Heat Exchanger Design
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ρV 2 calculation for shell & tube heat exchangers
ρV 2 is a key momentum-based check used to screen for vibration risk in shell-and-tube heat exchangers. This article explains how TEMA defines and applies ρV 2, with emphasis on correctly determining flow areas at critical locations.
By Thaung Aung, Principal Engineer, Covestro LLC
In today’ s fast-paced engineering environment, professionals increasingly rely on heat exchanger simulation software to determine critical ρV ² values. This article analyzes the ρV ² formulas provided in TEMA Standards Section 10, offering engineers deeper insight into these values— particularly valuable when equipment modifications become necessary. The ρV ² parameter( density multiplied by velocity squared) serves as a indicator in heat exchanger design, often referred to as a“ vibration check”; however, reader is advised to refer to the TEMA Standard, Section 6, Flow Induced Vibration, for complete vibration mechanisms.
In the term ρV ², density( ρ) shall be a known parameter in equipment design. Since volumetric flow rate( Q) remains constant throughout the system according to the Continuity principle, the calculating velocity( V) fundamentally becomes an exercise in determining the appropriate flow area( A) perpendicular to the flow direction at critical locations.
V( ft 3 / s) = Q( ft 3 / s) / A( ft 2)
Shell nozzle area( location 1) In the nozzle, flow is in one direction and perpendicular to its cross-sectional area; therefore, flow area is the area of the nozzle ID. ρV 2 ρV ² directly impacts the mechanical integrity and performance of heat exchangers by quantifying the momentum flux of fluid entering the equipment. TEMA defines a limit of ρV 2( lb / fts 2).
• < 1500 for noncorrosive, nonabrasive, singlephase fluids for the shell-side nozzle, Location 1 in Figure 1
• < 4000 for shell entrance and the bundle entrance, Location 2
• < 4000 for the bundle entrance, Location 3
Figure 2: Nozzle flow area.
The nozzle inner diameter( Dn) is used to calculate the nozzle inlet areas.
A n
( ft 2) =( πD 2 n( in2) / 4) ×( ft 2 / 144 in 2)
Shell entrance / exit area( Location 2) The following formula is used to find shell entrance / exit area:
A s
=( πD n h + F 1
((( π / 4) × D 2 n) ×(( P t – D t) x( F 2 P t))))
×( ft 2) / 144 in 2
Breakdown of the formula: At the shell entrance / exit, there are two flow paths: radial flow and axial flow represented in Figure 3.
Figure 1. Locations of shell-side fluid of shell & tube exchanger for ρV ² check.
Figure 3: Shell entrance radial and axial flows.
40 Heat Exchanger World October 2026 www. heat-exchanger-world. com