Basic Mechanical Engineering (BT-203) - Unit 5 Short Notes

How unit 5 is examined

Covers the steam engine, the air-standard cycles (Carnot, Otto, Diesel, Dual), two- and four-stroke petrol and diesel engines, and compressors; the cycle derivations and the engine sketches carry most of the marks.

Working principle of steam Engine

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Low weight</span>

Definition. A steam engine is a reciprocating heat engine in which high-pressure steam expands in a cylinder, pushes a piston, and the slider-crank mechanism converts the to-and-fro motion into rotary motion.

Key points.

1. The main parts are the cylinder, piston, piston rod, crosshead, connecting rod, crank, flywheel, steam chest, D-slide valve and eccentric.
2. In a double-acting engine, the D-slide valve, driven by the eccentric, admits steam alternately to either side of the piston, so every stroke is a power stroke.
3. While one side receives steam, the other side is open to exhaust, so used steam leaves through the exhaust port.
4. The piston rod and crosshead guide the piston in a straight line, and the connecting rod turns the crank, so reciprocating motion becomes rotary motion.
5. The flywheel stores energy during the power stroke and smooths the output speed.

Diagram. <figure class="ds-fig" style="margin:1.4rem 0;overflow-x:auto"><svg xmlns="http://www.w3.org/2000/svg" id="dsfig-u5-01" viewBox="0 0 510 166" width="510" height="166" role="img" aria-label="Double-acting steam engine: Cyl cylinder and piston, Slv D-slide valve in steam chest, Xh crosshead, Crk crank, Fw flywheel"><style>#dsfig-u5-01 .e{stroke:#454C5A;stroke-width:1.4;fill:none}#dsfig-u5-01 .e.hi{stroke:#2340B8;stroke-width:2.6}#dsfig-u5-01 .n{fill:#FFFFFF;stroke:#16181D;stroke-width:1.4}#dsfig-u5-01 .n.hi{fill:#E3E9FC;stroke:#2340B8;stroke-width:2.2}#dsfig-u5-01 .n.rb-b{fill:#16181D;stroke:#16181D}#dsfig-u5-01 .n.rb-r{fill:#BD3227;stroke:#BD3227}#dsfig-u5-01 text{font-family:"JetBrains Mono",ui-monospace,Menlo,Consolas,monospace;font-size:13px}#dsfig-u5-01 .t{fill:#16181D;font-weight:500}#dsfig-u5-01 .t.inv{fill:#FFFFFF;font-weight:700}#dsfig-u5-01 .kd{stroke:#16181D;stroke-width:1.2}#dsfig-u5-01 .dot{fill:#16181D}#dsfig-u5-01 .ann{fill:#2340B8;font-size:11px;font-weight:700}#dsfig-u5-01 .lbl{fill:#6F7787;font-family:system-ui,-apple-system,sans-serif;font-size:12px;font-weight:700}#dsfig-u5-01 .ptr{fill:#2340B8;font-size:12px;font-weight:700}#dsfig-u5-01 .ah{fill:#454C5A}#dsfig-u5-01 .ah.hi{fill:#2340B8}#dsfig-u5-01 .wl rect{fill:#FFFFFF;stroke:#DCE0E7}#dsfig-u5-01 .wl .t{font-size:12px;font-weight:700}#dsfig-u5-01 .wl.hi rect{fill:#2340B8;stroke:#2340B8}#dsfig-u5-01 .wl.hi .t{fill:#FFFFFF}html.dark #dsfig-u5-01 .e{stroke:#B1B7C3}html.dark #dsfig-u5-01 .e.hi{stroke:#8FA3FF}html.dark #dsfig-u5-01 .n{fill:#161920;stroke:#E6E8ED}html.dark #dsfig-u5-01 .n.hi{fill:#1E2748;stroke:#8FA3FF}html.dark #dsfig-u5-01 .n.rb-b{fill:#E6E8ED;stroke:#E6E8ED}html.dark #dsfig-u5-01 .n.rb-r{fill:#FF7E71;stroke:#FF7E71}html.dark #dsfig-u5-01 .t{fill:#E6E8ED}html.dark #dsfig-u5-01 .t.inv{fill:#0F1115}html.dark #dsfig-u5-01 .kd{stroke:#E6E8ED}html.dark #dsfig-u5-01 .dot{fill:#E6E8ED}html.dark #dsfig-u5-01 .ann{fill:#8FA3FF}html.dark #dsfig-u5-01 .lbl{fill:#858D9C}html.dark #dsfig-u5-01 .ptr{fill:#8FA3FF}html.dark #dsfig-u5-01 .ah{fill:#B1B7C3}html.dark #dsfig-u5-01 .ah.hi{fill:#8FA3FF}html.dark #dsfig-u5-01 .wl rect{fill:#161920;stroke:#2A2E37}html.dark #dsfig-u5-01 .wl.hi rect{fill:#8FA3FF;stroke:#8FA3FF}html.dark #dsfig-u5-01 .wl.hi .t{fill:#0F1115}</style><defs><marker id="ah23" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah" d="M0,1 L9,5 L0,9 z"/></marker><marker id="ahh23" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah hi" d="M0,1 L9,5 L0,9 z"/></marker></defs><path class="e" d="M153.2,50.5 L57.5,114.4" marker-end="url(#ah23)"/><path class="e" d="M59,126 L236,126"/><path class="e" d="M274,126 L365,126"/><path class="e" d="M403,126 L451,126"/><g class="wl"><rect x="81" y="74" width="47.1" height="18" rx="9"/><text class="t" x="104.5" y="83" dy=".35em" text-anchor="middle">steam</text></g><g class="wl"><rect x="130.7" y="117" width="33.6" height="18" rx="9"/><text class="t" x="147.5" y="126" dy=".35em" text-anchor="middle">rod</text></g><g class="wl"><rect x="292.4" y="117" width="54.3" height="18" rx="9"/><text class="t" x="319.5" y="126" dy=".35em" text-anchor="middle">conrod</text></g><circle class="n" cx="40" cy="126" r="18"/><text class="t" x="40" y="126" dy=".35em" text-anchor="middle">Cyl</text><circle class="n" cx="169" cy="40" r="18"/><text class="t" x="169" y="40" dy=".35em" text-anchor="middle">Slv</text><circle class="n" cx="255" cy="126" r="18"/><text class="t" x="255" y="126" dy=".35em" text-anchor="middle">Xh</text><circle class="n" cx="384" cy="126" r="18"/><text class="t" x="384" y="126" dy=".35em" text-anchor="middle">Crk</text><circle class="n" cx="470" cy="126" r="18"/><text class="t" x="470" y="126" dy=".35em" text-anchor="middle">Fw</text></svg><figcaption style="font-size:.82em;opacity:.72;margin-top:.45rem">Double-acting steam engine: Cyl cylinder and piston, Slv D-slide valve in steam chest, Xh crosshead, Crk crank, Fw flywheel</figcaption></figure>

