 good morning, you welcome you all to this session last class we have discussed the first law of thermodynamics we started discussing the first law of thermodynamics and then we defined a property enthalpy h which is the combination of intermolecular energy a part of the internal energy or in a stationary or closed system that is the internal energy plus the product of pressure and volume and we also recognize that this internal this enthalpy as a property of the system bears its physical significance relating to energy transfer in an open system or a flow process. So, today therefore, we will apply this first law for a flow system or a flow process or an open system and we will see how does enthalpy bear a physical significance with the energy transfer across the boundary of such an open system. So, for that what we do we just consider a flow system like this let us let us consider a device a flow device this is known as a flow device flow device well which has an inflow where there is continuously an inflow of fluid and continuously an outflow of fluid inflow and outflow of fluid and this flow device is connected with a shaft so that a shaft work is coming out in the form of the rotation of the shaft let us consider an infinite small amount of work d w d cut w as I explained earlier is coming over a time d t so that we can represent the d w d t as the rate at which the work is coming out from this flow device in the form of shaft work and also let us consider similar way infinite small amount of heat d cut q is added continuously over an interval of time d t so that we can represent the d q d t as a continuous rate of heat flowing or heat transfer into this flow device. Now, this flow device where there is a continuous flow of fluid at one section and continuous flow of fluid out another section it is flow in and flow out and developing both work and heat that means transferring in terms of work and heat with the surrounding is termed as an open system or a control volume in fact we consider a close a boundary circumscribing this flow device this way if we consider a boundary this way this this system within this fixed boundary is known as an open system or a control volume or a control volume which is characterized by this fixed boundary as I have already told you that a an open system is a control volume system or simply a control volume where where the boundary where the system or the control volume is characterized by the fixed boundary and across which the mass transfer takes place there is continuous in flow of fluid and there is continuous out flow of fluid. Now, if we want to make the conservation of energy statement for this open system or control volume it is very simple that we can write it like this the rate of rate of energy in flow to the control volume I write simply c v minus the rate of energy well out flow from c v must be equal to the rate of change of rate of change of energy within the control volume or the open system in in consideration within the c v this is the very simple and the preliminary statement of conservation of energy that the rate of energy in flow to control volume minus the out flow rate of energy out flow from control volume is equal to the rate of change of energy within the control volume now you see therefore we have to find out what are the in flow energy in flow quantities into the control volume and what are the out flow quantities very first case we see that we have considered the work is coming out in the form of the shaft work from the control volume this is one way the energy is coming out in the form of work and similarly the energy in the form of it is going into the control volume because we have considered this heat energy to be going into the control volume for the general deduction apart from this the energy quantities coming into the control volume due to the in flow of fluid mass across this section similarly the energy which is going out of the control volume are associated with the efflux of fluid mass from the control volume across this boundary so therefore we have to now recognize to know the different energies which are coming into the control volume or coming out of the control volume what are the energy quantities that are associated with the flow of a fluid stream so we have to first recognize that so what are the different quantity different energies different forms of energies that are associated with the flow of a fluid stream with the flow of a fluid stream the energy quantities or the different energies those are associated are first is intermolecular energy that is the kinetic and potential energy of the molecule intermolecular energy existing all substances under all conditions if it is at a temperature above than the absolute zero so this is the intermolecular energy number two is the kinetic energy this is because of the flow velocity though a fluid flow or fluid stream flowing stream possesses kinetic energy another energy is a very well known energy is the potential energy this is by virtue of its placement or virtue of its position in a conservative force field if there is no such external conservative force field so gravitational force field is there so gravitational potential energy is there apart from that there is another energy which is there in a flow of stream of fluid is the pressure energy that