 Welcome to today's lecture on industrial hydraulics and pneumatics. Now, today's lecture will be on pneumatic system and components and this will be introduction to that and the particular topic will be air preparation, compressor and accessories. Now, contrary to hydraulic system, pneumatic systems use pressurized compressible fluids. This means that in case of oil hydraulics, the fluid is compressible and incompressible and a pressurized fluid inside a conduit acts as a elastic body. Maybe it is like a solid member. Therefore, in that case particularly where with closed circuit, there is no change in pressure once it is the fluid is trapped. Of course, that depends on the load required we are moving, but in case of this compressible fluids air or gas, what happens the fluid after utilization it is exhaust to the nature and in that way pressure of the fluid reduces. So, for the constant pressure system it is not that much suitable also it is not suitable for very high power. So, but for the small applications small power applications tools and others you will find this pneumatic system is very useful and air is free of cost you are getting a free of cost only thing you have to prepare the air for utilizing into a system. Now, although other gases are used, but air is the most common compressible fluid although some gases are also used in pneumatic drives specially where the gas itself is one of the product or by product where the system is being used. However, air is the environment friendly chief safe readily available fluid media for pneumatic applications. For general purpose actuator drives manageable with low pressure usually 2 mega Pascal, 2 mega Pascal means it is 20 kg per centimeter square and you can see just a little above absolute pressure. Pneumatic system is preferred over hydraulic system where pressure may be as high as 80 mega Pascal. This means that in hydraulic system we can go up to 80 mega Pascal, but in normal case as you know that in oil hydraulics 20 to 25 mega Pascal is very common 80 mega Pascal is very special applications, but it is possible there. However, position or actuation at control velocity is not achievable with compressible fluids. This is a drawbacks with compressible fluids if you would like to control the position control or the velocity control then it is very difficult to achieve for a small magnitude small zone it is possible relatively larger zone larger range where the hydraulic fluid will be more useful. Pneumatic application in such areas are rare and where hydraulic oil cannot be used due to environment reason. Actually, we had in some cases it is compromised where the hydraulic oil cannot be used due to environmental reasons. So, better to go for pneumatic applications say for example, in case of food processing industry. Also less accurate performance is acceptable. In pneumatic system compressors typically the vane, lobes, screw or cylindrical piston type positive displacement machines are used to compress and store the air. Now here again I would like to mention that in case of pneumatics or the compressible fluid the machines the hydrostatic units are used that is pump and motor those are in nature positive displacement. This means that their volume displacement ideally is will be equal to their geometric displacement. It is not like hydro kinetic machines. For example, a blower if we consider a blower it is not a positive displacement machines unless it is a positive displacement machine is being used for a blower. So, I think you understand what is positive displacement that if you calculate the geometric volume displacement ideally that will displace the same amount of fluid. Now in case of compressible fluid definitely this volume is being compressed that means when the pressure is increasing that volume is being compressed. So, by the pump that much amount of is being pumped whereas it might be of higher pressure and then it is going into the reservoir that means collector and gradually you will find that if you ask that how what is the volume of air inside the reservoir. The answer is that what is the geometric volume of the reservoir that is the volume at any point only thing pressure is gradually being increased as you running the compressor. In case of oil hydraulics it is not that this means that in the conduit obviously always you have to say volume is equal to the that amount of volume. But you can say the your positive displacement machine also delivering the same amount of volume in case of the air it is not or gases. The compressed and stored air or gas used in operating pneumatic devices when whenever required by tapping in a regulated manner the air from storage vessel tank normally attest to and or integral with the compressor. This means that it is not that you are directly pumping this air to the system. In case of hydraulic system most of the cases you will find that there is no reservoir in between. If you consider at all there is a reservoir in between that you may consider the accumulator very small reservoir. But in case of pneumatic system there will be always a reservoir that means first the air is stored in a reservoir or receiver and then the air is used for the system. You can simply tap the air with the help of a regulator and can use it. Usually compressor is stopped at a set higher pressure than maximum operating pressure. Say for example, you are using a in your pneumatic systems in the in your works of or industry for machines