Engineering guide
The FDP module calculates the pressure drop in piping with fittings for compressible and incompressible adiabatic flow. In addition to the friction pressure drop of the straight pipe run, individual resistances such as bends, valves, dampers, orifices and nozzles as well as changes of cross-section (reducers, conical transitions) and the inlet pressure drop from a vessel are taken into account; geodetic elevation differences between inlet and outlet also enter the balance.
The basis is well-established sources of engineering fluid mechanics: Kalide ("Technische Strömungslehre"), Cerbe/Hoffmann ("Gastechnik") and the Phoenix-Rheinrohr documents on calculating pressure losses in piping. Liquids are calculated with constant density; gases with compressible adiabatic pipe flow, in which density and velocity change along the line.
Being able to calculate the pressure drop of a pipeline is the foundation of every hydraulic design in plant engineering: for sizing pumps and compressors, selecting nominal diameters, checking allowable flow velocities and balancing pressures between items of equipment.
Scope
- Pressure drop in pipes with fittings
Typical workflow
Define flow rate and medium
Volumetric or mass flow rate, inlet pressure and inlet temperature are specified; the medium is described by its density and dynamic viscosity. For gases, the inlet state is the starting point of the compressible calculation.
Describe the pipeline
The inside diameter, length and absolute roughness of the pipeline define the friction component; the geodetic inlet and outlet elevations capture the static head component of the pressure balance.
Determine flow regime and friction factor
The Reynolds number is formed from velocity, diameter, density and viscosity. The pipe friction factor λ follows in the turbulent range from the resistance law for rough pipes (Colebrook range), in the laminar range from λ = 64/Re.
Apply fittings and inlet
For each fitting — bends, valves, dampers, orifices, cross-section transitions — the resistance coefficient ζ is applied; the inlet pressure drop from the vessel accounts for the acceleration of the fluid from the vessel velocity to the pipe velocity.
Balance the pressure drop
The friction component, the sum of the individual resistances and the elevation component are combined into the total pressure difference. For compressible flow, the change of state along the line is taken into account, so that the outlet pressure is determined consistently with the changing specific volume.
Frequently asked questions
When do I have to calculate compressibly, and when is the incompressible calculation sufficient?
As a rule of thumb: if the pressure drop stays below about 5 to 10% of the absolute pressure, the incompressible calculation with the density at the mean state delivers sufficiently accurate results. With larger relative pressure reductions, the gas expands noticeably, and velocity and the friction component increase along the line — then the compressible adiabatic pipe flow calculation is required, as provided by the module.
Which roughness values are reasonable?
The absolute roughness depends on the material and its condition: new seamless steel pipes about 0.02 to 0.1 mm, galvanized pipes around 0.15 mm, rusted or encrusted lines considerably more. Since λ reacts sensitively to the relative roughness k/d in the transition range, the aged condition should be assumed for operating lines, not the as-new condition.
Why is the inlet from the vessel treated separately?
At the transition from the nearly stagnant vessel contents into the pipeline, the fluid must be accelerated to pipe velocity; in addition, a separation loss arises depending on the inlet geometry (sharp-edged, chamfered, rounded). The module captures both via the velocity in the vessel and the inlet pressure drop — if this component is forgotten, the calculated head is distinctly too optimistic for short lines.
Can ζ values from manufacturer catalogues be used?
Yes, and for valves this is actually preferable: catalogue values (ζ or Kvs) apply to the specific design and nominal size, whereas literature values are averages for classes of designs. Note that ζ values are always referenced to a defined reference velocity — for cross-section transitions typically to the velocity in the narrower cross-section.
Worked example
Water at 20 °C flows at 50 m³/h through a 100 m long steel pipeline with an inside diameter of 100 mm (absolute roughness 0.05 mm). The run contains two 90° bends (ζ = 0.3 per bend) and a shut-off valve (ζ = 4.0). Find the pressure drop of the horizontal line — a classic worked example of a pipe pressure drop calculation.
Given
| Volumetric flow rate Q | 50 m³/h |
|---|---|
| Inside diameter d | 100 mm |
| Pipe length L | 100 m |
| Absolute roughness k | 0.05 mm |
| Density ρ (water, 20 °C) | 998 kg/m³ |
| Dynamic viscosity η | 1.002·10⁻³ Pa·s |
| Individual resistances Σζ | 2 · 0.3 + 4.0 = 4.6 |
Solution
Flow velocity and Reynolds number
A = π/4 · d² = π/4 · (0.1 m)² = 0.007854 m²
v = Q/A = (50/3600 m³/s) / 0.007854 m² = 1.77 m/s
Re = v · d · ρ / η = 1.77 · 0.1 · 998 / 1.002·10⁻³ ≈ 1.76·10⁵ → turbulent
Friction factor according to Colebrook
With k/d = 0.05/100 = 0.0005, iterative evaluation of the Colebrook equation 1/√λ = −2·log[2.51/(Re·√λ) + k/(3.71·d)] yields:
λ ≈ 0.0190
Friction pressure drop of the straight run
ΔpR = λ · L/d · ρ/2 · v² = 0.0190 · (100/0.1) · (998/2) · 1.77² ≈ 29,700 Pa ≈ 0.297 bar
Pressure drop of the fittings and total pressure drop
Δpζ = Σζ · ρ/2 · v² = 4.6 · (998/2) · 1.77² ≈ 7,200 Pa ≈ 0.072 bar
Δptot = ΔpR + Δpζ ≈ 29,700 + 7,200 ≈ 36,900 Pa ≈ 0.37 bar
Result
| Flow velocity | 1.77 m/s |
|---|---|
| Reynolds number | 1.76·10⁵ |
| Friction factor λ | 0.0190 |
| Pressure drop, straight run | 0.297 bar |
| Pressure drop, fittings | 0.072 bar |
| Total pressure drop | approx. 0.37 bar |
Technical content source: LV-Solved-Problems-Content 628d313247e7