you have read in your fundamental fluid mechanics class what is that pressure energy or it may be termed as flow work this is because of the existence of pressure at a particular section in the flowing fluid as you know that it is because of the pressure a section a fluid layer at a section is capable of pushing the neighbouring layer to make its flow through the passage so therefore to maintain the flow the layer at any section the fluid layer at any section has to continuously push the neighbouring layer and by virtue of its pressure it can do so and it makes its way through so therefore we see to maintain a flow each and every section the fluid at each and every section does work on the neighbouring layer and that work is known as flow work whose magnitude is pressure times the specific volume per unit mass well that is the work per unit mass and if we look from this angle that this capability of doing this work by a particular layer of fluid at any section on its neighbouring layer to make its way through the flow is known as the energy which is inherent in the fluid or stored in the fluid layer and it is stored in the fluid layer in the form of pressure energy we tell it in the as pressure energy sometimes we refer it to as pressure energy or sometimes we refer it to as flow work so therefore we see what are the energy quantities that are associated with a flow of fluid stream one is the internal energy by virtue of its state thermodynamic state another is the kinetic energy by virtue of the flow velocity another is the potential energy by virtue of its position in a conservative force field and last one is the pressure energy by virtue of the pressure in the flow field so if we recognize this energy quantities then we can now come we can now recognize the energies which are coming into a into the control volume and going out of the control volume so therefore if we again see this one let us consider the rate of inflow of mass as d m 1 d t and let the outflow of mass as d m 2 d t the rate of outflow this is the rate of inflow of mass this is the rate of outflow of mass now to identify those energy quantities we will have to fix the state of the fluid at inlet let the inlet pressure is given by p 1 the corresponding specific volume is given by v 1 let the inlet velocity is given by v 1 and let from any arbitrary reference datum the elevation the vertical height at the inlet section is given by z 1 the corresponding quantity at outlet is given by p 2 with a subscript 2 v 2 that is the specific volume v 2 is the pressure velocity v 2 and also the elevation from a reference datum the vertical height as z 2 therefore with this nomenclature we can now write the rate of energy coming in to the control volume associated with the inflow of fluid as d m 1 d t that is the rate times the specific that is the per unit mass internal energy plus the flow work we write first that the pressure energy plus the kinetic energy per unit mass plus the potential energy we consider only the gravitational potential energy is present that means no other external conservative force field is there so this is the rate of energy coming into the control volume through the inflow of fluid mass well plus as we have already considered in this figure for this control volume this heat is being added at a rate of d q d t so we write d q d t so therefore this is the inflow of energy to the control volume similarly what is the outflow of energy from the control volume minus that is the energy quantities which are going out with the fluid stream at the outlet that is the outflow of fluid that becomes u 2 that is the internal energy at the outlet p 2 v 2 pressure energy per unit mass at the outlet fluid stream plus v 2 square by 2 plus g j 2 plus the work quantity because we have considered the for the control volume the shaft work is coming out then is control volume or the flow device or the open system develops work in the form that work is coming out in the form of the shaft work coming out to the surrounding so therefore we can write it this is equal to d w d t and difference d t minus very good minus and this will be equal to the rate of change of energy within the control volume where e c v is the energy in the control volume internal energy in the control volume at any instant internal energy in the control volume in the control volume in the c v at any instant ok this internal energy at any instant comprises all the energies in the control volume that is the intermolecular energy the kinetic energy due to the motions of fluid particles within the control volume plus the potential energy so this is the statement of the conservation of energy. So, now under a special and this you can consider as the general steady flow in a general sorry not steady general flow general energy equations for a flow process. We can consider this as the general energy equation general we can write it general energy equation general energy equation for a flow process for a flow process for a flow process or open system for an open or for an open system. Now for a special case when the flow process is steady as a special case for steady flow process for a steady flow process. When the flow process is steady that means we know the definition of a steady process or a steady flow field that means each and every point in this system the