**Recommendation on a standard method for evaluating cross-flooding arrangements**

THE MARITIME SAFETY COMMITTEE,

RECALLING Article 28(b) of the Convention on the International Maritime Organization concerning the functions of the Committee,

RECALLING ALSO resolution A.266(VIII) entitled “Recommendation on a standard method for establishing compliance with the requirements for cross-flooding arrangements in passenger ships”, adopted by the Assembly at its eighth session,

NOTING that the above Recommendation does not include provisions for cross-flooding arrangements other than pipes (i.e., cross-flooding times through ducts) or a provision to ensure adequate air ventilation for efficient cross-flooding (i.e., to account for the restrictive effect of air counter pressure during cross-flooding),

NOTING ALSO the revised SOLAS chapter II-1 subdivision and damage stability requirements for passenger and cargo ships, adopted by resolution MSC.216(82),

RECOGNIZING the need to establish a methodology for evaluating cross-flooding arrangements on ships subject to the applicable subdivision and damage stability requirements of SOLAS chapter II-1 to ensure uniform treatment of cross-flooding and equalization arrangements,

HAVING CONSIDERED the recommendations made by the Sub-Committee on Stability and Load Lines and on Fishing Vessels Safety at its fiftieth session,

- ADOPTS the Recommendation on a standard method for evaluating cross-flooding arrangements, the text of which is set out in the Annex to the present resolution;
- INVITES Governments to apply the annexed Recommendation to cross-flooding calculations and to bring the Recommendation to the attention of all parties concerned.

## Annex

### 01 Definitions

**1 Definitions**

S^{k}: | Sum of friction coefficients in the considered cross-flooding arrangement. | |

S (m): ^{2} | Cross-section area of the cross-flooding pipe or duct. If the cross-section area is not circular, then: | |

A = actual cross-section area P = actual cross-section perimeter | ||

Angle before commencement of cross-flooding. This assumes that the cross-flooding device is fully flooded but that no water has entered into the equalizing compartment on the opposite side of the damage (see appendix 1). | ||

Heel angle at final equilibrium | ||

Any angle of heel between the commencement of cross-flooding and the final equilibrium at a given time. | ||

Volume of water which is used to bring the ship from commencement of cross-flooding to final equilibrium . | ||

Volume of water which is used to bring the ship from any angle of heel to the final equilibrium . | ||

Head of water before commencement of cross-flooding, with the same assumption as for . | ||

Head of water when any angle of heel is achieved. | ||

Final head of water after cross-flooding ( h = 0, when the level inside the_{f}equalizing compartment is equal to the free level of the sea). |

### 02 Formulae

**2 Formulae****2.1** Time required from commencement of cross-flooding to the final equilibrium :

**2.2** Time required to bring the ship from any angle of heel to the final equilibrium :

**2.3** Time required from commencement of cross-flooding until any angle of heel is achieved:

**2.4** Dimensionless factor of reduction of speed through an equalization device, being a function of bends, valves, etc., in the cross-flooding system:

where *F* is not to be taken as more than 1.

Values for *k* can be obtained from appendix 2 or other appropriate sources.

**2.5** Cross-flooding through successive devices of different cross-section:

If the same flow crosses successive flooding devices of cross-section S_{1}, S_{2}, S_{3}… having corresponding friction coefficients k_{1}, k_{2}, k_{3}…, then the total k coefficient referred to S_{1} is:

**2.6** If different flooding devices are not crossed by the same volume, each k coefficient should be multiplied by the square of the ratio of the volume crossing the device and the volume crossing the reference section (which will be used for the time calculation):

**2.7** For cross-flooding through devices in parallel that lead to the same space, equalisation time should be calculated assuming that:

S · F = S_{1} · F_{1} + S_{2} · F_{2} + …

With for each device of cross-section S_{i}

### 03 Air pipe venting criteria

**3 Air pipe venting criteria3.1** In arrangements where the total air pipe sectional area is 10% or more of the cross-flooding sectional area, the restrictive effect of any air back pressure may be neglected in the cross-flooding calculations. The air pipe sectional area should be taken as the minimum or the net sectional area of any automatic closing devices, if that is less.

**3.2** In arrangements where the total air pipe sectional area is less than 10% of the cross-flooding sectional area, the restrictive effect of air back pressure should be considered in the cross-flooding calculations. The following method may be used for this purpose:

The *k* coefficient used in the calculation of cross-flooding time should take into account the drop of head in the air pipe. This can be done using an equivalent coefficient k_{e}, which is calculated according to the following formula:

### 04 Alternatives

**4 Alternatives**

As an alternative to the provisions in sections 2 and 3, and for arrangements other than those shown in appendix 2, direct calculation using computational fluid dynamics (CFD), time-domain simulations or model testing may also be used.

## Appendix 1

**Example for treatment of heel angles and water heads at different stages of cross-flooding**

See annex / Zie bijlage …….

**Figure 1**

## Appendix 2

**Friction coefficients in cross-flooding arrangement**

**Figure 2**

**Figure 13Cross-flooding through a series of structural ducts with 1 manhole**

Note: *k* is the friction coefficient related to each space between two adjacent girders. *k* is evaluated with effective cross-section area therefore in calculations use the real cross-section area A and not S_{equiv}. The pressure loss for entrance in the first manhole is already computed in the calculation, and k = 1 has to be added to take into account the outlet losses.

**Figure 14**

**Cross-flooding through a series of structural ducts with 2 manholes**

**Note:***k* is the friction coefficient related to each space between two adjacent girders. **k** is evaluated with effective cross-section area therefore in calculations use the real cross-section area A and not S_{equiv}. The pressure loss for entrance in the first manhole is already computed in the calculation, and k = 1 has to be added to take into account the outlet losses.

## Appendix 3

**Example using figures for a passenger ship**

Dimension of the considered cross-flooding pipe:

Diameter | D | = | 0.39 m |

Length | l | = | 21.0 m |

Cross-section area | S | = | 0.12 m^{2} |

Wall thickness | t | = | 17.5 mm |

k-values for the considered cross-flooding system:

Sufficient air venting is assumed to be in place.

From this follows:

Time required from commencement of cross flooding to the final equilibrium condition :

Head of water before commencement of cross-flooding:*H _{0} = 5.3m*

Volume of water which is used to bring the ship from commencement of cross-flooding to the final equilibrium condition:

*W*_{f } = 365m^{3}

Final head of water after cross-flooding:

*h _{f}* = 1.5

*m*

Time required to bring the vessel from the maximum allowable angle of heel for final stage of flooding to the final equilibrium condition :

Maximum allowable angle of heel for final stage of flooding | ||

Head of water when the maximum allowable angle of heel for final stage of flooding is achieved | ||

Volume of water which is used to bring the vessel from the maximum allowable angle of heel for final stage of flooding to the final equilibrium condition |

Time required from commencement of cross-flooding until the maximum allowable angle of heel for final stage of flooding is achieved: