Engineering task and calculation objective
The LOGI module calculates the pressure drop across grids and perforated plates in ducts and piping. Such internals are found throughout process equipment and plant engineering: as flow straighteners upstream of metering runs, as support and distributor trays in columns, as protective screens in intake ducts, or as support grids for packed beds and filters. Anyone who wants to calculate the pressure drop of a perforated plate needs its resistance coefficient as a function of geometry and Reynolds number – which is exactly what this module delivers.
Starting from the selected geometry, the fluid properties (density, dynamic or kinematic viscosity) and the mass or volume flow, the module determines the velocities in the free approach cross-section F1 and in the narrowest cross-section F0, the Reynolds number in F0, the resistance coefficient and, from that, the pressure drop. The calculation is based on the established resistance correlations for orifices, grids and perforated plates as documented in the standard literature (e.g. Idelchik, VDI Heat Atlas).
Calculation workflow
- Define the geometry: First, the geometry of the internal is selected: perforated plate or grid with the associated free area ratio F0/F1, hole diameter and plate thickness. The open-area ratio is the dominant parameter governing the resistance.
- Enter fluid properties and flow rate: Density and dynamic or kinematic viscosity of the fluid are specified together with the mass or volume flow; mass and volume flow are coupled via the density.
- Calculate velocities and Reynolds number: From the volume flow follow the approach velocity in F1 and the velocity in the narrowest cross-section F0. Using the hole dimension as the characteristic length, the Reynolds number in F0 is formed, which determines the range of validity of the resistance correlation.
- Determine the resistance coefficient: For the selected geometry, the correlation delivers the resistance coefficient as a function of open-area ratio, relative plate thickness and Reynolds number. At low Reynolds numbers, an additional viscosity-related contribution is added.
- Evaluate the pressure drop: The pressure drop follows from the resistance coefficient and the dynamic pressure of the reference velocity. It grows quadratically with the flow rate and disproportionately with decreasing open-area ratio.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Depth of grid | l | m |
| Mesh size (width) | a | m |
| Mesh size (height) | b | m |
| Grid thickness | s | m |
| Area of one mesh | F | m² |
| Circumference of one mesh | U | m |
| Bore diameter | dh | m |
| Free cross section area | F1 | m² |
| Cross section area of bores | F0 | m² |
| Porosity of cross setion | f | - |
| Density | ρ | kg/m³ |
| Kinematic viscosity | ν | m²/s |
| Mass flow | m | kg/s |
| Volume flow | V | m³/s |
| Velocity in F1 | w1 | m/s |
| Velocity in F0 | w0 | m/s |
| Reynolds number in F0 | Re0 | - |
| tau | τ = | - |
| lam | λ = | - |
| with | ε0 · Re0 = | - |
| Xsi_m | ξm = | - |
| Re>10^5) | ξ1qu = | - |
| Number of bores | z | - |
| Porosity in the mesh | f0 | - |
Calculated results
| Quantity | Symbol | Unit |
|---|---|---|
| Friction factor | ξ | - |
| Pressure drop | Δp | Pa |
Calculation options
Geometry
Grid · Perforated plate
Worked example
A perforated plate with sharp-edged holes (hole diameter 20 mm, open-area ratio F0/F1 = 0.40) is installed in a DN 200 pipe (inside diameter 200 mm). The pipe carries 250 m³/h of water at 20 °C (density 998 kg/m³, kinematic viscosity 1.004 · 10−6 m²/s). Find the hole velocity, Reynolds number, resistance coefficient and pressure drop – a worked example of a perforated plate pressure drop calculation.
Given values
| Pipe inside diameter D | 200 mm |
| Open-area ratio f = F0/F1 | 0.40 |
| Hole diameter d0 | 20 mm |
| Volume flow V̇ | 250 m³/h |
| Density ρ (water, 20 °C) | 998 kg/m³ |
| Kinematic viscosity ν | 1.004 · 10⁻⁶ m²/s |
Solution
Velocities in F1 and F0
Approach cross-section: F1 = π/4 · (0.2 m)² = 0.0314 m².
w1 = V̇ / F1 = (250/3600) / 0.0314 = 2.21 m/s.
Hole velocity: w0 = w1 / f = 2.21 / 0.40 = 5.53 m/s.
Reynolds number in the hole
Re0 = w0 · d0 / ν = 5.53 · 0.02 / 1.004 · 10−6 ≈ 1.1 · 10⁵ — the flow is fully turbulent, so the resistance coefficient is independent of Re.
Resistance coefficient (thin, sharp-edged perforated plate)
According to Idelchik, for the thin, sharp-edged perforated plate, referred to the hole velocity w0:
ζ0 = (1 + 0.707 · √(1 − f) − f)² = (1 + 0.707 · √0.60 − 0.40)² = 1.1476² = 1.32.
Referred to the approach velocity w1: ζ1 = ζ0 / f² = 1.32 / 0.16 ≈ 8.2.
Pressure drop
Δp = ζ0 · ρ/2 · w0² = 1.32 · 499 · 5.53² ≈ 20,100 Pa ≈ 0.20 bar.
Result
| Hole velocity w0 | 5.53 m/s |
| Reynolds number Re0 | ≈ 1.1 · 10⁵ |
| Resistance coefficient ζ0 (referred to w0) | 1.32 |
| Pressure drop Δp | ≈ 0.20 bar |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Which velocity is the resistance coefficient referred to?
This is the most common source of error: coefficients may be referred to the approach velocity in F1 or to the hole velocity in F0. The two differ by the factor (F1/F0)². The module reports both velocities separately; when comparing with literature values, the reference must match.
Why does the pressure drop rise so sharply at small open-area ratios?
On the one hand, the hole velocity grows inversely with the free cross-section, and the dynamic pressure enters quadratically. On the other hand, the jet contracts further downstream of sharp-edged openings (vena contracta), and the kinetic energy of the jet is largely dissipated as it re-expands.
What influence does the thickness of the perforated plate have?
For thin, sharp-edged plates, the jet contraction governs the loss. With increasing relative thickness (thickness to hole diameter), the flow reattaches inside the hole; pipe friction inside the hole is added, while at the same time the exit loss decreases. Rounded or chamfered hole edges reduce the coefficient significantly.
Does the calculation also apply to gases?
Yes, as long as the flow can be treated as incompressible, i.e. the pressure drop remains small compared with the absolute pressure (rule of thumb: Mach number in the hole below about 0.3). At higher pressure ratios, compressibility and possibly choked flow must be considered separately.