maximum is 1.5 megapascal. Maybe you are storing that air inside the reservoir at 2 megapascal. It automatically starts again when the stored air pressure reaches a minimum set value. This means that say for the reservoir 2 megapascal is the upper limit. So, when the pressure inside this reservoir will reach at 2 megapascal it will be automatically stopped and probably it will start again the minimum pressure what you need for the operations. Say for example, it might be 1 megapascal or might be 0.7 megapascal whereas maximum for some devices is 1.5. So, when it will reach that 0.75 or 1 megapascal it will start. But one thing we should remember that if we had to use that instrument or device which is which requires 1.5 megapascal then we have to set the lower pressure as 1.5 megapascal. So, then range will be 1.5 and 2 megapascal and also usually there will be a time set otherwise the compressor will run always. So, that is a design criteria that you have to design in a system suppose you are using this always it is 1.5 megapascal and very continuous consumption is there. Probably you have to set the compressor reservoir side in such a way at least your compressor can be stopped for 5 minutes while it is running otherwise question of heat generation and other problems are there. Usually from a centralized store air is supplied to various locations of an entire industrial plant. It might be single reservoir in it might be multiple usually not more than 2 reservoir are used to supply the plant. If the plant is very big sometimes it is more than 1 reservoir is used. After filtering and before the end applications a fine mist of lubricant is mixed to the air to prevent air in the moving components. Now usually if you find that air operated devices say for example air operated screwdriver. So, you just put say if you have observed in automobile industry they had to tight the screw may be in a line in a assembly line they have to tight a screw 100 screw per minutes say just for an example in that case every screw driving by the screwdriver is not possible. You will find the pneumatic screwdriver is there and it is set like that for this screwdriver device when the maximum torque is reached it will automatically slip. So, now in that case that is connected with a pneumatic systems. Now usually this moving component inside definitely there is moving component there is no separate lubricant inside. So, with the air you have to mix that lubricant normally with the air not with the other gas and other things in case of gas also you have to take care of that what type of lubricant you can mix. In case of air ordinary lubricant can be mixed, but before that your air should be all dust free and it should be dry. That means no moisture is allowed within this air. So, after filtration or such preparations again you have to mix with oil that is important this is required to lubricate the moving components. Air dryer is also used to eliminate moisture from air. So, as I have told that you have to use an air dryer a muffler is put at the exhaust to reduce noise. Now muffler means the silencer is usually used at the exhaust point. Now when you are using a system then the device you are driving. So, it might be after the replication there should have muffler. That means muffler in some cases you will find is an integral component or of the pneumatic device which you are using, but there is also inline muffler just to reduce the noise level. When the air is flowing through these components there will be noise you can you know it that when air blows to even if in nature also when air blows you can heard the sound. So, to reduce such noise there will be muffler or which is called silencer. Now next slide we will look into a pneumatic system I think that you cannot read this not that clear, but I would say that here there is a this is the compressor unit. This compressor unit is having the this is the driving unit and then may be filtered then cooler and after then this is the main reservoir and here there is a dryer at that point there is a dryer. And if you look into this what we find we have two parallel system connected to the same line. As I told in case of if you find that air is being utilized in such a way if you use single compressor then it will run it has to run for I mean continuously that is not permitted to look into the life of the compressor because during such process use air is generated this is due to the molecular action in within this air. Now, you one can have one compressor and may be two reservoirs or might be there is a big reservoir and two compressor this is usually safe system to use two compressor rather than manipulating something with the reservoir. And then it is also shown here say these are the two work point, but usually there will be huge I mean many work point. Now, these tools are called pneumatic tools and here this is the regulator filter and lubricator are used at a different point. Say each and every before each and every pneumatic tools you will find a filter regulator and lubricator is being used. So, this is a very schematic and very general system for a pneumatic there will be a pipeline throughout the industry. Now, in preparation of usable pressurized compressible fluids we need following major components one is that definitely a compressor is nothing, but a pump which is pumping the air or gas a receiver or a reservoir tank starting unloader and controller this is very important we will come