Answer frame. Open with the definition; draw the cylinder with piston, steam chest with D-slide valve, crosshead, connecting rod, crank and flywheel; describe steam admission on alternate sides, then motion conversion; close with the flywheel smoothing the speed.

Asked: [6 marks] (Jun 2025) With the help of a neat sketch describe the construction and working of a steam engine.

Carnot, Otto, Diesel and Dual cycles P-V & T-S diagrams and its efficiency

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">High weight</span>

Definition. An air-standard cycle is an ideal cycle in which air behaves as a perfect gas ($\gamma = 1.4$), all processes are reversible, and heat is added and rejected from outside. ==Thermal efficiency is the net work divided by the heat supplied, $\eta = 1 - Q_{out}/Q_{in}$.==

Diagram. <figure class="ds-fig" style="margin:1.4rem 0;overflow-x:auto"><svg xmlns="http://www.w3.org/2000/svg" id="dsfig-u5-02" viewBox="0 0 338 252" width="338" height="252" role="img" aria-label="Carnot cycle (P on the vertical axis, V across): 1-2 isothermal expansion, 2-3 adiabatic expansion, 3-4 isothermal compression, 4-1 adiabatic compression. In T-s it is a rectangle."><style>#dsfig-u5-02 .e{stroke:#454C5A;stroke-width:1.4;fill:none}#dsfig-u5-02 .e.hi{stroke:#2340B8;stroke-width:2.6}#dsfig-u5-02 .n{fill:#FFFFFF;stroke:#16181D;stroke-width:1.4}#dsfig-u5-02 .n.hi{fill:#E3E9FC;stroke:#2340B8;stroke-width:2.2}#dsfig-u5-02 .n.rb-b{fill:#16181D;stroke:#16181D}#dsfig-u5-02 .n.rb-r{fill:#BD3227;stroke:#BD3227}#dsfig-u5-02 text{font-family:"JetBrains Mono",ui-monospace,Menlo,Consolas,monospace;font-size:13px}#dsfig-u5-02 .t{fill:#16181D;font-weight:500}#dsfig-u5-02 .t.inv{fill:#FFFFFF;font-weight:700}#dsfig-u5-02 .kd{stroke:#16181D;stroke-width:1.2}#dsfig-u5-02 .dot{fill:#16181D}#dsfig-u5-02 .ann{fill:#2340B8;font-size:11px;font-weight:700}#dsfig-u5-02 .lbl{fill:#6F7787;font-family:system-ui,-apple-system,sans-serif;font-size:12px;font-weight:700}#dsfig-u5-02 .ptr{fill:#2340B8;font-size:12px;font-weight:700}#dsfig-u5-02 .ah{fill:#454C5A}#dsfig-u5-02 .ah.hi{fill:#2340B8}#dsfig-u5-02 .wl rect{fill:#FFFFFF;stroke:#DCE0E7}#dsfig-u5-02 .wl .t{font-size:12px;font-weight:700}#dsfig-u5-02 .wl.hi rect{fill:#2340B8;stroke:#2340B8}#dsfig-u5-02 .wl.hi .t{fill:#FFFFFF}html.dark #dsfig-u5-02 .e{stroke:#B1B7C3}html.dark #dsfig-u5-02 .e.hi{stroke:#8FA3FF}html.dark #dsfig-u5-02 .n{fill:#161920;stroke:#E6E8ED}html.dark #dsfig-u5-02 .n.hi{fill:#1E2748;stroke:#8FA3FF}html.dark #dsfig-u5-02 .n.rb-b{fill:#E6E8ED;stroke:#E6E8ED}html.dark #dsfig-u5-02 .n.rb-r{fill:#FF7E71;stroke:#FF7E71}html.dark #dsfig-u5-02 .t{fill:#E6E8ED}html.dark #dsfig-u5-02 .t.inv{fill:#0F1115}html.dark #dsfig-u5-02 .kd{stroke:#E6E8ED}html.dark #dsfig-u5-02 .dot{fill:#E6E8ED}html.dark #dsfig-u5-02 .ann{fill:#8FA3FF}html.dark #dsfig-u5-02 .lbl{fill:#858D9C}html.dark #dsfig-u5-02 .ptr{fill:#8FA3FF}html.dark #dsfig-u5-02 .ah{fill:#B1B7C3}html.dark #dsfig-u5-02 .ah.hi{fill:#8FA3FF}html.dark #dsfig-u5-02 .wl rect{fill:#161920;stroke:#2A2E37}html.dark #dsfig-u5-02 .wl.hi rect{fill:#8FA3FF;stroke:#8FA3FF}html.dark #dsfig-u5-02 .wl.hi .t{fill:#0F1115}</style><defs><marker id="ah24" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah" d="M0,1 L9,5 L0,9 z"/></marker><marker id="ahh24" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah hi" d="M0,1 L9,5 L0,9 z"/></marker></defs><path class="e" d="M59,40 L191,40" marker-end="url(#ah24)"/><path class="e" d="M220.5,57 L288.6,193.2" marker-end="url(#ah24)"/><path class="e" d="M279,212 L147,212" marker-end="url(#ah24)"/><path class="e" d="M117.5,195 L49.4,58.8" marker-end="url(#ah24)"/><g class="wl"><rect x="95.3" y="31" width="61.5" height="18" rx="9"/><text class="t" x="126" y="40" dy=".35em" text-anchor="middle">T1const</text></g><g class="wl"><rect x="217.1" y="117" width="75.9" height="18" rx="9"/><text class="t" x="255" y="126" dy=".35em" text-anchor="middle">adiabatic</text></g><g class="wl"><rect x="181.3" y="203" width="61.5" height="18" rx="9"/><text class="t" x="212" y="212" dy=".35em" text-anchor="middle">T2const</text></g><g class="wl"><rect x="45.1" y="117" width="75.9" height="18" rx="9"/><text class="t" x="83" y="126" dy=".35em" text-anchor="middle">adiabatic</text></g><circle class="n" cx="40" cy="40" r="18"/><text class="t" x="40" y="40" dy=".35em" text-anchor="middle">A1</text><circle class="n" cx="212" cy="40" r="18"/><text class="t" x="212" y="40" dy=".35em" text-anchor="middle">A2</text><circle class="n" cx="298" cy="212" r="18"/><text class="t" x="298" y="212" dy=".35em" text-anchor="middle">A3</text><circle class="n" cx="126" cy="212" r="18"/><text class="t" x="126" y="212" dy=".35em" text-anchor="middle">A4</text></svg><figcaption style="font-size:.82em;opacity:.72;margin-top:.45rem">Carnot cycle (P on the vertical axis, V across): 1-2 isothermal expansion, 2-3 adiabatic expansion, 3-4 isothermal compression, 4-1 adiabatic compression. In T-s it is a rectangle.</figcaption></figure> <figure class="ds-fig" style="margin:1.4rem 0;overflow-x:auto"><svg xmlns="http://www.w3.org/2000/svg" id="dsfig-u5-03" viewBox="0 0 252 338" width="252" height="338" role="img" aria-label="Otto cycle: 1-2 isentropic compression, 2-3 constant-volume heat addition, 3-4 isentropic expansion, 4-1 constant-volume heat rejection (draw T-s with two curved isochores)"><style>#dsfig-u5-03 .e{stroke:#454C5A;stroke-width:1.4;fill:none}#dsfig-u5-03 .e.hi{stroke:#2340B8;stroke-width:2.6}#dsfig-u5-03 .n{fill:#FFFFFF;stroke:#16181D;stroke-width:1.4}#dsfig-u5-03 .n.hi{fill:#E3E9FC;stroke:#2340B8;stroke-width:2.2}#dsfig-u5-03 .n.rb-b{fill:#16181D;stroke:#16181D}#dsfig-u5-03 .n.rb-r{fill:#BD3227;stroke:#BD3227}#dsfig-u5-03 text{font-family:"JetBrains Mono",ui-monospace,Menlo,Consolas,monospace;font-size:13px}#dsfig-u5-03 .t{fill:#16181D;font-weight:500}#dsfig-u5-03 .t.inv{fill:#FFFFFF;font-weight:700}#dsfig-u5-03 .kd{stroke:#16181D;stroke-width:1.2}#dsfig-u5-03 .dot{fill:#16181D}#dsfig-u5-03 .ann{fill:#2340B8;font-size:11px;font-weight:700}#dsfig-u5-03 .lbl{fill:#6F7787;font-family:system-ui,-apple-system,sans-serif;font-size:12px;font-weight:700}#dsfig-u5-03 .ptr{fill:#2340B8;font-size:12px;font-weight:700}#dsfig-u5-03 .ah{fill:#454C5A}#dsfig-u5-03 .ah.hi{fill:#2340B8}#dsfig-u5-03 .wl rect{fill:#FFFFFF;stroke:#DCE0E7}#dsfig-u5-03 .wl .t{font-size:12px;font-weight:700}#dsfig-u5-03 .wl.hi rect{fill:#2340B8;stroke:#2340B8}#dsfig-u5-03 .wl.hi .t{fill:#FFFFFF}html.dark #dsfig-u5-03 .e{stroke:#B1B7C3}html.dark #dsfig-u5-03 .e.hi{stroke:#8FA3FF}html.dark #dsfig-u5-03 .n{fill:#161920;stroke:#E6E8ED}html.dark #dsfig-u5-03 .n.hi{fill:#1E2748;stroke:#8FA3FF}html.dark #dsfig-u5-03 .n.rb-b{fill:#E6E8ED;stroke:#E6E8ED}html.dark #dsfig-u5-03 .n.rb-r{fill:#FF7E71;stroke:#FF7E71}html.dark #dsfig-u5-03 .t{fill:#E6E8ED}html.dark #dsfig-u5-03 .t.inv{fill:#0F1115}html.dark #dsfig-u5-03 .kd{stroke:#E6E8ED}html.dark #dsfig-u5-03 .dot{fill:#E6E8ED}html.dark #dsfig-u5-03 .ann{fill:#8FA3FF}html.dark #dsfig-u5-03 .lbl{fill:#858D9C}html.dark #dsfig-u5-03 .ptr{fill:#8FA3FF}html.dark #dsfig-u5-03 .ah{fill:#B1B7C3}html.dark #dsfig-u5-03 .ah.hi{fill:#8FA3FF}html.dark #dsfig-u5-03 .wl rect{fill:#161920;stroke:#2A2E37}html.dark #dsfig-u5-03 .wl.hi rect{fill:#8FA3FF;stroke:#8FA3FF}html.dark #dsfig-u5-03 .wl.hi .t{fill:#0F1115}</style><defs><marker id="ah25" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah" d="M0,1 L9,5 L0,9 z"/></marker><marker id="ahh25" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah hi" d="M0,1 L9,5 L0,9 z"/></marker></defs><path class="e" d="M198.6,284.6 L54.8,140.8" marker-end="url(#ah25)"/><path class="e" d="M40,107 L40,61" marker-end="url(#ah25)"/><path class="e" d="M53.4,53.4 L197.2,197.2" marker-end="url(#ah25)"/><path class="e" d="M212,231 L212,277" marker-end="url(#ah25)"/><g class="wl"><rect x="105.6" y="203" width="40.8" height="18" rx="9"/><text class="t" x="126" y="212" dy=".35em" text-anchor="middle">isen</text></g><g class="wl"><rect x="9.3" y="74" width="61.5" height="18" rx="9"/><text class="t" x="40" y="83" dy=".35em" text-anchor="middle">v-const</text></g><g class="wl"><rect x="105.6" y="117" width="40.8" height="18" rx="9"/><text class="t" x="126" y="126" dy=".35em" text-anchor="middle">isen</text></g><g class="wl"><rect x="181.3" y="246" width="61.5" height="18" rx="9"/><text class="t" x="212" y="255" dy=".35em" text-anchor="middle">v-const</text></g><circle class="n" cx="212" cy="298" r="18"/><text class="t" x="212" y="298" dy=".35em" text-anchor="middle">O1</text><circle class="n" cx="40" cy="126" r="18"/><text class="t" x="40" y="126" dy=".35em" text-anchor="middle">O2</text><circle class="n" cx="40" cy="40" r="18"/><text class="t" x="40" y="40" dy=".35em" text-anchor="middle">O3</text><circle class="n" cx="212" cy="212" r="18"/><text class="t" x="212" y="212" dy=".35em" text-anchor="middle">O4</text></svg><figcaption style="font-size:.82em;opacity:.72;margin-top:.45rem">Otto cycle: 1-2 isentropic compression, 2-3 constant-volume heat addition, 3-4 isentropic expansion, 4-1 constant-volume heat rejection (draw T-s with two curved isochores)</figcaption></figure>

