Fittings

Overview

In piping systems, fittings (elbows, tees, reducers) and valves allow for the change of direction, branching, and regulation of fluid flow. Identifying the pressure loss across these components is a critical step in pump sizing and system analysis. Unlike straight pipe friction, which is distributed along the length, fitting losses are often treated as “minor losses” (though they can be major in complex networks).

The K-Factor Method

The most common engineering approach is the Resistance Coefficient (K) method, where the head loss h_L is proportional to the velocity head:

h_L = K \frac{v^2}{2g} \quad \text{or} \quad \Delta P = K \frac{1}{2} \rho v^2

Equivalent Length Method

Another common method expresses the fitting’s resistance as an equivalent length (L_e) of straight pipe of the same diameter. A fitting with L_e/D = 50 produces the same pressure drop as a straight pipe section 50 diameters long.

Figure 1: Relative resistance of common fittings expressed as Equivalent Length (L/D). Globe valves induce massive turbulence and pressure drop compared to streamlined gate valves or elbows.

Python Libraries

These functions utilize the fluids library, which implements resistance models for hundreds of fittings and valves. The library provides validated implementations of industry standards like Crane TP-410 and Miller, ensuring high fidelity in pipe network analysis and pump sizing.

Conversion and Specific Fittings

Different industries and standards use different metrics for capacity and loss.

• CV_TO_K: Converts the imperial valve flow coefficient (C_v) to a dimensionless K-factor.
• K_TO_KV: Converts K-factor to the metric flow coefficient (K_v).
• K_GATE_VALVE, BEND_ROUNDED: Calculate K-factors for specific geometries based on standards like Crane TP-410 or Miller.

Native Excel Capabilities

Excel provides no built-in support for fitting losses. Users must manually: - Research resistance coefficients (K) or equivalent lengths (L/D) from handbooks. - Implement formulas for K that depend on Reynolds number (like Miller’s method). - Hand-code conversion between C_v, K_v, K, and L/D.

The Python functions provided here centralize these industrial standards, providing a unified and validated interface for piping system designers directly within their spreadsheets.

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.