Maharashtra HSC Workshop Science & Calculation cheat sheet

Machine guards must be in place before start-up; a guard removed for maintenance is refitted and checked before the machine is re-energised.

Lockout/tagout rule: isolate the energy source, lock it, tag it, and verify zero energy by attempting a start before working on the machine.

Eye protection is mandatory for grinding, chipping, turning and any operation producing flying chips; a face shield is added over goggles for grinding.

Fire classes: A solid combustibles (water/foam), B flammable liquids (foam, CO2, dry powder), C electrical (CO2, dry powder - never water), D metals (dry sand, special powder).

Safe lifting limit guide: keep the load close to the body, back straight, lift with legs; two-person lift above roughly 25 kg for a single worker.

Housekeeping rule: oily rags go into a closed metal bin, chips are cleared with a brush or hook - never by hand or with compressed air near skin.

No loose clothing, ties, rings or open sleeves near rotating spindles; long hair is tied back and confined under a cap.

Emergency stop buttons are red on yellow and must be tested at the start of each shift; report any defective stop immediately.

Vernier least count = 1 main-scale division − 1 vernier division = 1 mm − 0.98 mm = 0.02 mm for a 50-division vernier.

Vernier reading = main scale value at the zero of the vernier + (coinciding vernier division × least count).

Micrometer least count = pitch ÷ number of thimble divisions = 0.5 mm ÷ 50 = 0.01 mm.

Micrometer reading = barrel (sleeve) reading + (thimble division × 0.01 mm); add the 0.5 mm line if the thimble has passed it.

Zero error: if the vernier zero lies to the right of the main-scale zero, subtract the error; to the left, add it.

A dial gauge (dial test indicator) reads to 0.01 mm or 0.001 mm and is used for runout and concentricity checks, not for direct length.

Try square checks squareness to 90°; a surface plate plus dial gauge checks flatness and parallelism.

Steel rule accuracy is about ±0.5 mm; use it for marking out, not for precision acceptance of a machined dimension.

Plain carbon steel: low carbon (up to ~0.3% C) is ductile and weldable; medium carbon (~0.3–0.6% C) is stronger and heat-treatable; high carbon (>0.6% C) is hard and wear-resistant.

Cast iron has high compressive strength and damping but low tensile strength and is brittle; it is specified by grade number giving tensile strength in MPa.

Ductility is measured by percentage elongation in a tensile test; brittleness means little elongation before fracture.

Hardness scales: Brinell (HB) uses a hardened ball for softer metals; Rockwell C (HRC) uses a diamond cone for hardened steel; Vickers (HV) uses a diamond pyramid.

Toughness is energy absorbed before fracture (Izod/Charpy impact test); a tough material resists shock, a hard one resists scratching.

Aluminium is about one-third the density of steel (~2.7 vs ~7.85 g/cm³) with good conductivity and corrosion resistance but low melting point.

Annealing softens and relieves stress; hardening (quench) increases hardness but adds brittleness; tempering after hardening restores toughness.

Mild steel density ≈ 7850 kg/m³, aluminium ≈ 2700 kg/m³, copper ≈ 8900 kg/m³, brass ≈ 8500 kg/m³ - use these for mass calculations.

Density ρ = m / V, so mass m = ρ × V; keep units consistent (kg, m³, kg/m³) or convert (1 g/cm³ = 1000 kg/m³).

Cylinder volume V = πd²L/4 = πr²L; use this for round bar mass and for turned-volume removal.

Rectangular prism volume V = L × b × h; ring volume V = πL(D² − d²)/4 for a hollow tube.

Mass of a round bar: m = (π/4) d² L ρ, with d and L in metres and ρ in kg/m³ to get kilograms.

Area of a circle A = πd²/4; circumference C = πd; use π ≈ 3.1416 or 22/7 as the question requires.

Triangle area = ½ × base × height; trapezium area = ½(a + b) × h; sector area = (θ/360) × πr².

