Physics Investigatory Project: Bernoulli'S Theorem
Physics Investigatory Project: Bernoulli'S Theorem
Physics Investigatory Project: Bernoulli'S Theorem
INVESTIGATORY
PROJECT
2022 – 2023
BERNOULLI’S THEOREM
MADE BY: J.Sriram
INDEX
PRESSURE
EQUATION OF
CONTINUITY
DANIEL
BERNOULLI
INTRODUCTION TO
BERNOULLI’S THEOREM
BERNOULLI’S
EQUATION
EXPERIMENT
APPLICATION
CONCLUSION
BIBLIOGRAPHY
PRESSURE
Pressure, in the physical sciences, is the
Perpendicular force per unit area, or the stress at a point
within a confined fluid.
Fluid particles are subject only to pressure and their own weight.
If a fluid is flowing horizontally and along a section of a
streamline, where the speed increases it can only be because
the fluid on that section has moved from a region of higher
pressure to a region of lower pressure; and if its speed
decreases, it can only be because it has moved from a region of
lower pressure to a region of higher pressure. Consequently,
within a fluid flowing horizontally, the highest speed occurs
where the pressure is lowest, and the lowest speed occurs
where the pressure is highest.
BERNOULLI’S EQUATION
The equation is given as,
P + 1/2(ρ v2) + ρgh = 0
Where P is pressure, ρ is the density of the fluid, v is its velocity,
g is the acceleration due to gravity and h is the height of the
fluid from the ground.
Derivation
Thus, we can consider the work done on the fluid as – P2∆V. Therefore, the
total work done on the fluid is
W1 – W2 = (P1 − P2) ∆V
The total work done helps to convert the gravitational potential energy and
kinetic energy of the fluid. Now, consider the fluid density as ρ and the mass
passing through the pipe as ∆m in the ∆t interval of time.
be
The pilot tube and static port on an aircraft are used to determine the
airspeed of the aircraft. These two devices are connected to the
airspeed indicator, which determines the dynamic pressure of the
airflow past the aircraft. Dynamic pressure is the difference between
stagnation pressure and static pressure. Bernoulli's principle is used
to calibrate the airspeed indicator so that it displays the indicated
airspeed appropriate to the dynamic pressure.
The maximum possible drain rate for a tank with a hole or tap at the
base can be calculated directly from Bernoulli's equation, and is
found to be proportional to the square root of the height of the fluid
in the tank. This is Torricelli's law, showing that Torricelli's law is
compatible with Bernoulli's principle. Viscosity lowers this drain rate.
This is reflected in the discharge coefficient, which is a function of the
Reynolds number and the shape of the orifice.
CONCLUSION
Bernoulli's law states that if a non-viscous fluid is flowing along
a pipe of varying cross section, then the pressure is lower at
constrictions where the velocity is higher, and the pressure is
Higher where the pipe opens out and the fluid stagnates. Many
people find this situation paradoxical when they first encounter
it (higher velocity, lower pressure). Venturimeter, atomiser and
filter pump Bernoulli’s principle is used in venturimeter to find
the rate of flow of a liquid. It is used in a carburettor to mix air
and petrol vapour in an internal combustion engine. Bernoulli’s
principle is used in an atomiser and filter pump. Wings of
Aeroplane Wings of an aeroplane are made tapering. The upper
surface is made convex and the lower surface is made concave.
Due to this shape of the wing, the air currents at the top have a
large velocity than at the bottom. Consequently the pressure
above the surface of the wing is less as compared to the lower
surface of the wing. This difference of pressure is helpful in
giving a vertical lift to the plane.
BIBLIOGRAPHY
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