Minor Loss (K-Value) Calculator

Formula overview

D_in is inside diameter in inches, D_nom nominal size in inches — the 2-K and 3-K constants are defined on imperial diameters. K is dimensionless; ΔP comes out in Pa with ρ in kg/m³ and V in m/s.

  Crane TP-410     K = (L/D) · f_T
  Hooper 2-K       K = K1/Re + K∞ · (1 + 1/D_in)
  Darby 3-K        K = K1/Re + K_i · (1 + K_d / D_nom^0.3)

Then  ΔP = K · ρV²/2,  or as an equivalent length L_eq = K·D/f.

Worked example

Standard 90° elbow on a 6" line at Re = 100 000:

Crane:  L/D = 30, f_T ≈ 0.015
        K = 30 × 0.015 = 0.45

Hooper 2-K: K1 = 800, K∞ = 0.25, D_in = 6.065
        K = 800/100 000 + 0.25 × (1 + 1/6.065)
          = 0.008 + 0.291 = 0.30

A 50% spread between the two methods on the same fitting — and the
gap widens further as Reynolds number falls, where the K1/Re term in
the 2-K method grows and Crane stays flat.

Common mistakes

• Using Crane K-values at low Reynolds number. In laminar and transitional flow the true resistance rises sharply, and a fixed (L/D)·f_T can under-predict the loss by a large factor — viscous and small-bore service is where the 2-K or 3-K method earns its keep.
• Using the flowing friction factor instead of f_T in the Crane method. f_T is the fully turbulent factor for the pipe size, a fixed value per size, not the f computed for the actual flow.
• Mixing K bases. A K value belongs to a specific reference velocity and diameter. Applying a K derived for the fitting bore to the velocity in the adjoining line — or vice versa — is a common and silent error at reducers and valves with reduced ports.

FAQ