Why Does A Ship Float At Sea But Sinks In River?

Why Does A Ship Float At Sea But Sinks In River?

There is a misconception among most of us ( non mariners ) that ship float at sea but sinks in river water. Somehow it seems to be obvious as we don’t usually see ship in a river; Right? But in reality a ship floats deeper in river than that at sea due to change in specific density. If you look from a distance as the ship go from sea to river ( fresh water ); it seems the ship is going down slowly over the time as it is sinking. Special allowance with markings are given on ship for this purpose; ex:- Load Line.

To understand why this happen in first place; we need to understand principle of flotation or Archimedes principle in particular. In this post we will discuss displacement, buoyancy, draft and Archimedes principle; explaining how the same iron ship afloat easily at sea but float deeper in fresh water. You might won’t like but i will also use some numerical to explain this phenomenon. So let’s start with basis’s.

Understanding Mass And Volume Relation

In day to day life we use weight and mass interchangeably to such extent that even we sometimes seems to be confused of their distinguished meaning. Mass is the amount of matter a object or substance possess independent of its location or position in this universe. While weight is the force of gravity acting on that mass. Mass is fixed but the weight change from planet to planet and place to place; depending upon the change in force of gravity acting upon that mass.

Do you remember when we use to calculate our weight on mars and moon; the first time we knew the weight on moon is 1 / 6 times that on earth. I do remember doing such calculations without knowing the science behind it. Similarly i use to know the term volume without what it really is ! Volume is the amount of space a object or substance occupies; and the relation between the mass and its volume is called density.

The density of fresh water is 1.0 tonnes / m3 with one metric tonne weight for a volume of one cubic meter. On other hand sea water are heavier due to the presence of a number of salt’s dissolved in the water. With average salinity of 35 gram per 1000 ml of water it weights 1.025 tonnes / m3.

A person Floating In Dead Sea Without any Effort

Principle Of Flotation

According to Archimedes principle when we submerge a substance / object in fluid; there is apparent loss in its weight due to upward buoyant force. This upward force is equal and opposite to the weight of the water it displaced. When a ship displace water volume of more or equal weight in comparison to its own weight; the ship will float and this concept is called principle of flotation. So, a 100,000 tonne ship must displace at least 100,000 tonne of water to stay afloat.

There is two key force acting on a floating body, weight and buoyancy. For a ship to be stable and stay in equilibrium the center of gravity and buoyancy must be in a straight line. Suppose the ship weight is distributed uneven and is tilted on one side along the longitudinal axis; then the point at which original vertical line meets the line passing through center of gravity and buoyancy is called metacenter.

Now the ability of ship to return to its equilibrium position depends upon the center of gravity and metacenter. If the metacenter lie above the center of gravity; then the ship will regain its equilibrium. But when metacenter lies below the center of gravity; the weight and buoyant force leads the ship to topple ( overturn ) causing the ship to sink. To better understand the basic law of Archimedes principle and buoyancy behind this phenomenon simply refer to my old post.

Displacement, Draft And T.P.C Curve

The mass of a freely floating ship with its downward weight equals to the upward buoyant force is known as displacement. In other words displacement of a ship is the product of water density and volume of displacement. In simple words the mass of a ship is what called as displacement with its volume inversely proportional to the density.

Draft on other hand is the vertical distance between the water line and bottom of the hull. In simple words it is the distance of submerged part of the ship. Traditionally draft of a ship is obtained using the draft marks on the ship’s hull. There are six sets of draft marks on a commercial vessel on forward, astern and mid on both port and starboard. For those ( non mariners who don’t know these terms simply understand by Port = Left Side of Ship when propeller on the back; Starboard = Right side of the ship when propeller on the back; Forward is forward and astern is the back portion of the ship.

Displacement ( Δ ) = Volume of Displacement X Density of water

Now using these drafts marks and T.P.C curves we can obtain the displacement of a ship by an accuracy of 0.5%. T.P.C or tonnes per centimeter impression is the mass added or removed from a ship; to change its draft by a centimeter. It is a variable quantity depending upon the water plane area; and is given by T.P.C = 0.01 X Seawater density X water plane area. Water plane is the imaginary plane surface surrounded by water which pass through the ship horizontally.

Variation in water plane area with its draft leads to change in T.P.C; it is then plotted on the graph for a range of draft. The area between this curve and graph axis is then used to represent ships displacement at a given draft. While constructing T.P.C curve ship’s draft are generally represented on the vertical axis while the T.P.C on the horizontal.

Sample T.P.C Displacement Graph ( T.P.C )

Sample T.P.C Displacement Graph

Answering: Why Ship Float Deeper In River Then At Sea

Let’s take a practice example related to human. You might have been through the experience of swimming at sea. Don’t you find it easy to swim in calm sea then in swimming pool or river? You may not believe but in dead sea you won’t even have to put an effort to swim. But how is this possible? The laws responsible for such phenomenon are the same that governs ship floating deeper in river water.

As we know, Displacement Δ = Volume of Displacement X Water Density. So from the equation we get volume of displacement inversely proportional to water density. So when a ship move from sea water to fresh water the water density decrease. As from the T.P.C curve we knew ships displacement is proportional to its draft; hence the draft of a ship increase with increase in volume of displacement.

Let us assume you put a 100 gram miniature ship in tub filled with sea water. This ship displace a 100 gram of water in that tub; but when put in another tub filled with fresh water the ship still displace the same 100 gram of water but with more volume. This is because the weight of sea water is more than that of a fresh water due to dissolved salts and minerals. Therefore a ship ( miniature or real ) will float a little deeper in river then that at sea.

Numerical’s Related To The Topic

Q.1 A ship with 12240 m3 displaced volume go from sea to river. Find the displacement of the ship including the cargo to be displaced to maintain the same draft?

Ans: Displacement of ship = Volume of displacement X Water density

= 12240 X 1.025

= 12546 tonnes

Now, As we knew;

Displacement in Fresh waterFresh Water Density = Displcement at SeaSea water Density

Or,

Displacement in River = 12546 X 10001.025

∴ Cargo to be discharged to maintain same draft = 12546 – 12240

= 306 Tonnes

Q.2 A miniature ship with 7.5 cm draft in pound water of 1006 kg/m3 density is then transfered to a tub filled with sea water. How much will its draft in sea water ?

Ans: As there is no cargo discharged ( not possible with miniature ship ) the displacement remains same.

∴ Volume of displacement in sea water sea X Sea water Density = Volume of displacement in pound water X Pound water Density

Or,

12 = ρ1ρ2

Now we knew that the bock coefficient ( CB ) is the ratio of volume of displacement and product of draft, length and breath.

block cofficient

CB = LBD

Or, ∇ = CB X L X B X D; But as here CB , B and L are constant.

Therefore;

Draft at Fresh waterDraft at Sea = Density of Sea WaterDensity of Fresh Water

∴ New Draft =

7.5 X 10061025

= 7.365 cm.

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