Bernoulli's principle states that for an incompressible fluid flowing in a streamline manner, the sum of pressure, kinetic energy, and potential energy is constant at any point. It explains phenomena like lift in airplanes and boats. For airflow over an airplane wing, the faster-moving air over the top surface has lower pressure, creating an upward force. Bernoulli's principle also explains how drafts are formed when doors or windows are opened, allowing high-pressure hot air to rush out and low-pressure cool air to flow in. It governs the mechanics of sailing as well, with differential pressures creating lift on the sail to propel the boat forward.

1. R.GOKUL

2. What are the various applications of bernoulli?
 The applications of Bernoulli are
 Airflight
 Lift
 Baseball
 Draft
 sailing

3. Airflight
 One of the most common everyday applications of Bernoulli's
principle is in airflight. The main way that Bernoulli's principle
works in air flight has to do with the architecture of the wings of
the plane. In an airplane wing, the top of the wing is soomewhat
curved, while the bottom of the wing is totally flat. While in the
sky, air travels across both the top and the bottom concurrently.
Because both the top part and the bottom part of the plane are
designed differently, this allows for the air on the bottom to
move slower, which creates more pressure on the bottom, and
allows for the air on the top to move faster, which creates less
pressure. This is what creates lift, which allows planes to fly. An
airplane is also acted upon by a pull of gravity in which opposes
the lift, drag and thrust. Thrust is the force that enables the
airplane to move forward while drag is air resistance that opposes
the thrust force.

4. Lift
 One of the most common trends that occurs in the modern day physics
world is that of lift. Lift can be seen in many different ways, shapes, and
forms in our world. Lift is seen in airflight, as in my example above, as
well as in several of my forthcoming examples. But , what is lift exactly?
Most people define lift in terms of Bernoulli's principle which has some
validity to it, but the main way for one to define lift is through
Newton's three laws. While most accept that Bernoulli's principle is
what creates lift, some say that it leaves many unanswered questions.
For one, it says that upside down flight cannot happen. Also, many
people say that by using Bernoulli's principle to explain lift, it doesn't
take into account the fact that no where in the commonly accepted
defenition of lift, is there any mention of work, and lift can only take
place if there is a certain type of unit of work that we are all familiar
with, called power. The next most widely accepted definition of lift
involves Newton's three laws, specifically his first and third. (The first
is the law of intertia and the third is that for every acton there is an
equal and opposite reaction.)

5. Baseball
 Baseball is an example of where Bernoulli's principle is very visible in
everyday life, but rarely do most people actually take note of it. One
example in baseball is in the case of the curve ball. The entire pitch
works because of Bernoulli's principle. Since the stitches of the ball
actually form a curve, it is necessary for the pitcher to grip the seams of
the baseball. The reason as to why this is a necessity is that by gripping
the baseball this way, the pitcher can make the ball spin. This allows for
friction to cause a thin layer of air to engilf the misunderstanding of the
baseball as it is spinning, but since the ball is spinning in a certain
manner, this allows for more air pressure on the top of the ball and less
air pressure on the bottom of the ball. Therefore, according to
Bernoulli's principle there should be less speed on the top of the ball
than there is on the bottom of the ball. What transpires is that the
bottom part of the ball accelearates downwards faster than the top part,
and this phenomenon allows for the ball to curve downward, which
causes the batter to miscalculate the ball's position.

6. Draft
 And furthermore, another example of Bernoulli's principle in our
everyday lives is in the case of someone feeling a draft. We all at at least
one time or another, have experienced feeling a draft, and it is because
of Bernoulli's principle that we feel this draft. Let's say that in your
room, you are really hot, but you know that it is nice and cool both
outside your window and outside your door. If you open up your
window, to try and let fresh air in, there won't be much of a
temperature change, unless the door to your room is open to air out the
hot air. The reason why it works this way is that if the front door is
closed the door will become an area of high pressure built up from the
hot air, and right outside the door there is little pressure, meaning that
the rate at which the air enters will be in an incredibly high speed.
When you open the door, the pressure is relieved from the door on the
inside and the hot air exits quickly. When the hot air exits there is a lot
more pressure outside meaning that it will take awhile for the cool air
to come in. Once the hot air has flown out, the cool air will come in at a
fast speed, thus causing a draft.

