Estimate annular pressure loss from flow rate, hole and pipe diameters, fluid density and viscosity, or solve flow for a target loss, plus ECD.

Steady, fully developed Newtonian liquid in a stationary concentric annulus.

Use 0 for the circular-pipe limit.

Roughness and ECD (optional)
0.0018 in is a typical steel-pipe value; change it if you know yours.

Blank omits ECD. Use the depth spanned by the whole modeled flow path.

Annular Pressure Loss Formula

The calculator estimates straight-run friction pressure loss for steady, fully developed flow of a single-phase incompressible Newtonian liquid through a stationary concentric annulus. It uses the Darcy–Weisbach relationship in consistent SI units:

ΔP = fD × (L / Dₕ) × (ρ v² / 2)

Variables:

  • ΔP is friction pressure loss in pascals (Pa) when SI units are used
  • v = Q/A is mean velocity (m/s), with volume flow Q in m³/s and A = π(Do² − Di²)/4 in m²
  • f_D is the dimensionless Darcy friction factor; L is flow length (m), D_h = Do − Di is hydraulic diameter (m), and ρ is mass density (kg/m³)

Calculate Reynolds number Re = ρvD_h/μ using dynamic viscosity μ in Pa·s. For laminar flow below Re 2300, the calculator uses f_D = 64ζ/Re, with the concentric-annulus geometry correction ζ described in NASA KSC-STD-Z-0017 Rev A, section 7.4.2. Above Re 4000 it uses an approximate Swamee–Jain factor with effective diameter D_h/ζ in the roughness term. The linear friction-factor blend over Re 2300–4000 is an explicitly chosen smoothing assumption; transition results are heuristic.

What is Annular Pressure Loss?

Annular pressure loss refers to the pressure drop that occurs in the annular space between two concentric cylinders, such as in a wellbore during drilling operations. This pressure loss is influenced by factors such as the flow rate of the drilling fluid, the friction factor, and the geometry of the annular space. This simplified Newtonian model excludes eccentricity, pipe rotation, entrance and fitting losses, elevation head and non-Newtonian rheology. It does not validate drilling-mud or well-control predictions from a single viscosity input.

How to Calculate Annular Pressure Loss?

The following steps outline how to calculate the Annular Pressure Loss.

  1. First, enter the flow rate, concentric diameters, flow length, density, dynamic viscosity and absolute roughness using the selected units.
  2. Next, calculate area, mean velocity, hydraulic diameter and Reynolds number to select the declared friction-factor branch.
  3. Finally, apply ΔP = f_D(L/D_h)(ρv²/2). Reverse mode searches for the flow producing the target pressure loss and verifies the pressure residual.
  4. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Example inputs: outer passage ID 8.5 in, inner pipe OD 5 in, flow length 5000 ft, density 10 ppg, dynamic viscosity 20 cP, absolute roughness 0.0018 in and flow 500 US gpm.

The corrected geometry gives ζ ≈ 1.4930632, hydraulic diameter 3.5 in and Re ≈ 7017.74. The approximate turbulent model gives Darcy f ≈ 0.03534757 and friction pressure loss ≈ 91.409623 psi. At 4500 ft TVD, the corresponding ECD increase is about 0.390639 ppg and total ECD is about 10.390639 ppg.

ECD is optional and applies only when the modeled loss spans the entered true vertical depth to the surface: ECD (ppg) = fluid density (ppg) + ΔP (psi)/(0.052 × TVD (ft)), as defined by the SLB Energy Glossary. TVD is distinct from flow-path length. The calculator limits Re to 100 million and roughness/effective diameter to 0.05 as computational bounds; these do not establish accuracy for all geometries. The EPA EPANET manual documents the Swamee–Jain pipe approximation; this calculator’s annular adjustment and transition blend are separately declared.

Annular Pressure Loss Calculator screenshot