Fluids- Buoyancy and Stability Flashcards
How to find magnitude of point force equivalent to all the hydrostatic forces on a submerged object (FR)
Equal to area times average pressure. The average pressure is at the centroid of the plane. The point force is perpendicular to the surface.
Where does FR act on a submerged plane?
The centre of pressure. This is at the point where the total force either side is equal.
Why is the centre of pressure not at the centroid?
The total pressure below the centroid is greater than above it so there is a resultant moment about the centroid. FR must reproduce this moment.
How to use a pressure prism for a submerged rectangular plane
A virtual prism is formed using the pressure profile on the plane. It’s volume is equal to the magnitude of FR because it equals SPdA. The line of action if FR is through the centroid of the homogeneous prism (its centre of mass). True for any planar shape.
Position of centre of pressure formula
yP=yC+Ixx,C/[yC+P0/(ρgsinθ)]A
P,C and xx subscript
yC= distance between centroid to where the line through the plane touches the surface
P0 is atmospheric pressure (if acts on both fluid and plane cancels out)
ρ is density of fluid
θ is angle between plane and surface
A is area of plane
Ixx,C is second moment of area about the x axis around the centroid
For the second moment of area formulae, what are the sides a and b?
a is the side going into the page
b is the length of the plane along the page
Both when looking at plane side on
How to deal with a surface submerged in a multilayered fluid
Consider the parts in different fluids as different surfaces. Then can add the forces on each part.
What are the component forces on a submerged curved surface equal to?
The horizontal force on it is equal to the force on that projected area (not the area of the curved face if it was rolled out).
The vertical force on it is equal to the force on that projected area and the weight of the water between the surface and projection.
How to find resultant force on submerged curved surface using component forces
Use Pythagoras
What is true about FR on a circular surface?
Its line of action always passes through the centre of the circle since all the pressure forces are normal to the surface so pass through the centre.
What is buoyant force?
FB. The upward force (upthrust) a fluid exerts on a body immersed in it.
What is the Archimedes’ principle?
The buoyant force acting on a body of uniform density immersed in a fluid is equal to the weight of the fluid displaced by the body, and it acts upward through the centroid of the displaced volume.
What happens when the density of an object immersed in a fluid is less than, greater than, or equal to the density of the fluid?
When equal, the weight of object equals upthrust so there is no motion.
When density of object more, weight of object greater than upthrust so it sinks.
When density of object less, weight of object less than upthrust so it rises.
For a floating body, what is the relation between the volume ratio and density ratio?
Vsub/Vtot=ρbody/ρfluid
When is an immersed body, that is neutrally buoyant, stable, neutrally stable or unstable?
Stable when centre of gravity, G, is directly below the centre of buoyancy, B. Neutrally stable when G and B are coincident. Unstable if G is directly above B.
What happens when an immersed neutrally buoyant body experiences a small disturbance if it is stable, neutrally stable or unstable?
Stable: any small disturbance generates a restoring force that returns it to its initial position.
Neutrally stable: it will stay in the position it reaches after the disturbance.
Unstable: any disturbance causes it to move and not return to its original position and instead diverge from it.
Where is the centre of buoyancy?
The centre of mass of the displaced water
What is the metacentre, M?
The intersection point of the lines of action of the buoyant force through the body before and after rotation.
What is the metacentric height, GM?
The distance between the centre of gravity, G, and the metacentre, M.
How does the value of metacentric height tell you about stability?
When it is positive (M above G), the object is stable. When it is negative (M below G), the object is unstable. The larger it is, the more stable the floating body is.
Formula for metacentric height
GM=I0/Vsub - BG
I0 is second moment of area of waterline area
Vsub is volume of object submerged
BG is distance from B to G (negative if B above G)
What is second moment of area of waterline area?
The area occupied by the body that would otherwise be occupied by the free surface.
