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Hydrodynamic mass is the equivalent dynamic mass of external fluid vibrating with the tube. In liquid flow, the hydrodynamic mass per unit length of a tube confined within a tube bundle may be expressed by

Fig. 2-6 Hydrodynamic Mass in Two‐Phase Cross Flow: Comparison Between Theory and Experiments. (Note that m_ℓ is the hydrodynamic mass per unit length in liquid.)

(2.9)

where D_e is the equivalent diameter of the surrounding tubes and the ratio D_e/D is a measure of confinement. The effect of confinement is formulated by

(2‐10)

for a tube inside a triangular tube bundle (Rogers et al, 1984). Similarly, for a square tube bundle (Pettigrew et al, 1989a) confinement may be approximated by

(2‐11)

The hydrodynamic mass of tube bundles subjected to two‐phase cross flow may be calculated with Eq. (2-9) provided that the homogeneous density of the two‐phase mixture, ρ_TP, is used in the formulation (Pettigrew et al, 1989a). Figure 2-6 compares Eq. (2-9) to experimental data.

The total dynamic mass of the tube per unit length, m, comprises the hydrodynamic mass per unit length, m_h, the tube mass per unit length, m_t, and the mass per unit length of the fluid inside the tube, m_i:

(2‐12)

See Chapter 4 for more detail on hydrodynamic mass.