Water Distribution Network Upgrade in Lisbon, Portugal

Scenario

Municipal water utility upgrading a critical 10-km transmission main feeding central Lisbon. The project required retrofitting an existing DN100 (0.1 m nominal) carbon steel pipeline with a certified flow metering station. Constraints included: minimal head loss (< 25 kPa allowable permanent pressure loss), strict ISO 5167-2 compliance, no pipe diameter change (space-limited vault), and requirement for long-term stability under variable demand (5–15 m³/h). Fouling risk from aged infrastructure mandated robust beta ratio selection to mitigate sediment accumulation.

Given Data

• Pipe diameter = 0.100 m
• Fluid density = 998.2 kg/m³ (tap water at 20°C)
• Flow rate = 12.5 m³/h
• Dynamic viscosity = 0.001003 Pa·s (20°C)
• Operating pressure = 485,000 Pa (4.85 bar gauge)

Calculation

Using the Orifice Plate Beta Ratio Selector:

1. Reynolds number estimation (for validation): ( Re = \frac{4 \dot{V} \rho}{\pi D \mu} = \frac{4 \times (12.5/3600) \times 998.2}{\pi \times 0.100 \times 0.001003} \approx 440{,}000 ) → turbulent flow, valid for ISO 5167-2.
2. Tool computes optimal β balancing discharge coefficient stability, signal-to-noise ratio, and permanent loss. With inputs entered, the algorithm applies iterative ISO 5167-2-based correlations (including Cₑ and expansion factor Y) and energy loss models (ΔPₚₑᵣₘ ≈ (1 − β⁴) × (ρV²/2) × Kₗₒₛₛ), constrained by max ΔPₚₑᵣₘ ≤ 25,000 Pa.
3. Output converges at β = 0.582 — selected to maintain Cₑ uncertainty < 0.3% while holding permanent loss below threshold.

Result and Decision

• Recommended beta ratio (β): 0.582
• Orifice diameter: 0.0582 m (58.2 mm) — fabricated as stainless steel (316L), concentric, corner-tapped per ISO 5167-2.
• Permanent pressure loss: 23,850 Pa (23.9 kPa) — within 25 kPa limit. Installation proceeded with upstream/downstream straight runs (22D/8D) and ultrasonic verification; post-commissioning calibration confirmed ±0.8% accuracy over 3-month monitoring.

Lesson

Beta ratio selection must explicitly account for system-level pressure budget constraints—not just measurement accuracy. In municipal water systems, even modest permanent losses compound across networks, directly impacting pumping energy costs and reservoir drawdown schedules.