Volume of a cone = ⅓πr²h; volume of a sphere = (4/3)πr³ - needed for cast or forged blank estimates.

Mass of a steel round bar shortcut: m (kg) ≈ 0.006165 × d²(mm) × L(m) using ρ = 7850 kg/m³.

SI base units: metre (m), kilogram (kg), second (s), ampere (A), kelvin (K), mole (mol), candela (cd).

Force is the newton: 1 N = 1 kg·m/s²; 1 kgf = 9.81 N. Pressure is the pascal: 1 Pa = 1 N/m²; 1 bar = 10⁵ Pa = 100 kPa.

1 inch = 25.4 mm exactly; 1 foot = 0.3048 m; 1 mil = 0.001 inch = 0.0254 mm.

1 kgf/mm² = 9.81 N/mm² ≈ 9.81 MPa; tensile strength in kgf/mm² is multiplied by 9.81 to get MPa.

Power: 1 W = 1 J/s; 1 hp (metric) = 735.5 W; 1 hp (imperial) = 745.7 W; 1 kW = 1.341 hp.

Energy: 1 kWh = 3.6 × 10⁶ J = 3.6 MJ; 1 calorie = 4.186 J.

1 litre = 1000 cm³ = 0.001 m³; 1 tonne = 1000 kg; 1 g/cm³ = 1000 kg/m³.

Angle: 1 radian = 180/π ≈ 57.296°; 1° = 60 minutes = 3600 seconds of arc.

Metric to inch conversion: mm ÷ 25.4 = inch; inch × 25.4 = mm; fractional inch is converted via the decimal equivalent (e.g. 1/16 in = 0.0625 in = 1.5875 mm).

Percentage error = |measured − true| / true × 100; tolerance = upper limit − lower limit.

Percentage change = (new − old)/old × 100; a 5% shrinkage on a 200 mm casting gives 200 × 0.95 = 190 mm.

Allowance for shrinkage in casting: pattern size = finished size × (1 + shrinkage fraction).

Proportion by ratio: for a mix a:b:c, the quantity of a = total × a/(a + b + c).

Percentage composition: mass of element = (percentage/100) × total mass; alloying addition = % × charge mass.

Scales and drawings: a 1:5 drawing means drawing length × 5 = actual length; a 5:1 drawing means drawing length ÷ 5 = actual.

Taper/angle conversions: tan(θ/2) = (D − d)/(2L) for a taper half-angle in degrees.

Cutting speed V = πDN/1000 with V in m/min, D in mm, N in rpm; solve for N = 1000V/(πD).

Feed f is in mm/rev for turning and drilling; feed rate in mm/min = f × N.

Turning time T = L/(f × N) minutes, where L is the travel length including approach and overtravel (typically 2–5 mm each).

Drilling time T = (L + 0.3d)/(f × N) minutes, where 0.3d approximates the drill point approach.

Milling table feed = fz × z × N (feed per tooth × number of teeth × rpm); machining time = L/table feed.

Depth of cut in turning = (D − d)/2; material removal rate MRR ≈ V × f × depth of cut.

Cutting speed decreases as work diameter increases for a fixed rpm; large-diameter work needs lower rpm to keep V constant.

Abrasive wheel speed is limited by wheel grade; a wheel marked 35 m/s must not be run faster, so check the spindle rpm against wheel diameter.

Taper ratio = (D − d)/L; taper in percent = (D − d)/L × 100.

Half-angle: tan(θ/2) = (D − d)/(2L); set the compound slide to θ/2 for a taper turning job.

Taper per side (offset of tailstock) = L_total × (D − d)/(2 × L_taper).

Metric thread: pitch = 1/threads per mm; minor diameter ≈ d − 1.0825p; tap drill size ≈ d − p.

Unified/imperial thread: pitch = 1/TPI inch; tap drill size ≈ major diameter − 1/TPI (approximately).

Gear module m = d/T (pitch diameter ÷ number of teeth); circular pitch p = πm; addendum = m; dedendum = 1.25m.

