Bangladesh Inland Water Transport Authority (BIWTA)- 2025

Solution: (a) Thermal resistance: The opposition offered by a body to the flow of heat, defined as the ratio of temperature difference to heat flow rate (R = ΔT/Q). For conduction through a plane wall R = L/kA, for convection R = 1/hA (unit: K/W). Resistances in series and parallel are combined like electrical resistances.

(b) Thermal conductivity (k): The property of a material that indicates its ability to conduct heat; it is the heat flow per unit area per unit temperature gradient (Fourier’s law, q = −k dT/dx), unit W/m·K. Metals (copper ≈ 385, aluminium ≈ 205 W/m·K) are good conductors; insulators (glass wool, wood) have low k.

(c) Knocking: Abnormal combustion producing a sharp metallic noise. In SI engines it is caused by auto-ignition of the end gas before the flame front reaches it; in CI engines by a long ignition delay that lets too much fuel burn at once. It causes vibration, overheating, loss of power and damage.

(d) Safety valve: A boiler mounting that automatically releases steam when the pressure exceeds the safe working limit and closes when the pressure returns to normal, thus preventing explosion. Types: dead weight, lever, spring loaded and high steam–low water safety valves.

(e) Risk in project management: An uncertain event or condition which, if it occurs, affects project objectives (cost, time, quality, safety). Types: technical, financial, schedule, operational and external risks. Risk management involves identification, analysis (probability and impact), response planning (avoid, transfer, mitigate, accept) and monitoring and control.

Solution: Heat treatment is a controlled sequence of heating, holding (soaking) and cooling of a metal in the solid state to obtain the desired structure and properties without changing its shape.

• Annealing: heating above the critical temperature, soaking and slow cooling in the furnace — softens the metal, improves ductility and machinability and relieves internal stress.
• Normalising: heating about 40–50°C above the upper critical temperature and cooling in still air — refines the grain size and gives uniform structure with higher strength than annealing.
• Hardening: heating to the austenitic range and quenching in water or oil — forms martensite and gives high hardness and wear resistance.
• Tempering: reheating hardened steel below the lower critical temperature and cooling — reduces brittleness and internal stress and improves toughness.
• Case hardening (carburising, nitriding, cyaniding, induction and flame hardening): hardens only the surface while the core remains tough.

Solution: CAD (Computer Aided Design) uses computer software to create, modify, analyse and optimise 2D drawings and 3D models. Benefits: accuracy, quick modification, better visualisation, standard part libraries, analysis (FEA) and faster design.

CAM (Computer Aided Manufacturing) uses computers to plan and control manufacturing — generation of CNC tool paths, process planning and robot control. Benefits: automation, higher productivity, consistent quality, less scrap and reduced lead time.

Integrated CAD/CAM transfers the design directly to the machine, shortening the design-to-production cycle; it is widely used in the automobile, aerospace, shipbuilding, machine tool and consumer product industries.

Solution: Supercharging is the process of supplying air (or air–fuel mixture) to the engine at a pressure, and hence density, higher than atmospheric, by means of a compressor (supercharger) driven by the engine or by an exhaust gas turbine (turbocharger). More mass of air is inducted per cycle, so more fuel can be burnt and the power output increases.

Advantages: higher power output (about 30–50%) for the same engine size; compensation for power loss at high altitudes; better scavenging and combustion; reduced ignition delay and knocking tendency in CI engines; better power-to-weight ratio.

Disadvantages: higher thermal and mechanical loads on the engine; increased tendency to detonation in SI engines; extra cost, weight and complexity; power consumed to drive a mechanical supercharger.

Solution: Specific humidity (humidity ratio): mass of water vapour per kg of dry air, ω = 0.622 p_v/(p − p_v). Relative humidity: the ratio of the actual partial pressure (or mass) of water vapour in air to that of saturated air at the same temperature, φ = p_v/p_s × 100%.

Solution: In a positive displacement pump a definite volume of liquid is trapped in a chamber and is physically pushed (displaced) to the delivery side by a moving member — piston, plunger, gear, screw or vane. The discharge per stroke or revolution is fixed, so the flow depends almost only on speed and very little on the delivery pressure; such pumps develop high pressure, are self-priming and need a relief valve on the delivery side. Examples: reciprocating (piston/plunger) pump, gear pump, screw pump, lobe pump, vane pump, diaphragm pump.

Solution: A governor automatically regulates the fuel supply to keep the mean engine speed nearly constant under varying load. In a centrifugal governor, flyballs rotate with the engine. When the load decreases the speed rises, the balls fly outward and the sleeve rises, which through a linkage reduces the fuel supply (throttle). When the load increases the speed falls, the balls move inward, the sleeve lowers and the fuel supply is increased. Thus the engine speed is restored within a small range. (A flywheel controls cyclic fluctuations within a cycle; a governor controls mean speed over many cycles.)

Solution:

Solution: Stress σ = P/A (N/m²); strain ε = δL/L (dimensionless); modulus of elasticity E = σ/ε within the limit of proportionality — it represents the stiffness of the material (steel ≈ 200 GPa).

Solution: $$h_f=f\frac{L}{D}\frac{V^2}{2g}$$

where f is the Darcy friction factor, L the pipe length, D the diameter and V the mean velocity. The velocity is found from V = Q/A, f is taken as 64/Re for laminar flow or from the Moody chart (or Colebrook equation) for turbulent flow using Re and relative roughness ε/D, and h_f is then calculated. The pressure loss is Δp = ρgh_f and the pumping power required to overcome it is ρgQh_f.

