The Open-Top Tank That Holds 30 Litres Too Few
Your unit must fabricate an open-top rectangular water tank, external size 1.2 m × 0.8 m × 0.6 m high, from 2 mm mild steel sheet. The workshop adds 8 per cent to the net developed area for laps, stiffeners, grip and wastage. Sheet is bought in standard 2.5 m × 1.25 m sheets at Rs 70 per kg, and offcut scrap fetches Rs 26 per kg. Density of mild steel is 7,850 kg/m³. The customer requires the tank to hold at least 550 litres, and also asks whether 3 mm sheet should be used because it will be stronger. Delivery is in six days. The unit has one guillotine, one angle grinder and a 200 A arc welding set, no press brake, and the dealer in Bhubaneswar needs two days to supply extra sheet.
1. Calculate the net developed area, the gross area including the 8 per cent allowance, and decide how many standard sheets to order, with reasons.
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Net developed area, using outside dimensions and no top cover:
- Bottom: 1.2 × 0.8 = 0.96 m²
- Two long sides: 1.2 × 0.6 = 0.72 each = 1.44 m²
- Two short sides: 0.8 × 0.6 = 0.48 each = 0.96 m²
- Net = 3.36 m²
Gross = 3.36 × 1.08 = 3.63 m².
One sheet is 2.5 × 1.25 = 3.125 m², which is 0.50 m² short of the gross requirement, so one sheet cannot do the job even before cutting losses. Two sheets give 6.25 m², leaving about 2.62 m².
Decision: order 2 sheets today. The two-day dealer lead time against a six-day delivery leaves no room to order late, and a part-sheet purchase would add a splice in the bottom plate and one more day. The 2.62 m² leftover is not waste: reserve it for the top rim stiffener and the next job, and cost it at scrap value only in the quotation.
2. Calculate the mass of the finished shell and the true usable water capacity, and state what you would tell the customer.
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Mass: 3.36 m² × 0.002 m × 7,850 kg/m³ = 52.8 kg of finished plate, plus roughly 1 to 1.5 kg of weld metal and stiffener.
Purchase economics: bought mass 6.25 × 0.002 × 7,850 = 98.1 kg, costing 98.1 × 70 = Rs 6,869. The 2.62 m² offcut weighs 41.1 kg and at Rs 26/kg returns Rs 1,069, so the true material charge to this job is about Rs 5,800. Quote on that basis, not on the full sheet price.
Capacity: internal sizes about 1.196 × 0.796 × 0.598 m = 0.569 m³, that is 569 litres nominal. But a tank is never filled to the lip. With 50 mm freeboard the usable volume is 1.196 × 0.796 × 0.548 = 0.522 m³, about 522 litres, which fails the 550 litre requirement.
What to tell the customer: nominal 569 L, usable about 522 L at 50 mm freeboard, therefore not compliant as drawn. To guarantee 550 L usable, raise the height by about 60 mm to 0.66 m; that adds 0.24 m² of sheet (about 3.8 kg) and about 57 litres of usable volume. Put the freeboard figure in writing - an unwritten freeboard assumption is how tank disputes start.
3. The customer asks for 3 mm sheet instead of 2 mm. Advise with numbers.
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The pressure is small. Head at the bottom is about 1000 × 9.81 × 0.6 ≈ 5.9 kPa, so the plate is governed by handling stiffness, weld distortion and abuse, not by water pressure.
What 3 mm costs: shell mass 3.36 × 0.003 × 7,850 = 79.1 kg, 50 per cent heavier. Gross area is unchanged at 3.63 m² but purchase mass rises to about 147 kg and material cost to about Rs 10,300 before the scrap credit. Two people then struggle to turn and fit the shell, and the 200 A set needs a wider root gap and more electrode per metre.
What 3 mm buys: bending stiffness goes with the cube of thickness, so 3 mm is about 3.4 times stiffer than 2 mm. The same gain is obtained far more cheaply by rolling a 40 × 40 × 5 angle on the top rim and fitting one vertical stiffener at mid-span of each long side.
Recommendation: 2 mm shell with a stiffened rim meets the duty; offer 3 mm as a priced option (about 50 per cent more material) and record the customer's choice on the order. Do not silently upgrade - it destroys the quoted price.