This is a whole presentation on hydrostatic equilibrium a topic in fluid flow operations for chemical engineer made by me as a part of term work for our vgec college . Hope you will find its useful

1. Topic :-
Hydrostatic Equilibrium
Term Work by:-
Aniket Jha(200170105005)
Adarsh prajapati(200170105001)
Harmish Kotadiya(200170105002)
Prince Bhalala(200170105004)

2. Definition
 Hydrostatic equilibrium is the condition
of a fluid or plastic solid at rest,
which occurs when external forces,
such as gravity, are balanced by a
pressure-gradient force.In the
planetary physics of the Earth, the
pressure-gradient force prevents
gravity from collapsing the planetary
atmosphere into a thin, dense shell,
whereas gravity prevents the
pressure-gradient force from diffusing
the atmosphere into outer space.

3. Application of
hydrostatic equilibrium
In Fluids
(Fluid Mechanics)
In planets and stars
(planetary geology)

4. Atmospheric hydrostatic equilibrium

5.  The Atmosphere’s vertical pressure structure plays a critical role in
weather and climate
 The Atmosphere’s basic pressure structure is determined by
the hydrostatic balance of forces To a good approximation, every air parcel
is acted on by three forces that are in balance, leading to no net force .
 There are 3 forces that determine hydrostatic balance:
 One force is downwards (negative) onto the top of the cuboid from the
pressure, p, of the fluid above it. It is, from the definition of pressure
 Similarly, the force on the volume element from the pressure of the fluid
below pushing upwards (positive) is:
 Fbottom=pbottomA

 Finally, the weight of the volume element causes a force downwards. If
the density is ρ, the volume is V, which is simply the horizontal area A times
the vertical height, Δz, and g the standard gravity, then:
Ftop=−ptopA

6.  Fweight=−ρVg=−ρgAΔz
 By balancing these forces, the total force on the fluid is:
 ∑F=Fbottom +Ftop +Fweight =pbottomA−ptopA−ρgAΔz
 This sum equals zero if the air's velocity is constant or zero. Dividing by A,
 ptop−pbottom=−ρgΔz
 Ptop − Pbottom is a change in pressure, and Δz is the height of the volume element – a
change in the distance above the ground. By saying these changes are infinitesimally small,
the equation can be written in differential form, where dp is top pressure minus bottom
pressure just as dz is top altitude minus bottom altitude.
 dp=−ρgdz
 The result is the equation:
 dpdz=−ρg
 This equation is called the Hydrostatic Equation

7.  The Atmospheric pressure falls off exponentially with height at a rate given by the
scale height. Thus, for every 7 km increase in altitude, the pressure drops by about
2/3. At 40 km, the pressure is only a few tenths of a percent of the surface pressure.
Similarly, the concentration of molecules is only a few tenths of a percent, and since
molecules scatter sunlight, you can see in the picture below that the scattering is
much greater near Earth's surface than it is high in the atmosphere

8. Hydrostatic equilibrium in fluids
Hydrostatic equilibrium in fluids
Incompressible
fluids
Compressible
fluids

9. Incompressible fluids
 If the fluid is incompressible, so that the density is independent of the pressure, the
weight of a column of liquid is just proportional to the height of the liquid above the
level where the pressure is measured.

10. Compressible fluids
 Hydrostatic equilibrium is a little more complicated to apply to air, because air is very
compressible. The same principle still applies, but we now have to deal with a density that
varies with pressure and temperature
 For an ideal gas the density and pressure are related by the equation

11. Application
Application of Fluid Mechanics
Hydrostatic
Balance
Astrophysics Planetary Geology Atmosphere
modelling

12. Hydrostatic Balance
 The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids.
A hydrostatic balance is a particular balance for weighing substances in water. Hydrostatic
balance allows the discovery of their specific gravities. This equilibrium is strictly applicable
when an ideal fluid is in steady horizontal laminar flow, and when any fluid is at rest or in vertical
motion at constant speed. It can also be a satisfactory approximation when flow speeds are low
enough that acceleration is negligible

13. Astrophysics
 In any given layer of a star, there is a hydrostatic equilibrium between the outward
thermal pressure from below and the weight of the material above pressing inward.
The isotropic gravitational field compresses the star into the most compact shape
possible. A rotating star in hydrostatic equilibrium is an oblate spheroid up to a certain
(critical) angular velocity. An extreme example of this phenomenon is the star Vega,
which has a rotation period of 12.5 hours. Consequently, Vega is about 20% larger at the
equator than at the poles. A star with an angular velocity above the critical angular
velocity becomes a Jacobi (scalene) ellipsoid, and at still faster rotation it is no longer
ellipsoidal but piriform or oviform, with yet other shapes beyond that, though shapes
beyond scalene are not stable.[5]
 If the star has a massive nearby companion object then tidal forces come into play as
well, distorting the star into a scalene shape when rotation alone would make it a
spheroid. An example of this is Beta Lyrae.
 Hydrostatic equilibrium is also important for the intracluster medium, where it restricts
the amount of fluid that can be present in the core of a cluster of galaxies.
 We can also use the principle of hydrostatic equilibrium to estimate the velocity
dispersion of dark matter in clusters of galaxies

14. Planetary Geology
 The concept of hydrostatic equilibrium has also become important in determining whether
an astronomical object is a planet, dwarf planet, or small Solar System body. According to
the definition of planet adopted by the International Astronomical Union in 2006, one
defining characteristic of planets and dwarf planets is that they are objects that have
sufficient gravity to overcome their own rigidity and assume hydrostatic equilibrium. Such a
body will often have the differentiated interior and geology of a world (a planemo), though
near-hydrostatic or formerly hydrostatic bodies such as the proto-planet 4 Vesta may also
be differentiated and some hydrostatic bodies (notably Callisto) have not thoroughly
differentiated since their formation. Often the equilibrium shape is an oblate spheroid, as
is the case with Earth. However, in the cases of moons in synchronous orbit, nearly
unidirectional tidal forces create a scalene ellipsoid. Also, the purported dwarf
planet Haumea is scalene due to its rapid rotation, though it may not currently be in
equilibrium.

15. Atmospheric Modelling
In the atmosphere, the pressure of the air
decreases with increasing altitude. This
pressure difference causes an upward force
called the pressure-gradient force. The
force of gravity balances this out, keeping
the atmosphere bound to Earth and
maintaining pressure differences with
altitude