Fittings

Overview

In piping systems, fittings and valves are essential components that enable direction changes, flow branching, area transitions, and flow regulation. While straight pipe friction is distributed along the pipe length and calculated using the Darcy-Weisbach equation, fittings create localized pressure drops often termed “minor losses” (though they can dominate in complex networks with many fittings). Accurately quantifying these losses is critical for pump sizing, energy efficiency analysis, and overall system design.

Loss Coefficient (K). The pressure drop across a fitting is typically expressed using a loss coefficient K, where the pressure drop is \Delta p = K \frac{\rho v^2}{2}. Here, \rho is the fluid density and v is the velocity. The K value depends on the fitting geometry, Reynolds number, and surface roughness, and is determined through empirical correlations or experimental data. These tools implement correlations from authoritative sources such as Crane Technical Paper 410, Idelchik’s Handbook, and peer-reviewed studies.

Bends and Elbows. Pipe bends redirect flow, creating secondary flows and increased turbulence. BEND_ROUNDED calculates K for smooth elbows using correlations that account for bend radius and angle, while BEND_MITER handles miter bends (segmented elbows) which have higher losses. Special geometries like HELIX and SPIRAL account for coiled pipes used in heat exchangers and compact installations.

Contractions and Expansions. Area changes create losses due to flow acceleration or deceleration and associated turbulence. CONTRACTION_SHARP and CONTRACTION_ROUND compute K for reducers (decreasing diameter), while DIFFUSER_SHARP and DIFFUSER_CONICAL handle expansions (increasing diameter). Sharp transitions have higher losses than gradual, tapered transitions.

Entrances and Exits. Pipe entrances from reservoirs and exits to reservoirs represent special boundary conditions. ENTRANCE_SHARP, ENTRANCE_ROUNDED, ENTRANCE_BEVELED, and ENTRANCE_ANGLED calculate K for various entrance geometries, with sharp-edged entrances producing the highest losses. EXIT_NORMAL computes the loss when fluid discharges from a pipe into a large reservoir (typically K ≈ 1.0).

Valves. Valves regulate flow and create pressure drops that vary with valve type and opening position. Tools for common industrial valves include K_GATE_VALVE, K_GLOBE_VALVE, K_BALL_VALVE, K_BUTTERFLY_VALVE, and K_SWING_CHECK_VALVE. These use the Crane method, which relates K to an equivalent length of straight pipe.

Flow Coefficient Conversions. Valve manufacturers often specify performance using flow coefficients rather than K values. The imperial Cv and metric Kv coefficients represent the flow rate (in GPM or m³/h) at a 1 psi or 1 bar pressure drop, respectively. CV_TO_K, KV_TO_K, K_TO_CV, and K_TO_KV convert between these representations, enabling integration of manufacturer data into system hydraulic calculations.

These tools are implemented using the fluids library, which provides a comprehensive collection of correlations for fitting and valve losses validated against experimental data and industry standards.

Tools

Tool	Description
BEND_MITER	Calculate the loss coefficient (K) for a single-joint miter bend in a pipe.
BEND_ROUNDED	Calculate the loss coefficient (K) for a rounded pipe bend (elbow) using various methods.
CONTRACTION_ROUND	Calculate the loss coefficient (K) for a rounded pipe contraction (reducer).
CONTRACTION_SHARP	Calculate the loss coefficient (K) for a sharp edged pipe contraction (reducer).
CV_TO_K	Convert imperial valve flow coefficient (Cv) to loss coefficient (K).
DIFFUSER_CONICAL	Calculate the loss coefficient (K) for a conical pipe expansion (diffuser).
DIFFUSER_SHARP	Calculate the loss coefficient (K) for a sudden pipe expansion (diffuser).
ENTRANCE_ANGLED	Calculate the loss coefficient (K) for an angled sharp entrance to a pipe flush with a reservoir wall.
ENTRANCE_BEVELED	Calculate the loss coefficient (K) for a beveled or chamfered entrance to a pipe flush with a reservoir wall.
ENTRANCE_ROUNDED	Calculate the loss coefficient (K) for a rounded entrance to a pipe flush with a reservoir wall.
ENTRANCE_SHARP	Calculate the loss coefficient (K) for a sharp entrance to a pipe flush with a reservoir wall.
EXIT_NORMAL	Calculate the loss coefficient (K) for a normal pipe exit discharging into a reservoir.
HELIX	Calculate the loss coefficient (K) for a helical coil pipe section.
K_BALL_VALVE	Calculate the loss coefficient (K) for a ball valve using the Crane method.
K_BUTTERFLY_VALVE	Calculate the loss coefficient (K) for a butterfly valve using the Crane method.
K_GATE_VALVE	Calculate the loss coefficient (K) for a gate valve using the Crane method.
K_GLOBE_VALVE	Calculate the loss coefficient (K) for a globe valve using the Crane method.
K_SWING_CHECK_VALVE	Calculate the loss coefficient (K) for a swing check valve using the Crane method.
K_TO_CV	Convert loss coefficient (K) to imperial valve flow coefficient (Cv).
K_TO_KV	Convert loss coefficient (K) to metric valve flow coefficient (Kv).
KV_TO_K	Convert metric valve flow coefficient (Kv) to loss coefficient (K).
SPIRAL	Calculate the loss coefficient (K) for a spiral coil pipe section.