properties are invariant with time that means as a whole the properties within this control volume or the open system would be invariant with time this will happen when the mass flow rate at inlet and mass flow rate at outlet will be same. So, there will not be any mass accumulation within the control volume and at the same time the energy in flow to the control volume must be equal to the energy out flow from the control volume. So, that there is no change of energy within the control volume with time. So, that the energy quantity remains same the mass remains same. So, all the thermodynamic properties at each and every point within the control volume will remain same. So, this situation refers to a steady flow process. So, therefore we can write in those process first of all from mass point of view d m 1 d t is equal to d m 2 d t is equal to 0 that means the control volume mass will not increase sorry sorry sorry sorry I am sorry is constant let d m d t I am sorry this is constant otherwise for an general case we can write similar to energy conservation d m 1 d 2 minus d m 2 d 2 very correct d m c v d t which means the general conservation of mass the rate of mass in flow to the control volume minus rate of mass out flow from the control volume is equal to the rate of change of mass in the control volume. So, m c v is the mass of the control volume at any instant. So, for a steady flow this becomes 0 this is equal to d m d t. Similarly this becomes 0. So, if we now this is the general equation for a steady flow process, but conventionally this is written in a form like this if we divide the terms each and every term by the d m 1 d t or d m 2 d t which is equal to each other and let it be d m d t and divide each and every term by d m d t then we get an equation if we divide the terms on the left in the left hand side all the terms by d m d t then we get an equation in this form u 1 plus p 1 v 1 plus v 1 square by 2 plus g z 1 plus d q d m well is equal to what we can write u 2 plus p 2 v 2 plus v 2 square by 2 plus g z 2 plus d w d m difference is that here we what is seen what is implied by this equation the rate of energy in flow is equal to the rate of energy out from the control point each and every term represents the energy per unit mass it is more conventional to represents the energy quantities per unit mass this is the heat flow into the control volume per unit mass this is the workflow out of the control volume per unit mass this is the flow out of the control volume per unit mass this is the heat flow into the control volume per unit mass this is the workflow out of the control volume per unit mass in this equation this where the energy quantities on time basis the rate of energy coming in rate of heat coming in so rate of energy quantity going out rate of heat going rate of work coming out or going out but in general the for a steady flow process it is conventional to express this quantities in terms of mass so therefore each and every quantities energy per unit mass so energy coming in per unit mass is equal to energy going out per unit mass in the control volume and it is out of the control volume so this is known as steady flow energy equation the special case steady flow energy equation now you see that we have defined this summation of u plus p v as the enthalpy so specific internal energy plus pressure times specific volume can be defined as specific enthalpy since the enthalpy is defined as u plus p v you know u is an extensive property volume is an extensive property so if you define the corresponding intensive property by dividing it by the mass of the system we can define the specific enthalpy the sum of specific internal energy plus the product of pressure and specific volume so therefore we can write the equation in terms of the enthalpy quantities v one square by two plus g z one plus d q d m is equal to u two plus p two v two plus sorry we are writing h two plus v two square by two plus g z two plus d w d m this can be manipulated algebraically in this fashion that you can write this way that d q d m rather here you can write this way d w d m minus d q d m is equal to h one minus h two plus v one square minus v that means we are taking this here and we are writing this in the left hand side a simple algebraic manipulation h one minus h two d w m ok alright g z one minus z two divided oh ok this is g z one minus z two so you see that this is the final outcome of the steady flow energy equation but incidentally it happens that in all engineering devices all these things that heat transfer work transfer do not take place simultaneously and moreover the changes in potential energies and kinetic energies are sometimes neglected for example let us consider only the devices which have only work interactions which have only work interactions without any heat interactions let us consider turbine or compressor let us consider a turbine for example the simple case the turbine you know the turbine this is insulated let this is one this is two let this is insulated so in this case d w d t is there which is coming out whereas d q d t is zero or you can tell d w d m is there and d q d m is zero and if we neglect the change in the kinetic energy at the inlet and outlet of this turbine and also the changes in the potential energy then what we get we get from this equation you