Carnot. Heat added $Q_1 = mRT_1\ln(V_2/V_1)$ (1-2), heat rejected $Q_2 = mRT_2\ln(V_3/V_4)$ (3-4). Adiabatic processes 2-3 and 4-1 give $V_2/V_1 = V_3/V_4$, so the logs cancel:

$$\eta = \frac{Q_1 - Q_2}{Q_1} = 1 - \frac{T_2}{T_1}$$

Otto (constant volume). $Q_{in} = mc_v(T_3 - T_2)$, $Q_{out} = mc_v(T_4 - T_1)$. With $r = V_1/V_2$: $T_2/T_1 = T_3/T_4 = r^{\gamma-1}$, so $T_4 - T_1 = (T_3 - T_2)/r^{\gamma-1}$.

$$\eta_{Otto} = 1 - \frac{T_4 - T_1}{T_3 - T_2} = 1 - \frac{1}{r^{\gamma-1}}$$

Diesel (constant pressure). 1-2 isentropic compression, 2-3 constant-pressure heat addition, 3-4 isentropic expansion, 4-1 constant-volume rejection. $Q_{in} = mc_p(T_3 - T_2)$, $Q_{out} = mc_v(T_4 - T_1)$. With cut-off ratio $r_c = V_3/V_2$: $T_2 = T_1r^{\gamma-1}$, $T_3 = T_2r_c$, and $T_4 = T_3(r_c/r)^{\gamma-1} = T_1r_c^{\gamma}$. Then $\eta = 1 - \frac{T_4 - T_1}{\gamma(T_3 - T_2)}$ gives

$$\eta_{Diesel} = 1 - \frac{1}{r^{\gamma-1}}\left[\frac{r_c^{\gamma} - 1}{\gamma(r_c - 1)}\right]$$

Dual (Sabathe). 1-2 isentropic compression, 2-3 constant-volume heat addition, 3-4 constant-pressure heat addition, 4-5 isentropic expansion, 5-1 constant-volume heat rejection. With pressure ratio $\alpha = p_3/p_2$ and cut-off $\beta = V_4/V_3$:

$$\eta_{Dual} = 1 - \frac{1}{r^{\gamma-1}}\left[\frac{\alpha\beta^{\gamma} - 1}{(\alpha - 1) + \gamma\alpha(\beta - 1)}\right]$$

Key points.

1. Carnot efficiency depends only on the two temperatures and is the maximum possible between them, but the cycle is impractical.
2. Otto efficiency rises with compression ratio and depends on $\gamma$ only, not on heat added.
3. Diesel efficiency is below Otto at the same $r$, because $\left[\frac{r_c^\gamma-1}{\gamma(r_c-1)}\right] > 1$; it rises as cut-off falls.
4. At the same compression ratio: $\eta_{Otto} > \eta_{Dual} > \eta_{Diesel}$; Diesel runs at higher $r$, so it wins in practice.
5. Dual reduces to Otto when $\beta = 1$ and to Diesel when $\alpha = 1$.