7. Sailing
 In addition to the three items above, Bernoulli's principle is also the governing
theory that is behind sailing. Most people believe that sailing is just having a
big sail and that when you put it up, the wind just takes your boat and drags it
along the sea. This is not 100% correct. This is true only in the cases when the
boat is moving with the wind, otherwise it is not true. When the boat does not
travel with the wind, it usually moves perpendicular to the wind, and the boat
moves not because the wind drags it along, but because of the concept of lift,
which as mentioned above and in the case of airplanes, is what happens when
either a liquid or a gas act on an object. The same way that Bernoulli's principle
works for creating lift in airplanes, it works for creating lift in sails. All sail
boats have two parts to it: a sail which points north and a keel which points on
the opposite direction. If the speed of the air increases on the sail, there is less
pressure on the sail, and conversely there is less pressure on the keel but a
higher speed. Just like with an airplane this produces lift and propels the sail to
move in the water.

8. How do airplanes fly?
 As for the actual mechanics of lift, the force occurs when a
moving fluid is deflected by a solid object. The wing splits the
airflow in two directions: up and over the wing and down along
the underside of the wing.
 The wing is shaped and tilted so that the air moving over it
travels faster than the air moving underneath. When moving air
flows over an object and encounters an obstacle (such as a bump
or a sudden increase in wing angle), its path narrows and the
flow speeds up as all the molecules rush though. Once past the
obstacle, the path widens and the flow slows down again. If
you've ever pinched a water hose, you've observed this very
principle in action. By pinching the hose, you narrow the path of
the fluid flow, which speeds up the molecules. Remove the
pressure and the water flow returns to its previous state.

9.  As air speeds up, its pressure drops. So the faster-
moving air moving over the wing exerts less pressure
on it than the slower air moving underneath the wing.
The result is an upward push of lift. In the field of
fluid dynamics, this is known as Bernoulli's
principle.


10. Is this Bernoulli’s theorem applicable for a
turbulent flow of liquid?-comment
 Streamline flow. The motion of fluids can be very complex and
difficult to analyze. The turbulent flow of a mountain stream or
the complicated air movements of the atmosphere are examples
of this. However, there is an important type of fluid flow that is
relatively simple. It is the smooth, steady, non-turbulent flow of
a fluid through a tube called streamline flow or laminar flow.
See Fig. 1. The flow of fluid in a tube is of the streamline type if
the velocity is not too great and there are not bends or changes in
diameter so abrupt as to cause turbulence. With streamline flow
the path of any particle of fluid as it moves through the tube is
called a streamline. One can map the flow of fluid through a
tube by drawing a number of streamlines following the paths of
the particles of the liquid. The rate of flow can be represented by
the density of the streamlines. In streamline flow the velocity of
the fluid at any chosen point within the tube is always the same.

11.  Rate of flow of a fluid in a pipe. The rate of flow of a fluid in a pipe is given
by

R = Av

where A is the cross section area and v is the velocity of the fluid.

Example. A fluid is flowing at a velocity of 5 ft/sec in a pipe with a cross
section area of 2 ft2. Its rate of flow is then 10 ft3/sec.

 The equation of continuity. In steady state flow of an incompressible fluid
through a tube of varying cross section area

A1v1 = A2v2

 where v1, v2 are respectively the velocities of the fluid at cross sections A1, A2.