see that this becomes zero this becomes zero so simply and also this is zero that means the work coming out from the turbine in that case is h one minus h two therefore we see that for only work interacting devices for example in a turbine when work is coming out where the changes in kinetic and potential energies are negligible compared to the changes in the enthalpy it is the property enthalpy whose difference between the inlet and outlet state straight away give the work interaction quantity similarly in case of compressor if you see that is the reverse in case of a compressor if you see in case of a compressor see let us in case of a compressor if you see it is the same thing that if it is insulated let this is one and this is two and if it is insulated similar way d q d m is zero but it absorbs energy that means soft work is fading to the compressor that means it has d w d m but in this direction in that case also we can express the same equation that is in this case also d w d m is h one minus h two the same equation here h one is greater than h two always so that this quantity is positive work is coming out in this case h one is less than h two that means the enthalpy at the outlet is outlet section is more than that at inlet so that d w d m is negative which implies physically the work is going in similarly there are devices like heat exchanger where there is only heat input to a system for example a fluid flowing through a pipe flow and there is no work transfer that means d w d m is zero and if the flow area is uniform we can neglect the kinetic energy change that means v one is almost equal to v two and if we change the potential energies neglect the changes in the potential energy here also we can write from this equation you see this equation again we can write here making this zero minus d q d m is h one minus h two or d q d m is h two minus h one that means it is the difference of enthalpy which gives this heat transfer that means this is positive that means heat is added when h two is more than h one if h two is less than h one the heat is rejected so therefore we see now the physical significance of enthalpy is such that in flow devices steady flow devices the difference between the enthalpy at inlet and outlet section gives the net work and heat interactions by that device with the surroundings so for only work interacting devices it is in the work transfer is simply coming out as the difference in enthalpy provided the change in kinetic and potential energies are neglected and in all practical applications for those devices which interact in terms of either work or heat the changes in kinetic and potential energies are usually very small as compared to the changes in enthalpy so therefore it is the change in the enthalpy quantity which straight away giving the work so here you see the enthalpy in such system bears more or less the synonymous role as internal energy as if it is because of the release of enthalpy or absorption of enthalpy the work transfer takes place in a turbine the work is done because of the change in enthalpy so enthalpy bears the same physical significance or same physical entity as the internal energy does for a closed system similarly in a compressor the work is absorbed by virtue of which its enthalpy is raised because it is the difference of enthalpy which is giving the work quantity similarly in case of heat interacting devices where only heat interaction takes place it is by virtue of the change in enthalpy the heat energies coming out is equated with the change in enthalpy so therefore in this way we can tell that enthalpy bears a similar thing that is as internal energy does in a closed system but truly speaking it is not the internal energy it is a property of the system whose definition comes only by the mathematical expression h is equal to u plus p v now we see some more examples which may come in your compressible flow calculations that there is no heat and work interaction that means the flow takes place through a nozzle but there is a change in velocity for example the flow through a nozzle or a diffuser flow through a nozzle or a diffuser this is a nozzle this is a nozzle 1 and 2 and this is a diffuser flow through a nozzle and diffuser here what happens v2 is greater than v1 and here v2 is less than v1 that is 1 and 2 similarly the p1 here is greater than p2 here v2 is more less than v1 here p1 is less than p2 so pressure increases velocity decreases pressure decreases velocity increases in this case if you see the energy equation here again the common these two terms are zero so these terms we will take care of and if we neglect the potential energy changes to be zero because the there is no change or the change in the vertical heights at the inlet and outlet are small then here the equation tells like that h1 plus v1 square by 2 is equal to h2 plus v2 square by 2 now if you explicitly see it u1 plus p1 v1 plus v1 square by 2 that means this is the conservation of energy when heat and work quantities are not there the flow takes place in such a way the total energy comprising the enthalpy and the kinetic energies remains same that means here the kinetic energies created out of the enthalpies similarly here the kinetic energies are destroyed or kinetic energies are reduced the pressure energy the enthalpies are increased by