Example. Otto, $r = 8$, $\gamma = 1.4$: $\eta = 1 - 8^{-0.4} = 0.565$. Answer: 56.5%.

Answer frame. Open with the cycle's four processes; draw P-V and T-S with numbered points; write $Q_{in}$ and $Q_{out}$, then substitute the temperature ratios; close with the boxed efficiency. For Dual, list the five processes in order and add its efficiency.

Pitfall: Diesel adds heat at constant pressure using $c_p$ but rejects using $c_v$; using one specific heat for both loses the $\gamma$ in the formula.

Asked: [7 marks] (Jun 2022) Derive an expression for efficiency of Carnot cycle with neat sketches of PV and TS diagrams. Asked: [7 marks] (Nov 2022) Derive an expression for efficiency of Otto cycle with neat sketches of PV and TS diagrams. Asked: [7 marks] (Dec 2024) With a neat sketch, explain the working of Diesel and derive the expression for thermal efficiency. Asked: [7 marks] (Dec 2024) Write about the various processes involved in Dual cycle with P-V and T-S diagrams.

Working of two stroke and four stroke petrol and diesel engines

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">High weight</span>

Definition. An internal combustion engine burns fuel inside the cylinder. A four-stroke engine completes one cycle in four piston strokes (two crank revolutions); a two-stroke engine completes it in two strokes (one revolution). <mark>Petrol (SI) engines ignite a fuel-air mixture with a spark; diesel (CI) engines ignite injected fuel by the heat of highly compressed air.</mark>

Diagram. Draw the cylinder with piston, connecting rod, crankshaft, inlet valve, exhaust valve, and spark plug (petrol) or fuel injector (diesel); for two-stroke, draw the crankcase, inlet, transfer and exhaust ports and the deflector on the piston crown.

Key points.

1. The four-stroke petrol engine has cylinder, piston, spark plug, inlet valve, exhaust valve, connecting rod and crankshaft; the diesel engine replaces the spark plug with a fuel injector.
2. Suction: the piston moves down and the inlet valve is open; petrol draws mixture from the carburettor, diesel draws only air.
3. Compression: both valves are closed and the piston rises; diesel compression is much higher, so the air exceeds fuel auto-ignition temperature.
4. Power: petrol is ignited by a spark near TDC; diesel fuel injected near TDC ignites itself; expanding gases push the piston down, the only work-producing stroke.
5. Exhaust: the exhaust valve opens and the rising piston expels burnt gases; the cycle then repeats every two revolutions.
6. Two-stroke engine has no valves; the piston uncovers ports, with the crankcase acting as a pump.
7. Upward stroke: the piston compresses the charge above it (air for diesel, with fuel injected near TDC) while its rise draws fresh charge into the crankcase through the inlet port.
8. Downward stroke: combustion pushes the piston down; the exhaust port opens first, then the transfer port admits the crankcase charge to scavenge the cylinder, and the deflector on the piston crown directs it upward so fresh charge does not leave through the exhaust.

Answer frame. Open with the engine type and cycle length; draw the labelled sketch (or four small sketches, one per stroke, showing valve state and piston direction); develop suction, compression, power, exhaust, or upward then downward stroke for two-stroke; close with the number of power strokes per revolution and the ignition method.

Asked: [8 marks] (Nov 2022, Jun 2023, Dec 2024) Explain the working (and structure) of four stroke diesel engine with neat sketch. Asked: [8 marks] (Dec 2023) Explain the structure and working of four-stroke petrol engine with a neat sketch. Asked: [8 marks] (Jun 2025) Explain the structure and working of two stroke diesel engine with a neat sketch. Asked: [7 marks] (Jun 2022) Explain the working of two stroke petrol engine with neat sketch.

Working principle of compressor

<span style="display:inline-block;padding:.16em .6em;border:1.5px solid currentColor;border-radius:999px;font-size:.68em;font-weight:700;letter-spacing:.06em;text-transform:uppercase;opacity:.75">Medium weight</span>

Definition. A compressor is a machine that raises the pressure of a gas by supplying mechanical work; in a centrifugal compressor the pressure is raised by imparting kinetic energy to the air and then diffusing it. <mark>A centrifugal compressor converts the kinetic energy given by the rotating impeller into pressure in the diffuser and volute.</mark>

