A decrease in the density of the fluid in which a vessel floats requires an increase in the volume of displacement in order to satisfy static equilibrium requirements. Therefore, a ship moving from salt water to fresh water, for example, experiences an increase in draft, . This increase can be calculated by equating the increase in displacement volume to the volume of a layer of buoyancy of uniform thickness, , distributed over the original load waterplane. The increase in displacement volume,

where subscript S refers to salt water, subscript F to fresh water. But, on the assumption that the ship is "wall-sided," the equal layer of buoyancy is,

Hence,

and the increase in draft is,

where is displacement volume, is mass density, is waterplane area, and is specific gravity.

The centroid of the underwater body may shift, both vertically and longitudinally, with such a change in medium. In particular, an increase in draft as a result of a decrease in fluid density causes the vertical location of the center of buoyancy to rise with respect to the keel as a result of the increase in displacement volume, .

When a ship becomes partially supported by mud of mass density ' the volume of displacement must decrease to the point where the sum of products of volume of displacement in the medium multiplied by the density of the medium equals the weight of the vessel. Correspondingly, the center of buoyancy may be found, using methods by calculating the buoyant moment as the sum of products of buoyancy from each medium, multiplied by the distance to the centroid of each volume.

It is important to use the correct density of the water in making displacement calculations. There is about a percent difference between the density of fresh water, as in the Great Lakes, and the salt water of the oceans. The water in some rivers and harbors and off the mouth of estuaries is usually brackish, and its density may vary considerably with the tides. When draft readings are taken to determine displacement, samples of the water should be taken at the same time in order to determine its density.

In principle, since the density of water changes slightly with temperature, a correction should be made to account for any differences from an agreed upon temperature standard. Furthermore, the temperature coefficient of expansion of steel may influence the volume of displacement of a steel vessel slightly up to any waterline if the temperature of the steel differs significantly from the standard.

• Formulas For Area, Moment, Centroid, Moment of Inertia, and Gradius. - 2009-05-04 - 02:49:10
• Geometrical Modification to Lines. - 2009-05-04 - 01:43:43
• Definitions and Uses of Coefficients - 2009-05-03 - 11:48:25
• Displacement and Center of Buoyancy - 2009-05-03 - 12:28:00
• Use of Computer in Lines Definition, Mathematical Lines - 2009-05-02 - 03:04:08
• Methodical Lines In Ship Geometry - 2009-05-02 - 01:59:06
• Developable and Straight Frame Lines - 2009-05-02 - 01:27:07
• Offsets In Ship Geometry - 2009-05-02 - 12:10:24
• Developing a Set of Lines In Ship Geometry - 2009-05-01 - 01:34:25

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