Design of riveted steel pressure mains – estimate plate thickness with joint efficiency and corrosion allowance A pressure main (diameter = 1.0 m) experiences a static head difference of 180 m, and a water-hammer rise of 7.5 kg/cm^2. Riveted joint efficiency is 0.6, and a 3 mm corrosion allowance is required. Estimate the necessary plate thickness (choose the nearest standard value).

Introduction / Context:
Pressure pipelines are often designed using the thin-cylinder hoop-stress approach with allowances for joint efficiency and corrosion. Riveted joints reduce effective strength; water hammer adds to static pressure. This problem consolidates those considerations.

Given Data / Assumptions:

• Diameter D = 1.0 m = 100 cm.
• Static head = 180 m of water ≈ 180 * 0.1 kg/cm^2 ≈ 18 kg/cm^2 (more precisely ≈ 17.7–18.0).
• Water-hammer increment = 7.5 kg/cm^2.
• Joint efficiency η = 0.6.
• Corrosion allowance c = 3 mm = 0.3 cm.
• Adopt a typical allowable hoop stress for plate material, f_allow ≈ 1000 kg/cm^2 for working-stress design of riveted steel plates (representative of older practice).

Concept / Approach:
Use thin-cylinder hoop-stress relation including joint efficiency: t_req = (p_total * D) / (2 * f_allow * η) where p_total is the maximum operating pressure including surge. Add the corrosion allowance afterwards: t = t_req + c.

Step-by-Step Solution:
Compute total pressure: p_total ≈ 18 + 7.5 = 25.5 kg/cm^2.Compute required thickness without corrosion: t_req = (25.5 * 100) / (2 * 1000 * 0.6) = 2550 / 1200 ≈ 2.125 cm.Add corrosion allowance: t ≈ 2.125 + 0.3 = 2.425 cm ≈ 24.3 mm.Adopt nearest standard thickness → 25 mm.

Verification / Alternative check:
Using a slightly more precise static head conversion (≈17.7 kg/cm^2) yields t in the same vicinity; standardization still leads to 25 mm plates.

Why Other Options Are Wrong:

• 10–20 mm: insufficient given high combined pressure and reduced joint efficiency.
• 30 mm: conservative beyond typical need for the given assumptions.

Common Pitfalls:
Omitting water-hammer allowance or forgetting to divide by joint efficiency significantly underestimates thickness.

Final Answer:
25 mm