Buoyancy & Stability

Question 1

Archimedes Principle

Answer 1

A body in a fluid, whether floating or submerged,
is buoyed up by a force equal to the weight of the fluid displaced.

Question 2

Buoyant force

Answer 2

The upward force exerted by a fluid on a submerged object.
Fb=y(fluid).V(displaced)

Question 3

Properties of neutrally buoyant object?

Answer 3

✓ Weight of object (Fg) = Weight of fluid displaced (Fb)
✓ Stays at a given position whenever it is submerged

Question 4

Positively buoyant object

Answer 4

✓ Weight of object (Fg) < Weight of fluid displaced (Fb)
✓ Float freely

Question 5

Negatively buoyant object

Answer 5

✓ Weight of object (Fg) > Weight of fluid displaced (Fb)
✓ Sink

Question 6

Buoyancy Materials

Answer 6

1. Low γ and ρ
2. Do not absorb fluid
3. Compatible with the fluid
4. Ability to be formed into shapes
5. Ability to withstand fluid pressures
6. Abrasion resistance and damage tolerance
7. Attractive appearance

Question 7

Condition for stability of completely submerged bodies?

Answer 7

Condition: cg<cb

Fb acts through cg (centroid of Vdisplaced)
w acts through cg

Question 8

Cases for stability of completely submerged bodies?

Answer 8

cg<cb
* Angular displacement causes line of action to have offset
* Causing righting couple (stable equilibrium)

cg>cb
* When tilted, overturning couple is produced
* Cause the body to capsize (unstable equilibrium)

cg=cb
* Body stays as placed
* Neutral stability (neutral equilibrium)

Question 9

Stable

Answer 9

Body returns to its original position after being rotated about the
horizontal axis

Question 10

Stability of Floating Bodies?

Answer 10

cg<mc

Question 11

Metacentre (mc)

Answer 11

Intersection of vertical axis when body is in equilibrium and a
vertical line through new cb when body is slightly tilted

Question 12

MB

Answer 12

distance between the mc and the cb
MB= I / Vd

Question 13

Procedure for evaluating stability of floating bodies

Answer 13

1. Determine position of floating body
2. Locate cb and ycb (use bottom of body as reference)
3. Locate cg and ycg (use same reference)
4. Calculate MB = I / Vd
5. Calculate ymc = MB + ycb
6. If ymc > ycg, the body is stable
7. If ymc < ycg, the body is unstable

Question 14

Degree of stablity

Answer 14

*Measure of relative stability → metacentric height (MG)
distance between the mc and the cg (MG)
* MG = ymc – ycg