Pressure drop
kPa
Friction pressure loss over L.
Fluid mechanics · Pipe flow
Pipe pressure drop
Calculate velocity, Reynolds number, Darcy friction factor, pressure drop and head loss in a straight circular pipe.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
03
Results
Head loss
m
h_f = Δp/(ρg).
Volumetric flow
L/s
Flow through the pipe.
Mean velocity
m/s
v = Q/A.
Reynolds number
—
Identifies the flow regime.
Darcy friction factor
—
Dimensionless factor f.
Relative roughness
—
ε/D.
Pressure gradient
Pa/m
Δp/L.
Flow area
cm²
A = πD²/4.
Turbulent flow: f solved with Colebrook–White in 3 iterations, without intermediate rounding.
View calculation detailsFormulas, numerical substitution and results without intermediate roundingOpen ↓
Calculation note
Full calculation details
1. Flow area
Formula
—Substitution
—Result
—2. Flow and velocity
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—Substitution
—Result
—3. Reynolds number
Formula
—Substitution
—Result
—4. Relative roughness
Formula
—Substitution
—Result
—5. Friction factor
Formula
—Substitution
—Result
—6. Pressure drop
Formula
—Substitution
—Result
—7. Head and gradient
Formula
—Substitution
—Result
—Straight circular pipe with constant diameter and steady incompressible flow. Minor losses, elevation changes, pumps, valves and fittings are not included.
01Formulas and symbols
Relations used
A
πD²/4Flow areaRe
ρvD/μReynolds numberf
64/ReLaminar flowf
1/√f = −2 log₁₀(ε/(3,7D) + 2,51/(Re√f))Colebrook–WhiteΔp
f(L/D)ρv²/2Darcy–Weisbachhf
Δp/(ρg)Head loss02Assumptions and limits
Scope of validity
- Steady flow in a full pipe.
- Incompressible fluid with constant properties.
- Constant inside diameter and roughness.
- The range 2,300 ≤ Re < 4,000 is flagged as transitional: the displayed factor is indicative.
- Minor losses must be added separately.
03Validation example
Reference numerical case
- Water at 20°C, D = 50 mm, L = 10 m, Q = 2 L/s and ε = 0.045 mm.
- v = 1.01859 m/s; Re = 50,736; ε/D = 0.0009.
- f = 0.023694; Δp = 2.45394 kPa; hf = 0.25068 m.
04References
Technical references
- Darcy–Weisbach equation for major losses in straight pipes.
- Colebrook, C. F., turbulent flow in pipes with particular reference to the transition region between smooth and rough pipe laws.
- Fluid presets are typical values; confirm temperature and the fluid data sheet for contractual calculations.