Diagram. <figure class="ds-fig" style="margin:1.4rem 0;overflow-x:auto"><svg xmlns="http://www.w3.org/2000/svg" id="dsfig-u5-04" viewBox="0 0 596 80" width="596" height="80" role="img" aria-label="Centrifugal compressor: In inlet eye, Imp impeller with backward-curved vanes, Dif diffuser vanes, Vol volute casing, Out delivery"><style>#dsfig-u5-04 .e{stroke:#454C5A;stroke-width:1.4;fill:none}#dsfig-u5-04 .e.hi{stroke:#2340B8;stroke-width:2.6}#dsfig-u5-04 .n{fill:#FFFFFF;stroke:#16181D;stroke-width:1.4}#dsfig-u5-04 .n.hi{fill:#E3E9FC;stroke:#2340B8;stroke-width:2.2}#dsfig-u5-04 .n.rb-b{fill:#16181D;stroke:#16181D}#dsfig-u5-04 .n.rb-r{fill:#BD3227;stroke:#BD3227}#dsfig-u5-04 text{font-family:"JetBrains Mono",ui-monospace,Menlo,Consolas,monospace;font-size:13px}#dsfig-u5-04 .t{fill:#16181D;font-weight:500}#dsfig-u5-04 .t.inv{fill:#FFFFFF;font-weight:700}#dsfig-u5-04 .kd{stroke:#16181D;stroke-width:1.2}#dsfig-u5-04 .dot{fill:#16181D}#dsfig-u5-04 .ann{fill:#2340B8;font-size:11px;font-weight:700}#dsfig-u5-04 .lbl{fill:#6F7787;font-family:system-ui,-apple-system,sans-serif;font-size:12px;font-weight:700}#dsfig-u5-04 .ptr{fill:#2340B8;font-size:12px;font-weight:700}#dsfig-u5-04 .ah{fill:#454C5A}#dsfig-u5-04 .ah.hi{fill:#2340B8}#dsfig-u5-04 .wl rect{fill:#FFFFFF;stroke:#DCE0E7}#dsfig-u5-04 .wl .t{font-size:12px;font-weight:700}#dsfig-u5-04 .wl.hi rect{fill:#2340B8;stroke:#2340B8}#dsfig-u5-04 .wl.hi .t{fill:#FFFFFF}html.dark #dsfig-u5-04 .e{stroke:#B1B7C3}html.dark #dsfig-u5-04 .e.hi{stroke:#8FA3FF}html.dark #dsfig-u5-04 .n{fill:#161920;stroke:#E6E8ED}html.dark #dsfig-u5-04 .n.hi{fill:#1E2748;stroke:#8FA3FF}html.dark #dsfig-u5-04 .n.rb-b{fill:#E6E8ED;stroke:#E6E8ED}html.dark #dsfig-u5-04 .n.rb-r{fill:#FF7E71;stroke:#FF7E71}html.dark #dsfig-u5-04 .t{fill:#E6E8ED}html.dark #dsfig-u5-04 .t.inv{fill:#0F1115}html.dark #dsfig-u5-04 .kd{stroke:#E6E8ED}html.dark #dsfig-u5-04 .dot{fill:#E6E8ED}html.dark #dsfig-u5-04 .ann{fill:#8FA3FF}html.dark #dsfig-u5-04 .lbl{fill:#858D9C}html.dark #dsfig-u5-04 .ptr{fill:#8FA3FF}html.dark #dsfig-u5-04 .ah{fill:#B1B7C3}html.dark #dsfig-u5-04 .ah.hi{fill:#8FA3FF}html.dark #dsfig-u5-04 .wl rect{fill:#161920;stroke:#2A2E37}html.dark #dsfig-u5-04 .wl.hi rect{fill:#8FA3FF;stroke:#8FA3FF}html.dark #dsfig-u5-04 .wl.hi .t{fill:#0F1115}</style><defs><marker id="ah26" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah" d="M0,1 L9,5 L0,9 z"/></marker><marker id="ahh26" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto-start-reverse"><path class="ah hi" d="M0,1 L9,5 L0,9 z"/></marker></defs><path class="e" d="M59,40 L148,40" marker-end="url(#ah26)"/><path class="e" d="M188,40 L277,40" marker-end="url(#ah26)"/><path class="e" d="M317,40 L406,40" marker-end="url(#ah26)"/><path class="e" d="M446,40 L535,40" marker-end="url(#ah26)"/><g class="wl"><rect x="81" y="31" width="47.1" height="18" rx="9"/><text class="t" x="104.5" y="40" dy=".35em" text-anchor="middle">axial</text></g><g class="wl"><rect x="206.4" y="31" width="54.3" height="18" rx="9"/><text class="t" x="233.5" y="40" dy=".35em" text-anchor="middle">radial</text></g><circle class="n" cx="40" cy="40" r="18"/><text class="t" x="40" y="40" dy=".35em" text-anchor="middle">In</text><circle class="n" cx="169" cy="40" r="18"/><text class="t" x="169" y="40" dy=".35em" text-anchor="middle">Imp</text><circle class="n" cx="298" cy="40" r="18"/><text class="t" x="298" y="40" dy=".35em" text-anchor="middle">Dif</text><circle class="n" cx="427" cy="40" r="18"/><text class="t" x="427" y="40" dy=".35em" text-anchor="middle">Vol</text><circle class="n" cx="556" cy="40" r="18"/><text class="t" x="556" y="40" dy=".35em" text-anchor="middle">Out</text></svg><figcaption style="font-size:.82em;opacity:.72;margin-top:.45rem">Centrifugal compressor: In inlet eye, Imp impeller with backward-curved vanes, Dif diffuser vanes, Vol volute casing, Out delivery</figcaption></figure>

