ENGG2500 Chap.2 Buoyancy, Stability and Accelerating Fluids
Buoyancy, Stability and Accelerating Fluids
Distributed pressure creates both a resultant force and a line of action. On submerged plane surfaces, centroid pressure determines magnitude while the pressure distribution determines the centre of pressure. Buoyancy equals displaced-fluid weight and acts through the centre of buoyancy.
Floating stability depends on restoring moment geometry, while rigid-body acceleration replaces ordinary gravity with an effective body-force direction. The unifying task is to replace a field by a correctly located resultant, draw every other force on the same body and close force and moment equilibrium without merging magnitude and lever-arm calculations.
What this chapter covers
- 01
Resultant force on plane surfaces
- 02
Centroid and centre of pressure
- 03
Archimedes buoyancy relation
- 04
Floating equilibrium
- 05
Metacentre and initial stability
- 06
Free surfaces under acceleration
Worked example · free
A restrained pontoon
- 1Draw buoyancy upward and weight downward. Marks used here are not a published university marking scheme.
- 1Compute buoyancy as 17.66 kN.
- 1Compute weight as 15.89 kN.
- 1The required downward restraint is 1.77 kN.
Key terms
- Centre of pressure
- The centre of pressure is the point where a hydrostatic resultant acts.
- Centre of buoyancy
- The centre of buoyancy is the centroid of displaced fluid volume.
- Metacentre
- The metacentre locates the intersection used to assess small-angle floating stability.
- Effective gravity
- Effective gravity combines gravitational and imposed reference-frame acceleration.
Buoyancy, Stability and Accelerating Fluids FAQ
Why is the centre of pressure below the centroid?
Pressure on a non-horizontal surface grows with depth, so the lower portion carries more load than the upper portion. The weighted average location of that distributed load therefore lies below the geometric centroid, even though centroid pressure correctly gives the resultant magnitude.
What determines whether a floating body is stable?
A small rotation changes the displaced-volume shape and moves the buoyancy line of action. Stability requires the resulting buoyancy and weight forces to create a restoring moment. For initial stability, a metacentre above the centre of gravity gives a positive metacentric height.
How is an accelerating tank different from ordinary hydrostatics?
The liquid can remain at rest relative to an accelerating tank, but the relevant body force combines gravity with the opposite of the tank acceleration. The free surface becomes perpendicular to that effective acceleration, and pressure changes along the same effective-gravity direction.
How do I find a hydrostatic resultant on a plane surface?
Find the area and the depth of its centroid, evaluate pressure at that centroid and multiply by area for the resultant magnitude. Locate the centre of pressure separately using the pressure distribution and second moment of area. Put the force at that location before taking moments about a hinge or support.
What is the difference between centre of buoyancy and centre of gravity?
The centre of buoyancy is the centroid of displaced fluid volume and sets where the upward pressure resultant acts. The centre of gravity belongs to the body and sets where weight acts. Their relative positions and how buoyancy shifts during rotation determine whether a floating equilibrium produces a restoring or overturning moment.
Why can a submerged body need tension as well as buoyancy?
Buoyancy depends on displaced volume, while weight depends on body mass. If those forces are unequal, another support or tension is needed for static equilibrium. Draw that interaction explicitly. A cable holding a light body down has the opposite direction from a cable supporting a heavy body upward.
Which way does the free surface tilt in an accelerating tank?
Construct the effective gravity vector by combining downward gravity with the inertial acceleration opposite the tank motion. The free surface is perpendicular to that vector. A quick physical check is that the liquid piles toward the end opposite the tank acceleration, where the effective body force points more strongly.
Why calculate moments after hydrostatic force?
A force magnitude alone does not determine whether a gate opens, a body rotates or a support is overloaded. The centre of pressure supplies the lever arm. Taking moments about a hinge or support then connects the distributed pressure field to the mechanical reaction or cable force the design must carry.
Exam move
Separate every submerged-surface problem into magnitude, location and rigid-body equilibrium. Sketch the surface and free level, calculate centroid depth and resultant magnitude, then compute or reason about the centre of pressure before taking moments. For buoyancy, draw the body alone and place weight through the centre of gravity, buoyancy through the centre of displaced volume and any cable or support at its attachment.
Check vertical force balance before discussing stability. For floating bodies, practise a small rotation sketch that shows the shifted buoyancy line and whether it creates a restoring moment. For accelerating tanks, draw effective gravity first and make the free surface perpendicular to it, then use one known free-surface pressure to calculate elsewhere.
Revisit the sign of every moment using the picture instead of relying on a memorised formula. Close each answer by stating stable or unstable, upward or downward restraint, and the physical direction of the resultant.