virtue of the kinetic energy you see that this is the expression so this expression holds good for this type of flow now I will deduce the Bernoulli's equation which you have already read at your fluid mechanics class the Bernoulli's equation from this principle or from this equation of energy equation for a steady flow process what is Bernoulli's equation if you recall Bernoulli's equation is basically the equation for conservation of energy it is a mathematical statement for the conservation of energy for the flow of fluid but this is not the Bernoulli's equation perfectly this is the broad statement now what type of energy conservation in Bernoulli's equation we consider only the mechanical energy we see how the total mechanical energies conserved that is why it is known as mechanical energy equation this is the conservation of mechanical energy and we seek a simplified form of this conservation of energy in certain special cases of fluid that means in case of flow of an inviscid steady flow of fluid inviscid steady flow of fluid what we know that in Bernoulli's equation if you recapitulate your Bernoulli's equation Bernoulli's equation Bernoulli's equation we know that the pressure energy p by rho sometimes we can write it in terms of the specific volume or 1 by rho these are synonymous but usual convention is that in fluid mechanics we use it as 1 by rho we use density rather instead of specific volume but in thermodynamics we prefer this is a convention the specific volume so p by rho plus v square by 2 we know this expression g z is equal to constant what does it mean so this quantity as we have seen is the pressure energy of the flow work per unit mass this quantity is the kinetic energy per unit mass in a flow of fluid and this quantity is the potential energy unit mass so some of these three quantities give the total mechanical energy per unit mass in the flow of the fluid which are associated with the fluid stream and Bernoulli's equation tells that for an inviscid incompressible what are the conditions inviscid incompressible steady flow of a fluid these three things are constant and this is constant only along a streamline if the fluid is rotational and if the fluid is irrotational this constant is constant throughout the flow field this very important again I tell you this is the recapitulation in many times this question is asked in an interview or in a vahibhavoshi what is Bernoulli's equation and what are its restriction see if you tell the Bernoulli's equation it is basically the conservation of mechanical energy sort of those mechanical energies associated with the flow of a fluid stream this is the pressure energy or the flow work the kinetic energy and the potential energy usually we will consider the gravitational potential energy so some of these three energy will be constant provided there is no energy interactions from outside so first condition there is no heat and work interactions in the fluid flow from outside number two there is no change from mechanical energy to other form of energy or intermolecular energy which we physically call it as dissipation of energy or degradation of energy from the second law of thermodynamic because energy is converted from a higher grade to a lower grade so there is no such conversion which is only possible if the friction of the fluid is absent that means fluid is non viscous or inviscid see inviscid fluid and fluid is incompressible pressure remains same sorry and sorry density remains same density does not change in the flow so for an incompressible inviscid and steady flow of fluid without any work and heat interactions this three quantities p by rho represents the pressure energy per unit mass the phi square by two represents the kinetic energy per unit mass and gz represents the gravitational potential energy per unit mass some of these three quantities remain constant but this constant value remains same only along the streamline only along the streamline but for a rotational flow but for any rotational flow this is constant throughout now I like to tell you I do not know whether you know these things from your basic fluid mechanics class that why this is constant along streamline why in a rotational flow and what is the difference between rotational and irrotational flow from the energy concept from the energy viewpoint from the viewpoint of energy transfer you know the rotational and irrotational flow definition is that a flow is said to be irrotational when the rotation is 0 rotation of fluid element that is the curl of the velocity vector is 0 how do you define the rotation of a fluid element it is the average angular velocity of the two adjacent linear sides of a fluid element which are initially perpendicular and this is given by the curl of the velocity vector three rotation component in three coordinate directions so if the rotation is 0 flow is irrotational but if the rotation is not 0 the curl of the velocity vector is not 0 then the flow is rotational from the energy point of view in a rotational flow there is always a work interactions work is either given to the fluid from inside outside or work is extracted from the fluid from outside from the inside to the outside so because of this work given to the fluid or taken from the fluid the constant varies from streamline to streamline but if there is no work