Key points.

1. Air enters axially through the eye of the impeller and is turned radially outward by the vanes.
2. The rotating impeller raises both the kinetic energy and the static pressure of the air by centrifugal action.
3. The diffuser, a set of stationary divergent passages, slows the air and converts kinetic energy into static pressure.
4. The volute casing collects the air from the diffuser and delivers it, further converting velocity to pressure.
5. Surging is unsteady, pulsating flow with flow reversal at low mass flow and high pressure ratio, causing severe vibration.
6. Choking is the maximum possible mass flow, reached when the Mach number becomes 1 at the throat; more flow is impossible.
7. Stalling is flow separation from the blades due to excessive angle of attack at low flow, causing a loss of pressure rise; on the characteristic curve, surge and stall lie at low flow and choke at high flow.

Answer frame. Open with the definition; draw the eye, impeller, diffuser and volute; explain entry, impeller action, then diffuser and volute; close with the pressure rise. For the short note, define surging, choking and stalling with one cause each and sketch the characteristic curve marking the three regions.

Asked: [6 marks] (Dec 2023) Write short notes on surging, choking and stalling. Asked: [6 marks] (Jun 2023) Explain the working principle of the centrifugal compressor.

Last-minute revision

• Carnot efficiency: $\eta = 1 - T_2/T_1$, the maximum between two temperatures.
• Otto: $\eta = 1 - 1/r^{\gamma-1}$; $r = 8$, $\gamma = 1.4$ gives 56.5%.
• Diesel: $\eta = 1 - \frac{1}{r^{\gamma-1}}\left[\frac{r_c^\gamma - 1}{\gamma(r_c - 1)}\right]$, with heat added at constant pressure.
• Dual: heat added partly at constant volume and partly at constant pressure; five state points.
• At the same $r$: Otto > Dual > Diesel efficiency.
• Petrol engine: spark ignition, $r$ about 6-10; diesel engine: compression ignition, $r$ about 15-20.
• Four-stroke: one power stroke per two revolutions; two-stroke: one per revolution.
• Two-stroke uses ports and a crankcase; the deflector stops fresh charge escaping.
• Steam engine: D-slide valve admits steam alternately to both sides, slider-crank gives rotary motion.
• Centrifugal compressor: impeller adds velocity, diffuser and volute convert it to pressure.
• Surging is flow reversal, choking is Mach 1 at the throat, stalling is blade flow separation.

Memory hooks

• Suction, Compression, Power, Exhaust: "SCPE", the four-stroke order.
• Otto = Opposite of Diesel in heat addition: Otto constant Volume, Diesel constant Pressure.
• Dual = Otto's volume step then Diesel's pressure step, two additions.
• Surge = Slow flow, Choke = Chokes at Mach 1, Stall = blade Separation.
• Two-stroke: "Up compresses and sucks, down burns and scavenges."

Coverage checklist

• Working principle of steam Engine: steam engine construction and working (Jun 2025).
• Carnot, Otto, Diesel and Dual cycles P-V & T-S diagrams and its efficiency: Carnot (Jun 2022), Otto (Nov 2022), Diesel (Dec 2024), Dual (Dec 2024).
• working of Two stroke & Four stroke Petrol & Diesel engines: four-stroke diesel (Nov 2022, Jun 2023, Dec 2024), four-stroke petrol (Dec 2023), two-stroke diesel (Jun 2025), two-stroke petrol (Jun 2022).
• Working principle of compressor: surging, choking, stalling (Dec 2023), centrifugal compressor (Jun 2023).