Gear ratio = T_driven/T_driver = N_driver/N_driven; for a compound train multiply the individual stage ratios.

Helix angle and lead: lead = πd × tan(helix angle) for a helical gear or worm; lead of a worm = πm × number of starts.

Ohm's law V = IR; power P = VI = I²R = V²/R for DC and resistive AC loads.

Three-phase power P = √3 × V_L × I_L × cos φ; single-phase P = V × I × cos φ.

Motor input power = output power / efficiency; line current I = P_out /(√3 × V × cos φ × η).

Synchronous speed of an induction motor N_s = 120f/P (f in Hz, P = number of poles); slip = (N_s − N)/N_s.

Motor full-load current rule of thumb: about 1.3–1.5 A per kW at 415 V three-phase with cos φ ≈ 0.85 and η ≈ 0.88.

Star-delta starting reduces phase voltage by 1/√3, so starting torque falls to one-third of the direct-on-line value.

Fuse and cable sizing: continuous current must not exceed the rated device current; derate for ambient temperature and grouping.

Energy in kWh = power (kW) × time (h); a 7.5 kW motor running 8 h consumes 60 kWh.

Material cost = mass required × rate per kg; add a scrap/wastage allowance (often 5–10%) to the finished mass.

Total cost = material + labour + machine overhead + factory overhead + administrative/selling overhead + profit.

Machining cost = (machine hour rate) × (machining time in hours); machine hour rate includes depreciation, power, maintenance and floor area.

Labour cost = labour rate per hour × hours worked; for a batch, multiply by the number of pieces.

Selling price = total cost × (1 + profit percentage); if profit is on selling price, price = cost/(1 − profit fraction).

Break-even quantity = fixed cost / (selling price per unit − variable cost per unit).

Material requirement for a batch = single-piece mass × batch size × (1 + wastage fraction).

Cost per component falls as batch size rises because fixed setup cost is spread over more pieces: cost/piece = setup/n + variable cost.

First-angle projection: the view from the front is placed above the top view; third-angle places the top view above the front view.

A section view uses hatching at 45° to show cut material; hidden edges become visible solid lines in the section.

Geometric tolerance symbols: ⌀ for diameter, R for radius, ⊥ perpendicularity, ∥ parallelism, ⌖ position, ◎ concentricity.

A dimension marked with a tolerance like 25 ±0.05 means limits 24.95 to 25.05 mm and tolerance 0.10 mm.

Surface roughness Ra is the arithmetic mean deviation in micrometres; a ▽ symbol with a number gives the Ra value.

Scale calculation: actual length = drawing length × scale denominator for a reducing scale; divide for an enlarging scale.

Coordinate/datum dimensioning measures from a single datum; chain dimensioning accumulates tolerance, so datum dimensioning is preferred.

Countersink and chamfer geometry: chamfer length = depth × tan(half-angle); a 90° countersink of depth t gives diameter increase 2t.

Lubricant viscosity is specified by ISO VG number (kinematic viscosity in cSt at 40 °C); SAE grades apply to engine oils.

Bearing life L₁₀ = (C/P)³ × 10⁶ revolutions for ball bearings, where C is dynamic capacity and P the equivalent load.

Grease is used where oil retention is difficult and speeds are low; oil is used for high speed and heat removal.

Preventive maintenance schedule is set by running hours or calendar interval, whichever comes first; record vibration and temperature trends.

Energy saving: replacing a 5 kW motor with a 4 kW high-efficiency unit running 2000 h/year saves 2000 kWh per year at full load.

Power consumed by a pump or fan follows the affinity laws: flow ∝ N, head ∝ N², power ∝ N³ - a 10% speed cut saves about 27% power.

Air leak cost: a 1 mm hole at 6 bar leaks roughly 1.2–1.5 L/s, so leak surveys are a direct energy saving.

Overall equipment effectiveness OEE = availability × performance × quality, each expressed as a fraction.