interaction along with no heat interaction then the fluid behavior is irrotational so it is both in visit and irrotational but it may be an in visit flow but rotational flow where the work interaction may take place from outside to the fluid or inside that means between the flow of fluid with the surrounding this is very important so if you discard the work interaction that means flow of an in visit fluid without any work interactions from the surroundings also no heat interactions from the surrounding then the fluid behaves as an irrotational in visit irrotational flow and in visit irrotational flow is synonymous to isentropic flow in thermodynamics isentropic flow without work interactions you can write isentropic flow without work interaction now let us immediately recapitulate hurriedly how we can derive these equations now from the steady flow energy equations now you see this is the steady flow energy equation general steady flow energy equations now if we apply this to a fluid irrotational flow of fluid irrotational in visit steady flow of fluid so we start with the steady flow energy equation so irrotational flow means there is no work or heat interaction this is 0 so therefore we can write that the steady flow energy equation takes the form h 1 plus v 1 square by 2 plus g z 1 is h 2 plus v 2 square by 2 plus g z 2 this it is very simple we can write from a differential in a differential form as d of we can write h rather we write this d h plus d v square by 2 plus d of g z is equal to 0 because if you integrate it between section 1 and 2 you get h 2 minus h 1 plus v 2 square by 2 minus v 1 square by 2 plus g z 2 minus z 1 you can write this thing now if we recollect the thermodynamic property relation which i will discuss again in this class that d d s is equal to d u plus p d v and we can write h is equal to u plus p v so d h is equal to d u plus p d v plus v d p sorry so if you replace the d u in terms of d h we can write d h is t d s minus v d p this is a very useful relationship which we get i will explain this in the next class also d h is t d s plus v d p yes d h is t d s plus v d p alright so if you substitute this we get that so for an isentropic flow so i have told you that in visit irrotational flow is synonymous to an isentropic flow without working direction d h is v d p so if i replace it we get v d p plus d v square by 2 plus d of g z is 0 so if we integrate this equation well if we integrate this equation we get integration of v d p plus integration of d v square by 2 plus integration of d g z is equal to 0 so far we have put the constraint of isentropicness of the flow isentropic that is the flow is isentropic that is in visit without any work interaction but incompressibility has not put into consideration if we put the incompressibility into fact that this v comes out from the integration plus sorry it is constant after integration it is constant very good d v square by 2 plus integration of d d z is equal to constant ok so therefore we can write after integration p by rho v can be written as 1 upon rho plus v square by 2 plus g z is simply constant and this is constant without the flow field and this is simply the mechanical energy equation for an in visit for an in visit steady irrotational irrotational these are the condition incompressible flow in gravitational full flow field in gravitational force field that means if a in visit steady irrotational incompressible flow in gravitational force field takes place the rotational flow means that there is from the energy point of view no energy interaction neither heat nor work this sum of this three energy quantities remain constant that means the mechanical total mechanical energy that is the pressure energy kinetic energy and this thing constant but if we we draw this constant of in visit that means the flow becomes real that is a real fluid that is which has got viscosity it may be steady it may be irrotational it may be incompressible because you know the flow of liquids are always incompressible they are changing density associated with the change in pressure is very small then what happens the sum of this three mechanical energy will not be constant because then a part of the mechanical energy either from the pressure of the velocities the agency friction of the fluid or friction between the fluid and the solid wall that is the consequence of fluid viscosity in that case also the conservation of energy will come into picture because energy is neither created not destroyed some form of the mechanical energy is converted into intermolecular energy through the friction which will be taken care of by this intermolecular energy which has been taken care of so therefore all the energy in the mechanical energy in the equation of conservation of energy for a real fluid we use a term as loss which is meant as the loss in mechanical energy so some form of mechanical energy is lost that means has disappeared but it has taken place in the other form as the intermolecular energy so this conversion with term is as a loss in the mechanical energy equation because this is a loss from the sense of mechanical energy that means the mechanical energy as a whole well this is because of the friction so this is all about the principle of application of first law conservation of energy to an open system any question thank you