Pipe Flow Area
Engineering fundamentals for flow and velocity calculations
1. Area Calculation
Flow area is the internal cross-sectional area available for fluid flow. It's fundamental to velocity calculations, pressure drop analysis, and equipment sizing.
Basic Formula
Internal flow area:
A = π × d² / 4
Practical forms:
A (in²) = 0.7854 × d²
A (ft²) = 0.005454 × d² [d in inches]
A (ft²) = 0.7854 × d² [d in feet]
Where d = inside diameter
Inside Diameter
d = D - 2t
Where:
d = Inside diameter
D = Outside diameter (nominal or actual)
t = Wall thickness
Note: Always use actual wall thickness, not nominal.
Schedule designation alone doesn't define wall thickness.
Metal Area (Pipe Wall)
Cross-sectional metal area:
A_metal = π/4 × (D² - d²)
A_metal = π × (D - t) × t
A_metal = π × t × (D - t)
Used for: weight calculation, stress analysis
2. Velocity Relationships
Flow area connects volumetric flow rate to fluid velocity through the continuity equation.
Continuity Equation
Q = A × v
Rearranged:
v = Q / A (velocity from flow rate)
A = Q / v (required area for target velocity)
Q = A × v (flow rate from velocity)
Practical Velocity Formulas
Liquid velocity (ft/s):
v = 0.4085 × Q / d²
Where Q = flow rate (gpm), d = ID (inches)
Gas velocity (ft/s):
v = 60 × Q_acfm / A_ft²
Or at standard conditions:
v = 0.4615 × Q_scfm × (P_std/P) × (T/T_std) × Z / d²
Gas velocity (ft/s) simplified:
v = Q_MMSCFD × 6.316 × T × Z / (P × d²)
Where T in °R, P in psia, d in inches
Recommended Velocities
| Service |
Typical Velocity |
Maximum |
| Water (suction) |
2–4 ft/s |
5 ft/s |
| Water (discharge) |
5–8 ft/s |
12 ft/s |
| Crude oil |
3–6 ft/s |
10 ft/s |
| NGL/LPG |
3–5 ft/s |
8 ft/s |
| Steam (low pressure) |
80–120 ft/s |
150 ft/s |
| Steam (high pressure) |
100–150 ft/s |
200 ft/s |
| Natural gas (transmission) |
20–40 ft/s |
60 ft/s |
| Natural gas (distribution) |
40–60 ft/s |
100 ft/s |
| Compressed air |
20–30 ft/s |
50 ft/s |
API RP 14E erosional velocity: For two-phase flow, v_e = C / √ρ_m where C = 100–150 (conservative to less conservative) and ρ_m = mixture density (lb/ft³). This limits velocity to prevent erosion-corrosion.
3. Reference Tables
Standard Pipe Flow Areas
| NPS |
OD (in) |
Schedule |
Wall (in) |
ID (in) |
Area (in²) |
Area (ft²) |
| 2" |
2.375 |
40 |
0.154 |
2.067 |
3.356 |
0.0233 |
| 4" |
4.500 |
40 |
0.237 |
4.026 |
12.73 |
0.0884 |
| 6" |
6.625 |
40 |
0.280 |
6.065 |
28.89 |
0.2006 |
| 8" |
8.625 |
40 |
0.322 |
7.981 |
50.03 |
0.3474 |
| 10" |
10.750 |
40 |
0.365 |
10.020 |
78.85 |
0.5476 |
| 12" |
12.750 |
Std |
0.375 |
12.000 |
113.1 |
0.7854 |
| 16" |
16.000 |
Std |
0.375 |
15.250 |
182.7 |
1.269 |
| 20" |
20.000 |
Std |
0.375 |
19.250 |
291.0 |
2.021 |
| 24" |
24.000 |
Std |
0.375 |
23.250 |
424.6 |
2.948 |
| 30" |
30.000 |
Std |
0.375 |
29.250 |
672.0 |
4.666 |
| 36" |
36.000 |
Std |
0.375 |
35.250 |
976.0 |
6.778 |
Area Ratios
Area ratio between pipe sizes:
A₂/A₁ = (d₂/d₁)²
Examples:
12" to 8": (12/8)² = 2.25× area increase
Velocity decreases by same ratio: v₂ = v₁ × (d₁/d₂)²
4. Hydraulic Diameter
For non-circular cross-sections or partially filled pipes, hydraulic diameter is used in flow calculations.
Definition
Hydraulic diameter:
D_h = 4 × A / P_w
Where:
A = Flow area
P_w = Wetted perimeter
For circular pipe (full flow):
D_h = 4 × (πd²/4) / (πd) = d
For annulus (pipe in pipe):
D_h = D_o - D_i (outer ID minus inner OD)
Common Cross-Sections
| Shape |
Hydraulic Diameter |
| Circular (full) |
D_h = d |
| Circular (half full) |
D_h = d |
| Annulus |
D_h = D_outer - D_inner |
| Square (side a) |
D_h = a |
| Rectangle (a × b) |
D_h = 2ab/(a+b) |
| Equilateral triangle |
D_h = a/√3 |
Partially Filled Pipe
Flow at depth h in horizontal pipe:
A = r² × [arccos((r-h)/r) - ((r-h)/r) × √(1-((r-h)/r)²)]
P_w = 2r × arccos((r-h)/r)
D_h = 4A / P_w
At 50% full: D_h = d (same as full pipe)
At 80% full: D_h ≈ 1.22d (higher than full!)
5. Applications
Reynolds Number
Re = ρ × v × D_h / μ = v × D_h / ν
Using practical units:
Re = 7742 × Q × SG / (d × μ)
Where:
Q = flow (gpm)
d = ID (inches)
μ = viscosity (cP)
SG = specific gravity
Line Sizing Example
Problem: Size a water line for 500 gpm at max 8 ft/s
Required area:
v = 0.4085 × Q / d²
8 = 0.4085 × 500 / d²
d² = 204.25 / 8 = 25.5
d = 5.05 inches minimum
Select 6" Sch 40:
ID = 6.065 in
v = 0.4085 × 500 / 6.065² = 5.55 ft/s ✓
Orifice and Restriction Areas
Beta ratio (orifice sizing):
β = d_orifice / d_pipe
Area ratio:
A_orifice / A_pipe = β²
Typical ranges:
- Orifice plates: β = 0.2–0.75
- Control valves: sized for Cv at design flow
- Restrictions: pressure drop ∝ 1/A²
Common Uses
- Line sizing: Select pipe diameter for target velocity
- Pump selection: Calculate suction/discharge velocities
- Pressure drop: Velocity head = v²/2g
- Flow measurement: Orifice and venturi sizing
- Heat transfer: Convection coefficient correlations
- Erosion analysis: Check against erosional velocity limits
References
- ASME B36.10M – Welded and Seamless Wrought Steel Pipe
- API RP 14E – Design and Installation of Offshore Production Piping
- Crane Technical Paper 410 – Flow of Fluids