Bernoulli's theorem states that for an incompressible liquid in a continuous stream, the total energy of a particle remains constant along its path, assuming no frictional losses. The theorem has limitations, such as uniform velocity assumptions and neglecting external forces and energy losses due to heat and shear. It finds practical applications in devices like pitot tubes, orifice meters, and venturi meters for measuring fluid flow and discharge.

2. BERNOULLI’S THEOREM
• It states “for a perfect incompressible liquid, flowing in a continuous
stream, the total energy of a particle remains the same, while the particle
moves from one part to another”. This statement is based on the
assumption that there are no losses due to friction in the pipe.
Mathematically
𝑇𝑜𝑡𝑎𝑙 𝐻𝑒𝑎𝑑 = 𝑃𝑜𝑡𝑒𝑛𝑡𝑖𝑎𝑙 𝐻𝑒𝑎𝑑 + 𝐾𝑖𝑛𝑒𝑡𝑖𝑐 𝐻𝑒𝑎𝑑 + 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝐻𝑒𝑎𝑑
𝐻 = 𝑍 +
𝑣2
2𝑔
+
𝑝
𝜔
= 𝐶𝑜𝑛𝑠𝑡𝑎𝑛𝑡

3. LIMITATIONS OF BERNOULLI’S THEOREM
1. The Bernoulli’s equation derived by assuming that the velocity of every
element of the liquid across any cross section of the pipe is uniform.
Practically it is not true.
2. The Bernoulli’s equation has been derived under the assumption that the
external force, except the gravity force, is not acting on the liquid, but in
actual practice it is not so. There are always some external forces acting on
the liquid which effect the flow of the liquid.
3. Bernoulli’s equation has been derived on the assumption that there is no
loss of energy of the liquid particle while flowing. In fact, some kinetic
energy is converted into heat energy & some energy is lost due to shear
force.
4. If a liquid is flowing in a curved path, the energy due to centrifugal force is
neglected.

4. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
• The Bernoulli’s equation is the basic equation which has the widest
applications in Hydraulics. This equation is applied for the derivation of
many formulas and hydraulic devices. Though the Bernoulli’s equation has
a number of practical applications but the following are the mostly used
hydraulic devices on the principles of Bernoulli’s equation:
1. Pitot Tube
2. Orifice Meter
3. Venturi Meter

5. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
1) PITOT TUBE:
A Pitot Tube is an instrument to determine the velocity of flow at the
required point in a pipe or a stream. A Pitot Tube consist of a glass tube bent
a through 90o. The lower end of the tube faces the direction of the flow. The
liquid rises up in the tube due to the pressure exerted by the flowing liquid.
By measuring the rise of liquid in the tube, we can find out the velocity of the
liquid flow.
𝑉 = 2𝑔ℎ

6. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
2) ORIFICE METER:
An Orifice meter is used to measure the discharge in pipe. An Orifice meter
consists of a plate having a sharp edged circular hole known as an Orifice. The
plate is fixed inside a pipe. A mercury manometer is connected with it to know
the difference of pressure between the pipe & the throat or in other pipe.
𝑄 = 𝐶
𝑎1 − 𝑎2
𝑎1
2
− 𝑎2
2
2𝑔ℎ
Q= Discharge, C= Co-efficient of Orifice meter,
𝑎2= Area of Orifice, g= Gravitational Acceleration,
h= Pressure difference of liquid head, 𝑎1= Area of Pipe

7. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
3) VENTURI METER:
A Venturi meter is an apparatus for finding out the discharge of a liquid
flowing in a pipe. A Venturi meter consists of the following three parts:
a) Converging Cone: it is a short pipe which converges from diameter of
the pipe to a smaller diameter (Throat dia). Its length is taken upto 2.5
times the dia of pipe. The slopes of converging sides is between 1:4 to
1:5. It is also called inlet of Venturi Meter.
b) Throat: It is the middle smaller portion of the Venturi meter. Its dia is
kept constant. Its diameter is taken upto ¼ to ½ of the diameter of the
pip.

8. PRACTICAL APPLICATION OF BERNOULLI’S THEOREM
3) VENTURI METER:
c) Diverging Cone: it is a pipe, which diverges from a throat diameter to a
larger diameter of pipe. The divergent cone is also known as outlet of
the Venturi meter. The length of the divergent cone is about 3 to 4 times
than that of the convergent cone.
Venturi meter can be connected with pipe horizontally & vertically. In both
states, the discharge can be found by:
𝑄 = 𝐶𝑘
𝑎1 − 𝑎2
𝑎1
2
− 𝑎2
2
2𝑔ℎ
C= Constant of Venturi meter (0.97 avg Value), k= Co-efficient of Orifice
Meter, 𝑎1= Area of Pipe, 𝑎2= Area of Throat of the Venturi Meter

9. VENTURI METER
PRACTICAL APPLICATION OF BERNOULLI’S THEOREM