Engineering task and calculation objective
The RDV module calculates the tube-side pressure drop in shell-and-tube heat exchangers according to Verfahrenstechnische Berechnungsmethoden, Part 1: Heat Exchangers (VCH, Weinheim 1987), a German process engineering reference. From the geometry of the unit — tube inside diameter, number of tube-side passes, tubes per pass, tube length, nozzle diameters, straight-tube or U-tube construction — and the fluid properties, the individual pressure drop contributions are reported separately and summed to the total pressure drop.
Having to calculate the tube-side pressure drop is part of every heat exchanger design and rating: it decides the required pump or compressor power, compliance with the pressure drop limit granted by the customer, and indirectly the choice of the number of passes, which in turn sets the flow velocity and thus the heat transfer. The module covers the frictional pressure drop in the tubes (with viscosity and convection corrections for heated or cooled flow), the losses at inlet, outlet and the turnarounds between passes, as well as the pressure drops in the inlet and outlet nozzles; a fouling factor accounts for service conditions.
Through its links to the property and geometry modules of the ATLAS program system, almost all input values can be imported, so that the pressure drop and heat transfer calculations are consistently based on the same data.
Standard and calculation basis: Verfahrenstechnische Berechnungsmethoden / Teil 1: Wärmeübertrager VCH Verlagsgesellschaft, Weinheim, 1987
Calculation workflow
- Fluid properties at the mean state: The mean temperature is formed from the inlet and outlet temperatures; density, dynamic viscosity, thermal conductivity and specific heat capacity of the fluid are evaluated there — optionally for liquid or gas, for gases additionally with the inlet pressure.
- Geometry and flow cross-section: The tube inside diameter follows from the tube outside diameter and wall thickness; together with the number of tubes per pass, this yields the flow cross-section and from it the flow velocity in the tubes.
- Frictional pressure drop in the tubes: The friction factor (Fanning factor, isothermal) is determined from the Reynolds number and adjusted with the correction factors for viscosity (wall temperature effect for heating/cooling) and convection. Over the total tube length of all passes, this gives the friction contribution.
- Inlet, outlet and turnaround losses: For the inlet, the outlet and the turnarounds between passes — depending on the number of passes and the construction (straight tube or U-tube) — a resistance coefficient is applied and the associated pressure drop is calculated from the dynamic pressure.
- Nozzle losses: From the inside diameters of the inlet and outlet nozzles, the velocities there and the pressure drops in the inlet and outlet nozzles are determined separately.
- Total pressure drop: Summing according to ΔP = Ft·ΔPt + ΔPe + ΔPN,e + ΔPN,a yields the total pressure drop, where the fouling factor Ft increases the friction contribution for the fouled service condition.
Input quantities
| Quantity | Symbol | Unit |
|---|---|---|
| Mean temperature ϑm = (ϑe +ϑa) / 2 | ϑm | °C |
| Mean temperature ϑm = (ϑe +ϑa) / 2 | ϑm | °C |
| Density | ρ | kg/m³ |
| Density | ρ | kg/m³ |
| Specific heat capacity | cp | J/(kg·K) |
| Thermal conductivity | λ | W/(m·K) |
| Dynamic viscosity | η | mPa·s |
| Dynamic viscosity | η | mPa·s |
| Inside nozzle diameter (inlet) | dN,e | m |
| Inside nozzle diameter (outlet) | dN,a | m |
| Number of tube-side passes | nP | - |
| Number of tubes per pass | nR | - |
| Length of one tube | L | m |
| Tube inside diameter | di | m |
| Tube outside diameter | da | m |
| Tube wall thickness | s | m |
| Mass flow | m | kg/s |
| Mean velocity in the tube | w | m/s |
| Reynolds number | Re | - |
| Prandtl number | Pr | - |
| Grashof number | Gr | - |
| Friction factor (inlet, outlet and baffle) | Ke | - |
| Fanning friction factor (tube, isothermal) | ξis | - |
| Correction factor for the viscosity | Φ | - |
Calculation options
Type: Straight tube / U-tube?
Straight tube · U-Tube · Bends
Fluid: liquid / gaseous?
Liquid · 1
Worked example
Water at 20 °C flows at w = 1.5 m/s through the tubes of a two-pass shell-and-tube heat exchanger (2 passes, tube length 4 m per pass, tube inside diameter di = 16 mm). This worked example estimates the frictional pressure drop in the tubes (smooth tubes, clean condition, without nozzle and turnaround losses).
Given values
| Tube inside diameter di | 16 mm |
| Flow path length L (2 × 4 m) | 8 m |
| Flow velocity w | 1.5 m/s |
| Density ρ (water, 20 °C) | 998 kg/m³ |
| Dynamic viscosity η (water, 20 °C) | 1.0 mPa·s |
Solution
Reynolds number
Re = ρ · w · di / η = 998 · 1.5 · 0.016 / 0.001
Re ≈ 23,950 — turbulent flow.
Friction factor (smooth tube, Blasius)
λ = 0.3164 / Re0.25 = 0.3164 / 23,9500.25
λ ≈ 0.0254
Frictional pressure drop
Δpt = λ · (L/di) · (ρ/2) · w² = 0.0254 · (8/0.016) · (998/2) · 1.5²
Δpt ≈ 14,300 Pa ≈ 0.14 bar
For the complete verification, the losses for inlet, outlet and turnarounds, the nozzle losses, and the fouling factor applied to the friction contribution are added.
Result
| Reynolds number Re | ≈ 23,950 |
| Friction factor λ | 0.0254 |
| Frictional pressure drop Δpt | ≈ 0.14 bar |
All values are illustrative. The applicable standard and project-specific boundary conditions remain authoritative.
Frequently asked questions
Why is the friction contribution multiplied by a fouling factor?
Deposits narrow the tube cross-section and increase the wall roughness; both raise the frictional pressure drop in service considerably compared with the clean as-new condition. The fouling factor Ft therefore specifically scales the friction contribution ΔPt, while nozzle and turnaround losses remain essentially unchanged. Anyone calculating only the clean condition underestimates the pressure drop over the service life.
What is the viscosity correction factor for?
In heated or cooled tubes the viscosity at the wall deviates from that at the mean temperature. When heating a liquid, the wall viscosity drops and the pressure drop comes out lower than an isothermal calculation would give; when cooling, the opposite occurs. The correction factor — typically applied as a power of the viscosity ratio — captures this effect; for viscous media such as oils it is substantial.
How does the number of tube-side passes influence the pressure drop?
Doubling the number of passes at the same tube count halves the cross-section per pass and doubles the velocity; since the friction loss grows roughly with the square of the velocity and additionally with the flow path length, the pressure drop rises roughly with the third power of the number of passes. On top of that, turnaround losses are added for each pass change. The number of passes is therefore the most important lever in the trade-off between good heat transfer and permissible pressure drop.
Does the calculation also apply to gases?
Yes, the module distinguishes between liquid and gaseous fluids. For gases, the density is determined from the inlet pressure and the mean temperature. The prerequisite remains that the pressure drop is small compared with the absolute pressure; at relative pressure drops above a few percent, the density change along the path would have to be taken into account.