1. Pressure Drop Overview
Pressure drop in piping systems results from friction between the fluid and the pipe wall (major losses) and from changes in flow direction, velocity, or cross-sectional area at fittings, valves, and other components (minor losses). Accurate pressure drop calculations are essential for pump and compressor sizing, control valve selection, and ensuring adequate delivery pressure.
Total System Pressure Drop
The total pressure drop in a piping system is the sum of friction losses in straight pipe, losses through fittings and valves, elevation changes (static head), and acceleration losses (for compressible flow). In typical facility piping, fitting and valve losses often equal or exceed straight pipe friction losses, making accurate minor loss estimation critical.
Pressure Drop Components
ΔPtotal = ΔPfriction + ΔPfittings + ΔPelevation + ΔPacceleration
ΔPfriction = Darcy-Weisbach friction in straight pipe
ΔPfittings = Losses through valves, elbows, tees, reducers
ΔPelevation = ρgΔz (static head difference)
ΔPacceleration = Velocity change losses (significant for gas flow)
Key References
| Reference | Scope | Application |
|---|---|---|
| Crane TP-410 | Flow of Fluids Through Valves, Fittings, and Pipe | Industry standard for K-factors, equivalent lengths, and flow calculations |
| Perry's Chemical Engineers' Handbook | Comprehensive fluid mechanics reference | Friction factors, two-phase flow, non-Newtonian fluids |
| Cameron Hydraulic Data | Pipe friction data and pump selection | Liquid piping, pump NPSH calculations |
| GPSA Engineering Data Book | Gas processing fluid mechanics | Gas and two-phase flow in facility piping |
2. Darcy-Weisbach Equation
The Darcy-Weisbach equation is the fundamental equation for calculating pressure drop due to friction in pipe flow. It applies to all Newtonian fluids (liquids and gases) in all flow regimes (laminar and turbulent).
General Form
ΔP = f × (L/D) × (ρV²/2)
Where: ΔP = pressure drop (Pa or psf), f = Darcy friction factor (dimensionless), L = pipe length (ft or m), D = pipe inside diameter (ft or m), ρ = fluid density (lb/ft³ or kg/m³), V = fluid velocity (ft/s or m/s)
Practical Engineering Form
For liquids (psi):
ΔP = f × L × ρ × V² / (2 × gc × D × 144)
Head loss form (ft of fluid):
hL = f × (L/D) × V² / (2g)
Reynolds Number
The Reynolds number determines whether flow is laminar or turbulent and is used to find the friction factor from the Moody diagram or Colebrook equation:
Re = ρVD / μ = VD / ν
Laminar flow: Re < 2,100
Transitional flow: 2,100 < Re < 4,000
Turbulent flow: Re > 4,000
Flow Regime in Practice
In virtually all midstream facility piping at normal operating conditions, flow is fully turbulent (Re > 10,000 and often > 100,000). Laminar flow conditions may occur in very viscous fluids (heavy oil, glycol) in small-diameter piping at low velocities. The flow regime determines which friction factor correlation to use and whether the roughness of the pipe wall affects the friction factor.
3. Friction Factor Determination
The Darcy friction factor (f) depends on the Reynolds number and the relative roughness of the pipe wall (ε/D). For laminar flow, the friction factor depends only on Reynolds number. For turbulent flow, both Reynolds number and roughness affect the friction factor.
Friction Factor Equations
Laminar flow (Re < 2,100):
f = 64 / Re
Turbulent flow — Colebrook-White (implicit):
1/√f = −2 log10(ε/3.7D + 2.51/(Re√f))
Turbulent flow — Churchill (explicit approximation):
f = 8[(8/Re)12 + (A + B)−1.5]1/12
Pipe Roughness Values
| Pipe Material | Roughness ε (inches) | Roughness ε (mm) |
|---|---|---|
| Commercial steel (new) | 0.0018 | 0.046 |
| Commercial steel (corroded) | 0.006–0.06 | 0.15–1.5 |
| Stainless steel | 0.0002 | 0.005 |
| Drawn tubing | 0.00006 | 0.0015 |
| Cast iron | 0.01 | 0.26 |
| Galvanized iron | 0.006 | 0.15 |
| PVC / plastic | 0.00006 | 0.0015 |
| Concrete | 0.012–0.12 | 0.3–3.0 |
Fully Rough Flow Zone
At sufficiently high Reynolds numbers, the friction factor becomes independent of Reynolds number and depends only on relative roughness. This is the fully rough (fully turbulent) zone on the Moody diagram. For commercial steel pipe with ε = 0.0018", this occurs at Re > approximately 106 for 4" pipe and Re > approximately 107 for 24" pipe. In this zone, increasing flow velocity does not change the friction factor, simplifying calculations significantly.
