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Recap
In this course you have learnt the following
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- Forces acting on a fluid element in isolation are of two
types;
- Body force : Body forces act over the entire volume
of the fluid element and are caused by external agencies
- Surface force. Surface forces, resulting from the
action of surrounding mass on the fluid element, appear
on its surfaces.
- Normal stresses at any point in a fluid at rest, being
directed towards the point from all directions, are of equal
magnitude. The scalar magnitude of the stress is known as
hydrostatic or thermodynamic pressure.
- The fundamental equations of fluid statics are written
as
 ,  ,  with respect
to a cartesian frame of reference with x - y plane as horizontal
and axis z being directed vertically upwards. For an incompressible
fluid, pressure P at a depth h below the free surface can
be written as p = Po + ρ gh, where Po is the local atmospheric
pressure.
- At sea-level, the international standard atmospheric pressure
has been chosen as Patm = 101.32 kN/m2. The pressure expressed
as the difference between its value and the local atmospheric
pressure is known as gauge pressure.
- Piezometer tube measures the gauge pressure of a flowing
liquid in terms of the height of liquid column. Manometers
are devices in which columns of a suitable liquid are used
to measure the difference in pressure between two points
or between a certain point and the atmosphere. A simple
U-tube manometer is modified as inclined tube manometer,
inverted tube manometer and micro manometer to measure a
small difference in pressure through a relatively large
deflection of liquid columns.
- The hydrostatic force on anyone side of a submerged plane
surface is equal to the product of the area and the pressure
at the centre of area. The force acts in a direction perpendicular
to the surface and its point of action, known as pressure
centre, is always at a higher depth than that at which the
centre of area lies. The distance of centre of pressure
from the centre of area along the axis of symmetry is given
by
- For a curved surface, the component of hydrostatic force
in any horizontal direction is equal to the hydrostatic
force on the projected plane surface on a vertical plane
perpendicular to that direction and acts through the centre
of pressure for the projected plane area. The vertical component
of hydrostatic force on a submerged curved surface is equal
to the weight of the liquid volume vertically above the
submerged surface to the level of the free surface of liquid
and acts through the centre of gravity of the liquid in
that volume.
- When a solid body is either wholly or partially immersed
in a fluid, the hydrostatic lift due to net vertical component
of the hydrostatic pressure forces experienced by the body
is called the buoyant force. The buoyant force on a submerged
or floating body is equal to the weight of liquid displaced
by the body and acts vertically upward through the centroid
of displaced volume known as centre of buoyancy.
-
The equilibrium of floating or submerged bodies requires
that the weight of the body acting through its centre of
gravity has to be colinear with an equal buoyant force acting
through the centre of buoyancy. A submerged body will be
in stable, unstable or neutral equilibrium if its centre
of gravity is below, above or coincident with the centre
of buoyancy respectively. Metacentre of a floating body
is defined as the point of intersection of the centre line
of cross-section containing the centre of gravity and centre
of buoyancy with the vertical line through new centre of
buoyancy due to any small angular displacement of the body.
For stable equilibrium of floating bodies, metacentre M
has to be above the centre of gravity G. M coinciding with
G or lying below G refers to the situation of neutral and
unstable equilibrium respectively. The distance of metacentre
from centre of gravity along the centre line of cross-section
is known as metacentric height and is given by.
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Congratulations!
you have finished Chapter 2 from
Module 1.
To
view the next lecture select it from the left hand
side menu of the page
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