in cranes, hoists and lifts, where the spring applies the brake if power fails.

Internal expanding shoe brake (vehicle drum brake)

Construction:

• A brake drum is fixed to the wheel and turns with it.
• Two semicircular shoes with friction lining are pivoted on a fixed back plate inside the drum.
• A cam (mechanical brake) or a hydraulic wheel cylinder sits between the free ends of the shoes.
• Return springs hold the shoes away from the drum.

Working:

1. When the driver presses the brake pedal, the cam turns or the wheel cylinder pistons move outward.
2. The shoes expand and press against the inside of the drum.
3. Friction between the lining and the drum slows the wheel, and the kinetic energy becomes heat.
4. When the pedal is released, the return springs pull the shoes back.

Advantages: enclosed, so protected from dirt and water; compact; high braking torque. Used in cars, trucks and motorcycles (rear wheels).