4. Fittings & Valve Losses (K-Factor Method)
Pressure losses through fittings and valves are expressed using resistance coefficients (K-factors). The pressure drop through a fitting is proportional to the velocity head:
ΔPfitting = K × ρV² / (2 × gc × 144) (psi)
hL = K × V² / (2g) (ft of head)
Common K-Factor Values (Crane TP-410)
| Fitting / Valve | K-Factor Formula | K at fT = 0.015 |
|---|---|---|
| 90° standard elbow | 30 fT | 0.45 |
| 90° long radius elbow | 20 fT | 0.30 |
| 45° standard elbow | 16 fT | 0.24 |
| Standard tee (flow through run) | 20 fT | 0.30 |
| Standard tee (flow through branch) | 60 fT | 0.90 |
| Gate valve (full open) | 8 fT | 0.12 |
| Globe valve (full open) | 340 fT | 5.10 |
| Ball valve (full bore, full open) | 3 fT | 0.05 |
| Check valve (swing) | 100 fT | 1.50 |
| Butterfly valve (full open) | 45 fT | 0.68 |
Where fT is the friction factor for fully turbulent flow at the pipe size, from Crane TP-410 Table A-26. The K-factor is independent of Reynolds number in the turbulent range.
Reducers and Expanders
Sudden contraction: K = 0.5(1 − d²/D²)
Sudden expansion: K = (1 − d²/D²)²
Gradual contraction (θ < 45°): K ≈ 0.8 sin(θ/2)(1 − β²)
Gradual expansion (θ < 45°): K ≈ 2.6 sin(θ/2)(1 − β²)²
Where d = smaller diameter, D = larger diameter, β = d/D
Velocity Basis for K-Factors
K-factors must be applied using the velocity in the pipe at the fitting connection point. For reducers and expanders, the convention is to use the velocity in the smaller pipe. When summing K-factors for a piping system with multiple pipe sizes, all K-factors must be converted to a common velocity basis before adding. This is done by multiplying K by (dcommon/dactual)4.
5. Equivalent Length Method
An alternative to K-factors is the equivalent length method, which expresses the loss through each fitting as an equivalent length of straight pipe that would produce the same friction loss. The total equivalent length is added to the actual pipe length in the Darcy-Weisbach equation.
Leq = K × D / fT
ΔPtotal = f × (Lactual + ∑Leq) × ρV² / (2gcD × 144)
Typical Equivalent Lengths (Pipe Diameters)
| Fitting | L/D | Leq for 4" Pipe (ft) | Leq for 8" Pipe (ft) |
|---|---|---|---|
| 90° standard elbow | 30 | 10 | 20 |
| 90° long radius elbow | 20 | 6.7 | 13.3 |
| 45° elbow | 16 | 5.3 | 10.7 |
| Tee (through run) | 20 | 6.7 | 13.3 |
| Tee (through branch) | 60 | 20 | 40 |
| Gate valve | 8 | 2.7 | 5.3 |
| Globe valve | 340 | 113 | 227 |
| Ball valve (full bore) | 3 | 1.0 | 2.0 |
| Check valve (swing) | 100 | 33 | 67 |
K-Factor vs. Equivalent Length
Both methods give the same result when used correctly. The K-factor method is generally preferred because K is independent of pipe size (for the same fitting type), while equivalent lengths must be recalculated for each pipe diameter. The equivalent length method can introduce errors when the actual friction factor differs from fT used to derive the equivalent length. Use the K-factor method for detailed engineering calculations and the equivalent length method for quick estimates and rule-of-thumb sizing.
6. Gas Flow Considerations
Pressure drop calculations for compressible (gas) flow require special treatment because gas density, velocity, and volume change as pressure decreases along the pipe. For facility piping where pressure drop is less than 10% of inlet pressure, the incompressible Darcy-Weisbach equation can be used with average conditions.
