 friends, myself Deshmukh Sachin working as assistant professor in civil engineering department of waltz and stoke technologies to lappour. Today we are going to study of Bernoulli's theorem or we can say it is a Bernoulli's equation or Bernoulli's principle. At the end of this particular topic we are able to calculate total energy at a particular section and also we can calculate the loss of head of water when it is passing from one section to another section. Daniel Bernoulli, he was a Swiss scientist born in 70s and who has done lot of work in fluid mechanics, he is pioneer of many of the equations, he is pioneer of we can say many tedious works in the fluid mechanics and has simplified it and given a very simpler equations in the fluid mechanics. Before to start or before to go for this Bernoulli's theorem, we must know what are the different energies possessed, potential energy, kinetic energy and pressure energy. These are the three important energies on which this Bernoulli's theorem, Bernoulli's equation is dependent, potential energy it is a type of energy due to the property of its state that is where it is laying. If a pipeline is there you have to see from ground level if you are taking into account what is the height of that particular pipeline, what is the height of that particular flow conditions and that you have to take into account. Particularly we are taking z small z as a potential energy from the ground line or the datum line that is its energy, kinetic energy it is with respect to its motion and it is calculated by the velocity head you can say it is v square upon 2 g v square upon 2 g and pressure energy this is due to the pressure of the liquid and it cone as a p by w where p is the pressure and w is the specific weight of the water. When you are keeping the tubes pressure tubes or you can say Bernoulli's tubes on a pipeline you can find the rise of pressure if you can keep on the pipeline you can observe the water level is rising just focus on this focus on this here this is a pipeline here glass tubes are attached and the water level is rising water level is rising over here due to pressure see here different diameters are there different diameters are there water level is rising this is a p by w pressure upon specific weight specific weight. So the equation states that the total head of liquid in motion is the sum of its potential head kinetic head and pressure head. So if you are going to calculate in head it is z potential energy v square upon 2 g kinetic energy and p by w it is a pressure energy in meters head is going to calculate in meters if you are going to calculate in energy e that is a total energy z plus v square upon 2 g plus p by w but the unit is Newton meter per kg of water keep in mind. The Bernoulli's theorem which is also known as Bernoulli's principle states that the sum of all the energies are same from section any section if you are taking section 1 1 to section 2 2 provided that the flow is steady irrotational and frictionless and definitely the fluid is incompressible let us go through this. Now here you can observe the frictional loss friction loss this is a topmost side topmost level and this is the when it is travelling from this point to this point there are some losses occurred this is a friction loss. Now this is the derivation for Bernoulli's theorem consider an ideal incompressible liquid through a non uniform pipe as shown in the figure let us consider two sections let us consider two sections LL and MM then this is transferred to this one this is P1 this is P2 V1 is the velocity of liquid at LL Z1 is height of LL above atom A1 is area of pipe at that upper section similarly all these all these P2 V2 Z2 and A2 corresponding values at the bottom level this bottom level okay Z1 and Z2 these are the potential energies of the sections Z1 and Z2 these are the potential energies of the section this is DL1 this is DL2 and by the continuity of equation that we know Q is equal to A1 V1 is equal to A2 V2 that discharge is not going to change okay by starting with derivation you have to find out this weight weight of the liquid within work done which is equal to force into distance or displacement similarly calculate the work done total work done then loss of potential energy first calculate the work done like this step by step then loss of potential energy then what is a kinetic energy gain in the kinetic energy that you have to calculate and also loss of potential energy plus work done by the pressure which is a gain in kinetic energy put this this equation equal to the previous one simplified all these are the energies simplified you will get P1 by W plus V1 square upon 2g plus Z1 is equal to P2 by W plus V2 square upon 2g plus Z2 P1 by W it is the pressure energy at section 11 or LL V1 square upon 2g it is a kinetic head or kinetic energy or velocity here you can say at section 11 Z1 it is a static energy or you can say potential energy at one similarly the pressure energy plus kinetic energy plus the static energy at section 2 this is a Bernoulli's equation but it is observed that this equation this particular total energy is not equal to this one there are some losses occurred therefore again Bernoulli has done many experiments and he modified this equation he modified this equation that we are going to study in the next topic this modified equation states that this P1 upon W plus V1 square upon 2g plus Z1 is equal to P2 upon W plus V2 square upon 2g plus Z2 plus losses these losses are again of two types these losses are of two types that is major loss and minor loss major loss is by friction and minor loss there are many that is by change in the direction change in the diameter elbow right angle shape like this pause the video and give the answer of this Bernoulli equation is applicable only for irrotational flow viscous flow in viscid incompressible flow and compressible flow the answer is C in viscid incompressible flow because we are assuming there is a less viscosity or zero viscosity water is incompressible and it is in the static condition velocity is also not there static condition okay. So Bernoulli's equation is applicable only for in viscid and incompressible flow this is the answer now most important this Bernoulli's equation where we are going to use we are going to use or applying in this venturi meter here we are taking section 1 1 okay and section 2 2 is a pipe diameter and this is a throat diameter and here we can apply the equation z1 z1 plus p1 upon w plus v1 square upon 2g is equal to z2 plus p2 upon w plus v2 square upon 2g second one is orifice meter it is orifice plate here you can observe here you can apply here you can apply the Bernoulli's equation what is the orifice meter it is a tool or it is instrument to measure the discharge and which is kept at the bottom or which is kept at the side of the tank third one is rotameter okay see the flow it is a float see the flow over here you can apply the Bernoulli's here here and fourth one which is most important pitot tube here you can apply the Bernoulli's equation section 1 and section 2 the pitot tubes here water level rises over here this is a flowing in this so these are the four important applications these are the reference books go through it thank you