Solution: $$Re=\frac{\rho VD}{\mu }=\frac{VD}{\nu }$$

Re < 2000: laminar (fluid particles move in parallel layers, parabolic velocity profile); 2000 < Re < 4000: transition; Re > 4000: turbulent (random eddying motion, flatter velocity profile).

Solution: $$N=\frac{1000V}{\pi D}=\frac{1000\times 60}{\pi \times 120}=159\text{rpm}$$

Solution: $$\eta =1-\frac{1}{r^{\gamma -1}}=1-\frac{1}{8^{0.4}}=0.565=56.5\%$$

Solution: $$Q=C_{d}a\sqrt{2gH}=0.62\times 0.01\times \sqrt{2\times 9.81\times 5}=0.0614{\text{m}}^3/\text{s}$$

Solution: $$Q_L=\frac{10,000(4.187\times 20+335)}{24\times 3600}=\frac{4.187\times 10^6}{86,400}=48.47\text{kW},W=\frac{48.47}{3.5}=13.85\text{kW}$$

∴ Compressor power = 13.85 kW (Answer)

Solution: $$P=\eta \rho gQH=0.85\times 1000\times 9.81\times 0.085\times 50=35.44\text{kW}$$

$$N_s=\frac{N\sqrt{P}}{H^{5/4}}=\frac{600\times \sqrt{35.44}}{50^{1.25}}=\frac{600\times 5.953}{132.96}=26.9$$

∴ Specific speed ≈ 27 (Answer)

Solution: x = 6mn/(m + n), so x/3m = 2n/(m + n) and x/3n = 2m/(m + n). By componendo-dividendo,

$$\frac{x+3m}{x-3m}=\frac{2n+m+n}{2n-m-n}=\frac{m+3n}{n-m},\frac{x+3n}{x-3n}=\frac{3m+n}{m-n}$$

$$\text{Sum}=\frac{(m+3n)-(3m+n)}{n-m}=\frac{2(n-m)}{n-m}=2\text{(Proved)}$$

Solution: $$\text{(a)}{\int }_0^1\left(x+x^3\right)dx={\left[\frac{x^2}{2}+\frac{x^4}{4}\right]}_0^1=\frac{3}{4}$$

2. Put x² = z, so x dx = dz/2:

$$\int x^3{e}^{x^2}dx=\frac{1}{2}\int z{e}^{z}dz=\frac{1}{2}(z-1)e^z+C=\frac{1}{2}{e}^{x^2}\left(x^2-1\right)+C$$

Solution: When two articles are sold at the same price with equal gain and loss of x%, there is always a loss of x²/100 % = 100/100 = 1% loss. (Check: cost prices in ratio 9 : 11; selling price 9.9 each; total cost 20, total sale 19.8; loss 1%.)

Solution: α + β = −b, αβ = c.

$$\text{Sum}=(\alpha +\beta )+\frac{\alpha +\beta }{\alpha \beta }=-\frac{b(c+1)}{c},\text{Product}=\alpha \beta +2+\frac{1}{\alpha \beta }=\frac{(c+1{)}^2}{c}$$

∴ Required equation: cx² + b(c + 1)x + (c + 1)² = 0 (Answer)

উত্তর: প্রমথ চৌধুরী (‘সবুজপত্র’ পত্রিকার মাধ্যমে)।

উত্তর: তারাশঙ্কর বন্দ্যোপাধ্যায়।

উত্তর: ক্রিয়াপদের মূল অংশকে ধাতু বলে।

উত্তর: তিন প্রকার — বাংলা (খাঁটি বাংলা), তৎসম (সংস্কৃত) ও বিদেশি উপসর্গ।

উত্তর: বিভক্তিযুক্ত শব্দ ও ধাতুকে পদ বলে।

উত্তর: চাগতাই তুর্কি ভাষায়।

উত্তর: ত্রিপিটক (বৌদ্ধ ধর্মগ্রন্থ)।

উত্তর: আলালের ঘরের দুলাল (প্যারীচাঁদ মিত্র)।

উত্তর: গীতিকাব্য (কালিদাস)।

উত্তর: শিশুসাহিত্যিক (ননসেন্স ছড়া)।

উত্তর: অগ্নিবীণা।

উত্তর: নবীন (অপরিণামদর্শী)।

উত্তর: ফরাসি।

উত্তর: বড় রকমের চুরি।

উত্তর: মধ্যপদলোপী কর্মধারয় (মৌ-সংগ্রহকারী মাছি)।

উত্তর: মেঘনাদবধ কাব্য (মাইকেল মধুসূদন দত্ত)।

উত্তর: সৈয়দ মুজতবা আলী।

Answer: Enterprise.

Answer: Active (awaken).

Answer: Hostility (inhospitality).

Answer: Something very easy.

Answer: Release.

Answer: Sierra Leone.

Answer: Arundhati Roy.

Answer: Tim Berners-Lee.

Answer: Mercury.

Answer: Diamond.

Answer: 32°F.

Answer: Argentina (2022); Brazil (5 titles).

Answer: Ankara.

Answer: All of them.

Answer: Historic paddle steamer of Bangladesh.

Answer: 1 bar ≈ 14.5 psi.

Answer: .BAK

Answer: 50 Hz.

Answer: 21 June.