Engineering task and calculation objective
The L1.2 module calculates the pressure drop of single-phase flow through pipes according to the VDI Heat Atlas (VDI-Wärmeatlas), 12th edition 2019 — the standard German reference for heat transfer and fluid flow. It covers pipes with circular cross-section as well as non-circular cross-sections (via the hydraulic diameter), annular gaps and helically coiled tubes, in which centrifugal force generates secondary flows and increases the friction factor compared with a straight pipe.
Being able to calculate pipe friction pressure drop is the foundation of every hydraulic design task in plant engineering: sizing pumps and fans, dimensioning piping and heat exchanger tube bundles, checking permissible flow velocities and distributing volume flows among parallel branches. The governing quantity is the pipe friction factor λ, which depends on the Reynolds number and, in the turbulent regime, additionally on the relative wall roughness.
The calculation follows the well-established laws: Hagen-Poiseuille for laminar flow, Blasius or Konakov for hydraulically smooth turbulent pipes, and the Colebrook equation for the transition and rough regimes. The pressure drop then follows from Δp = λ·(L/d)·ρ·w²/2 with pipe length, diameter, density and flow velocity.
Standard and calculation basis: VDI-Wärmeatlas, 12. Auflage 2019
Calculation scope
- Pressure drop in flowed through circular pipes
- Pressure drop in flowed through noncircular pipes
- Coils
- Annuli
Calculation workflow
- Define the geometry and pipe form: The pipe form is selected: straight circular pipe, non-circular cross-section, annular gap or helically coiled tube. For non-circular cross-sections, the hydraulic diameter is formed from four times the cross-sectional area divided by the wetted perimeter; for coils, the coil and tube diameters additionally enter the calculation.
- Determine the flow regime: From velocity or mass flow rate, diameter and kinematic viscosity, the Reynolds number is calculated. It decides the flow regime: laminar below about Re = 2,300, turbulent above; in coiled tubes, the stabilizing curvature shifts the critical Reynolds number to higher values.
- Evaluate the pipe friction factor: In the laminar regime, λ = 64/Re applies (circular pipe; for other cross-sections with a geometry-dependent constant). In the turbulent regime, λ is determined for smooth pipes according to Blasius or Konakov, and for rough pipes according to Colebrook from the Reynolds number and the relative roughness k/d; in fully rough flow, λ depends on k/d only.
- Account for additional influences: For coiled tubes, the increase in the friction factor due to the secondary flow is corrected via the ratio of tube to coil diameter; for annular gaps, the radius ratio enters. Non-isothermal flow can be captured via property corrections (wall-to-bulk viscosity ratio).
- Calculate the pressure drop: The friction pressure drop follows from Δp = λ·(L/d)·ρ·w²/2. For geodetic elevation differences or density changes, the corresponding terms of the extended Bernoulli equation are added; fittings and components are supplemented via separate resistance coefficients (module L1.3).
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Pipe length | l | m |
| Pipe inside diameter | di | m |
| Free flow cross-section | f | m² |
| Wetted perimeter | u | m |
| Absolute roughness | k | m |
| Density | ρ | kg/m³ |
| Velocity | w | m/s |
| Dynamic viscosity | η | mPa·s |
| Factor for shape of cross-section | φ | - |
| Laminar flow | Re | - |
| Laminar flow | Recrit | - |
| Spiral diameter | DC | m |
| Spiral pitch | h | m |
| Volume flow per pipe | VR | m³/s |
| Total mass flow | mg | kg/s |
| Number of pipes with parallel flow | NR | - |
| Mass flow per pipe | mR | kg/s |
| Hydraulic diameter (Di-da) | dh | m |
| Total mass flow | mg | kg/s |
| Inside diameter of external pipe | Di | m |
| Outside diameter of internal pipe | da | m |
| Hydraulic diameter | dh | m |
| Kinematic viscosity | ν | m²/s |
| Geometry of the cross-section | Rechteckrohr | – |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Drag coefficient | ξ | - |
| Drag coefficient | ξ | - |
| Pressure drop | Δp | Pa |
| Laminar flow | Re | - |
| Laminar flow | Recrit | - |
| Flow pattern | turbulent | - |
Calculation options
Geometry of the cross-section
Any · rectangular
Type of tube
Straight pipes · Coils · Straight pipes with noncircular cross-section · Annulus
Worked example
Water at 20 °C flows at 1.5 m/s through a hydraulically smooth pipe with an inside diameter of 50 mm and a length of 25 m. Calculate the friction pressure drop in this worked example.
Given values
| Inside diameter d | 50 mm |
| Pipe length L | 25 m |
| Flow velocity w | 1.5 m/s |
| Density of water (20 °C) ρ | 998 kg/m³ |
| Kinematic viscosity ν | 1.004·10⁻⁶ m²/s |
Solution
Determine the Reynolds number
Re = w·d/ν = 1.5 m/s · 0.05 m / 1.004·10⁻⁶ m²/s = 74,700
The flow is turbulent (Re > 2,300) and lies within the range of validity of the Blasius equation (Re < 10⁵).
Pipe friction factor according to Blasius
λ = 0.3164/Re0.25 = 0.3164/74,7000.25 = 0.0191
Calculate the pressure drop
Δp = λ · (L/d) · ρ · w²/2
Δp = 0.0191 · (25/0.05) · 998 kg/m³ · (1.5 m/s)²/2
Δp = 0.0191 · 500 · 1,122.75 Pa ≈ 10,700 Pa ≈ 0.107 bar
Result
| Reynolds number Re | 74,700 (turbulent) |
| Pipe friction factor λ | 0.0191 |
| Friction pressure drop Δp | approx. 10,700 Pa ≈ 0.107 bar |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Above which Reynolds number is the flow turbulent?
In a straight pipe, the critical Reynolds number is about 2,300; below it, the flow is stably laminar. Between roughly 2,300 and 10,000 lies a transition region with increased uncertainty in the friction factor — for design purposes this region should be avoided or treated conservatively. In coiled tubes, the curvature has a stabilizing effect, so transition occurs only at significantly higher Reynolds numbers.
When may I calculate with a 'hydraulically smooth' pipe?
If the wall roughness elements lie completely within the viscous sublayer, they do not influence the friction — the pipe behaves as smooth. Whether that applies depends on the ratio of roughness height to viscous sublayer thickness, i.e. on k/d and Re. Drawn stainless steel and plastic pipes are usually hydraulically smooth; scaled, encrusted or cast-iron lines must be calculated with roughness according to Colebrook. When in doubt, the rough calculation delivers the conservative pressure drop.
How accurate is the hydraulic-diameter approach for non-circular cross-sections?
For turbulent flow, the hydraulic diameter delivers good results with errors of typically a few percent. In the laminar regime, however, it fails: there, the product λ·Re depends on the cross-sectional shape (circular pipe 64, plane gap 96, square 57). The VDI Heat Atlas provides shape-specific constants for this, which the module uses.
Why does a coiled tube have a higher pressure drop than a straight pipe of the same length?
The centrifugal force drives the faster core fluid outward and generates a twin-vortex secondary flow (Dean vortices). This increases the wall shear stress and thus the friction factor — the more so, the larger the ratio of tube diameter to coil diameter. At the same time, the secondary flow improves the heat transfer — coiled tubes thus buy better heat transfer at the cost of higher pressure drop.