12.  Derivation. Consider the fluid flow shown in Fig. 2 where the cross-section area at point 1 is A1 and
at point 2 is A2. In time t, the fluid at point 1 will advance a distance of d1 = v1t and a volume of liquid
equal to A1d1 = A1v1t will pass point 1. Similarly, the volume of fluid passing point 2 in time t will be
A2v2t. The volume of fluid passing points 1 and 2 in time t must be equal so

 A1v1t = A2v2t

and

 A1v1 = A2v2

which is the equation of continuity for the steady flow of an incompressible liquid.

Bernoulli’s Theorem. Bernoulli’s theorem states a relationship between pressure, velocity and
elevation at points along a flowing stream of fluid . Given: steady, streamline flow of an
incompressible, nonviscous fluid in a tube of varying diameter. Then for any two points along the
flow

p + ρgh + ½ ρv2 = constant

13.  Derivation. Consider the fluid flow shown in Fig. 2 where the cross-section area at point 1 is A1 and
at point 2 is A2. In time t, the fluid at point 1 will advance a distance of d1 = v1t and a volume of liquid
equal to A1d1 = A1v1t will pass point 1. Similarly, the volume of fluid passing point 2 in time t will be
A2v2t. The volume of fluid passing points 1 and 2 in time t must be equal so

 A1v1t = A2v2t

and

 A1v1 = A2v2

which is the equation of continuity for the steady flow of an incompressible liquid.

Bernoulli’s Theorem. Bernoulli’s theorem states a relationship between pressure, velocity and
elevation at points along a flowing stream of fluid . Given: steady, streamline flow of an
incompressible, nonviscous fluid in a tube of varying diameter. Then for any two points along the
flow

p + ρgh + ½ ρv2 = constant

14.  where ρ is the density of the fluid and p, v and h are the pressure,
velocity and height (i.e. elevation) at any chosen point in the
stream.

 In words, the theorem states that at any two points along the
stream the sum of the pressure (p), the potential energy of a unit
volume of the fluid (ρgh) and the kinetic energy of a unit volume
of the fluid (½ ρv2 ) has the same value.

Bernoulli’s equation assumes streamline frictionless flow. If the
tube is smooth, large in diameter, short in length and if the fluid
has a small viscosity and flows slowly, the frictional resistance
may be small enough to neglect.


15. Why is it not advisable for us to stand very close
to a speeding train?
 One of the basic theorems in fluid dynamics states that,
The sum of kinetic, potential and pressure energy of a streamlined flow are constant. This
can be assumed to be effective for turbulent flow with slight adjustments.
This is known as the Bernoulli's Theorem.
So now,
Let us take pressure energy to be P;
Kinetic energy to be K; and
Potential energy to be U.
According to the theorem,
P + U + K= constant
Now K varies with the square of the velocity of air which is higher near the edge as it is in
contact with the moving train (although it fades away with distance)
For the Bernoulli's to still hold good, either P or U will have to decrease to account for the
increased Kinetic Energy near the edges.

16.  Since, average potential energy of air here will not
undergo much change,
Hence, the pressure decreases near the edge and
the relatively higher pressure behind you tends to
push you towards the moving train (yes, you're
pushed and not pulled).
This effect tends to fade away, as mentioned earlier,
with increasing distance from the edge. This is why
there's a safety line drawn at most of the stations and it
is advisable to stay behind them when the train
approaches.

17. Mention the various types of flow of liquids.
 Viscous or non-viscous
 Rotational or irrotational
 Compressible or non-compressible

18. Differentiate between compressible and non-
compressible.
 Fluid flow can
be compressible or incompressible, depending on whether
you can easily compress the fluid. Liquids are usually
nearly impossible to compress, whereas gases (also
considered a fluid) are very compressible.
 A hydraulic system works only because liquids are
incompressible — that is, when you increase the pressure
in one location in the hydraulic system, the pressure
increases to match everywhere in the whole system. Gases,
on the other hand, are very compressible — even when
your bike tire is stretched to its limit, you can still pump
more air into it by pushing down on the plunger and
squeezing it in.