CIVL2611 Chap.4 Buoyancy and Floating Stability
Buoyancy and Floating Stability
Buoyancy is the resultant of the hydrostatic pressure field and equals the weight of displaced fluid. This chapter distinguishes fully submerged and floating equilibrium, locates the centre of buoyancy, and introduces the metacentre for small-angle floating stability. The diagrams keep weight, buoyancy and their points of action separate.
Archimedes' principle makes surrounding-fluid density and displaced volume the inputs to buoyancy, while body mass determines weight. A fully submerged released object can accelerate upward or downward before drag develops; a floating object instead adjusts its submerged volume until buoyancy equals weight.
The centre of buoyancy is the centroid of the displaced fluid and may shift when a floating body heels because its underwater geometry changes. That shift distinguishes floating stability from the fixed-centre analysis of a completely submerged body. For small heel, the waterplane second moment and displaced volume determine BM, which combines with the gravity-centre position to give metacentric height.
Positive GM signals an initial restoring tendency, but it does not prove large-angle or dynamic safety. Original block, pontoon and barge problems connect the force picture to computed acceleration, submerged fraction and stability. Directional checks predict how raised cargo reduces stability and how greater waterplane width can strengthen the initial restoring response.
What this chapter covers
- 01
Archimedes' principle
- 02
Displaced volume
- 03
Centre of buoyancy
- 04
Submerged equilibrium
- 05
Floating volume fraction
- 06
Metacentric height and restoring tendency
Worked example · free
Released submerged block
- +1Calculate buoyancy as 4,708.8 newtons upward.
- +1Calculate weight as 3,531.6 newtons downward.
- +1Find net force as 1,177.2 newtons upward.
- +1Divide by mass to obtain 3.27 metres per square second upward.
- +1State that drag develops after motion starts.
Key terms
- Displaced volume
- The volume of surrounding fluid replaced by the submerged portion of a body.
- Centre of buoyancy
- The centroid of the displaced-fluid volume through which buoyancy acts.
- Metacentre
- The small-angle intersection used to assess the restoring tendency of a floating body.
Buoyancy and Floating Stability FAQ
Does body density determine buoyancy?
Buoyancy depends directly on surrounding-fluid density, gravity and displaced volume. Body density affects weight and therefore the resulting motion or floating fraction, but it does not replace fluid density in Archimedes' expression.
What fraction of a uniform body floats below water?
For static floating equilibrium, submerged fraction equals average body density divided by fluid density. This follows by equating body weight with the weight of displaced fluid and cancelling gravity and total volume.
When is metacentric height used?
Use metacentric height for initial small-angle stability of a floating body because its centre of buoyancy shifts as the immersed shape changes. A completely submerged body uses the relative positions of fixed gravity and buoyancy centres instead.
Exam move
Draw the body and waterline, then mark G and B before writing forces. Write body mass or average density beside G and displaced volume with surrounding-fluid density beside B. This visual separation prevents the two densities from entering the wrong force. Practise three states with the same object: fully submerged and held, released from rest, and floating in equilibrium.
In the first, an external tether or support may complete the balance. In the second, weight and buoyancy create an initial acceleration before drag grows. In the third, displaced volume adjusts until buoyancy equals weight. Calculate all three so the stage of motion becomes part of the answer.
For floating fractions, derive the density ratio from force equilibrium rather than memorising it, then check that an object less dense than the fluid has a fraction between zero and one. Stability requires a second set of distinctions. For a completely submerged body, rotate the sketch slightly and draw the separated vertical lines through fixed G and B. Decide whether their couple restores or overturns.
For a floating body, redraw the underwater shape after heel and show B shifting. Add M only for the small-angle floating analysis. Calculate BM from the waterplane second moment divided by displaced volume, place G using the stated BG distance and form GM with a consistent datum. Predict how raising cargo or widening the waterplane changes the result before computing.
If the sign contradicts that prediction, inspect the waterplane axis and point ordering. Check whether the requested conclusion concerns initial small-angle stability or a wider dynamic situation. A positive GM is a local restoring result, not a complete safety guarantee for waves or large heel.
Finish each practice answer with that model boundary and keep an error log for displaced-volume geometry, density choice, force direction, waterplane second moment and vertical datum. Revisit any negative metacentric height by drawing the resulting overturning couple rather than accepting the sign without interpretation. Name the equilibrium being tested.