OTEC Cold-Water Pipe Optimizer (2D Cross-Section)

Cold-Water Pipe (CWP) Design

Pipe diameter D 2.0 m

Flow velocity v 1.5 m/s

Pipe depth L 1000 m

Surface–deep ΔT 20.0 °C

Live Output

Net electrical power

— kW

Mass flow

—

Gross thermal power

—

Pumping loss

—

Reynolds no.

—

How it works

An OTEC plant pumps cold deep water up a long Cold-Water Pipe (CWP) to condense the working fluid of a Rankine cycle driven by warm surface water. The CWP is the single most expensive and most sensitive component: a narrow, fast pipe costs less steel but wastes power on friction; a wide, slow pipe recovers more net power but costs more to build. This 2D cross-section renders the real depth profile — pan and zoom through it — alongside a live power curve.

Flow:      A = πD²/4,  Q = vA,  ṁ = ρQ            (ρ = 1025 kg/m³ seawater)
Gross:     Q_th = ṁ · c_p · ΔT_hx           (c_p = 4000 J/kg·K, ΔT_hx = 3°C heat-exchanger approach)
           η_Carnot = ΔT / T_warm,  η_actual ≈ 0.30 · η_Carnot
           P_gross = η_actual · Q_th
Friction:  Re = ρvD/μ,  f ≈ 0.316 / Re^0.25          (Blasius correlation, turbulent flow)
           ΔP = f (L/D)(ρv²/2)
Pumping:   P_pump = ΔP · Q / η_pump              (η_pump = 0.85)
Net:       P_net = P_gross − P_pump

Diameter D — friction loss falls steeply with diameter, which is why real CWPs are 3–11 m wide despite the extra steel. The power-vs-diameter panel on the right traces this trade-off live.
Velocity v — more flow means more heat delivered, but pumping power grows with v³, so past a point every extra litre/second costs more than it earns. Particle speed in the cross-section is tied to the real transit time L/v, not a cosmetic animation rate.
Depth L — a deeper pipe adds friction length; here L only affects pumping loss to isolate the diameter/velocity trade-off (the depth view auto-fits to L, or drag/scroll to inspect any section).
ΔT — the Carnot ceiling on thermal-to-electric conversion; OTEC's whole appeal and whole limitation is that this gradient is only 15–24°C, so η_actual rarely exceeds 2–3%.

Push D too small at a given v and P_net turns negative — the plant would spend more electricity pumping seawater than the temperature gradient can ever give back, which is exactly why CWP sizing is treated as OTEC's primary engineering bottleneck rather than an afterthought.

Cold water flow (CWP) Warm surface layer

drag to pan • scroll/pinch to zoom