Compressibility Effects
For ΔP/P1 < 10%: Use Darcy-Weisbach with average density
ρavg = Pavg × MW / (Z × R × T)
For ΔP/P1 > 10%: Use isothermal or adiabatic compressible flow equations
Isothermal Compressible Flow (Crane TP-410 Method)
P1² − P2² = (G² × R × T) / (gc × A² × MW) × [f(L/D) + ∑K + 2 ln(P1/P2)]
Where G = mass flow rate (lb/s), A = pipe cross-sectional area (ft²), MW = molecular weight, T = absolute temperature (R), R = 1545 ft·lbf/(lbmol·R)
Choked Flow
As pressure drop increases, gas velocity increases. When velocity reaches the speed of sound (Mach 1) at the pipe exit, flow becomes choked and further downstream pressure reduction cannot increase flow rate.
| Parameter | Significance |
|---|---|
| Mach number = 1 | Maximum velocity; choked condition at pipe exit |
| Critical pressure ratio | P2/P1 below which flow is choked |
| Maximum mass flux | Determined by pipe diameter, inlet conditions, and friction |
Sonic Velocity Limit
In facility piping, choked flow typically occurs at control valves, restriction orifices, and relief valves rather than in straight pipe runs. However, piping systems designed for very high velocity (greater than 60% of sonic velocity) should be checked for acoustic vibration and erosion concerns. The recommended maximum gas velocity in facility piping is typically 60–80 ft/s for continuous service and up to 200 ft/s for intermittent service (e.g., blowdown piping).
7. Two-Phase Flow
Two-phase (gas-liquid) flow occurs frequently in midstream facility piping, particularly in production gathering systems, separator inlet piping, and slug catchers. Two-phase pressure drop is significantly higher than single-phase flow and depends on the flow pattern.
Flow Patterns
| Pattern | Description | Typical Occurrence |
|---|---|---|
| Stratified | Gas on top, liquid on bottom; smooth or wavy interface | Low velocity horizontal flow; large diameter pipe |
| Slug | Alternating plugs of liquid and gas; high pressure fluctuations | Moderate velocities; most common pattern in production piping |
| Annular | Gas core with liquid film on pipe wall | High gas velocity; predominant pattern at high GOR |
| Bubble | Discrete gas bubbles in continuous liquid phase | Low GOR; nearly liquid-full pipe |
| Mist | Liquid droplets entrained in continuous gas phase | Very high gas velocity; post-separator gas piping with carryover |
Two-Phase Pressure Drop Methods
| Method | Application | Accuracy |
|---|---|---|
| Beggs & Brill | Horizontal, inclined, and vertical pipe flow | Good for most oil and gas applications |
| Lockhart-Martinelli | Horizontal flow; separated flow model | Good for low-pressure applications |
| Dukler | Horizontal and slightly inclined flow | Good for gas-condensate systems |
| Homogeneous model | Simple approximation; treats mixture as single phase | Quick estimate; tends to underpredict ΔP |
Slug Flow Design Concerns
Slug flow generates dynamic forces on pipe supports, induces vibration, and causes intermittent liquid surges at equipment inlets. When piping design analysis predicts slug flow, the mechanical design must account for: (1) slug force on elbows and tees (F = ρLAVslug²), (2) pipe support spacing for dynamic loads, (3) slug catcher or surge volume at downstream equipment, and (4) potential for slug-induced water hammer at sudden area changes.
8. Design Practice
Practical piping design requires balancing pressure drop against pipe cost, support requirements, erosion limits, and noise generation. Industry guidelines provide recommended velocity limits that implicitly control pressure drop per unit length.
Recommended Velocity Limits
| Service | Recommended Velocity | Max ΔP/100 ft |
|---|---|---|
| Gas (general facility) | 60–80 ft/s | 0.5–1.0 psi |
| Gas (compressor suction) | 30–50 ft/s | 0.1–0.3 psi |
| Gas (compressor discharge) | 40–60 ft/s | 0.3–0.5 psi |
| Steam | 100–150 ft/s | 0.5–1.5 psi |
| Water (general) | 5–10 ft/s | 2–5 psi |
| Pump suction (water) | 3–5 ft/s | 0.5–1.0 psi |
| Hydrocarbon liquid | 5–8 ft/s | 2–4 psi |
| Glycol | 3–6 ft/s | 1–3 psi |
Erosional Velocity
Verosional = C / √ρm (API RP 14E)
Where C = empirical constant (typically 100–150 for continuous service, up to 200 for intermittent), ρm = mixture density at flowing conditions (lb/ft³)
Pressure Drop Budget
In facility design, the total allowable pressure drop between the supply point and the consuming equipment is a fixed budget that must be allocated among pipe runs, fittings, control valves, and equipment. Control valves typically require 10–50% of the system pressure drop for proper rangeability. The remaining budget must accommodate piping friction, fitting losses, and elevation changes. Oversizing pipe reduces friction loss but increases capital cost. Undersizing increases operating cost through higher compression requirements.