to that what it is then we need filters. Now, this filters is not again the suction strainer there will be there after the compression we need a filter online filter to make the air dust frame. Then we need definitely a regulator and valves we need a lubricator as mentioned mufflers and silencer after cooler we need a after cooler means usually the air before entering into the machine we need to cool it because the air we exhaust into nature. So, we do not need after cooling means it is not after using this air in case of oil hydraulics what is done usually after the application we take back that oil to the reservoir and before that we use the cooler. In that case before utilization a cooler is used, but after cooler term is used after all process that mean drying etcetera then the cooling is done and finally it is used. Then air dryers and we need indicators that is pressure temperature etcetera wherever required also sometimes a set of pressure and indicator is kept to inspect the pressure and temperature at different point that is sometimes needed because there will be very big pipeline for the supply of the air pressure sometimes it is very difficult to find where the pressure drop actual pressure drop is occurring. So, for that purpose we need separate unit pressure and in temperature indicator. Now, we will come to this components what are the components and the most important is the compressor now if you look into the types of compressor then most common is the reciprocating piston compressor and then again the piston compressor and diaphragm compressor diaphragm compressor means in that case a diaphragm is being moved by some means and that also compresses the air. But then rotary piston compressor this is sliding vane rotary compressor you see one is that rotary piston and another is called rotating piston anyway we a rotary piston means usually a volume is trapped and then that is compressed by compressing the variable area. In case of reciprocating normally the stroke length varies area does not vary whereas, in case of rotary pistons you will find area is varying say gear pump like that low pump etcetera. Then this rotary compressor again sliding vane rotary compressor two axles screw compressor say like gears and etcetera that also fall in this category and roots blow over and then another it is a flow compressor that radial flow compressor axial flow compressor these are two different types of separate flow compressor. But we shall concentrate on these are the some special types these are used for not normally such big system very small systems these are used. But reciprocating piston compressor this is very common particularly piston type and among the rotary pistons both sliding vane and two axles screw or the gear type compressor are mostly used. So, we shall concentrate on these items only. Now reciprocating type reciprocating cylindrical single piston cylinder type compressor may be of single may be of single or multiple this means that it has meaning that single means suppose there is a two pistons that is not that may not be two stage only two pistons are being used they are compressing the air at a same pressure whereas, you may find two pistons but that is two stage that mean in first stage one piston is compressing the air and second stage other piston the compressing that air that means suppose you have to raise the pressure up to two megapascal first piston may be raising the pressure not exactly half it might be 0.75 megapascals and then second piston that compressed air is being further energized to make the pressure two megapascals. So, that is called two stage similarly there may have three stage also. So, we use single or multiple stage now if I look into this figures the left hand side this figure a that shows a reciprocating two stage compressor but before that I would say that depending on pressure capacity if the pressure capacity is one megapascal usually in that case we can go for single stage then it is if it is 3.5 then two stage then if it is 17.5 megapascal it is in the higher side and as well we have to go for three stage and for 35 megapascal this is four stage. Now, 35 megapascals means it is very high the this is a definitely special applications normally interest of fluid power we use normally 25 say 21 megapascal is equal to 3000 psi 21. So, 35 means it is more than 4000 psi normally there is no such applications but if it is required then we have to go for four stage and normally reciprocating type is not suitable for that usually screw compressor is used for such compressions. Anyway if we come to this compressing machines what we find here is one set of piston cylinder here is another set of piston cylinder and here this is the third. If you look into these two these two are identical even they are having the same discharge valves suction valve these are same. Now, these two cylinders together pumping the air for the first stage that means from the nature the air is being taken and that is being pumped that is being compressed to reach a certain amount of pressure say for example, two stage mean this is 3.5 probably it is being raised up to 1.5 only then this total compressed air now that total compressed air what the two piston has done that volume has reduced that for that only a single piston can pressurize that amount of air further to 3.5 and that is the second stage piston cylinder. Now, the other details you can study of your own from this figure. Now, if we look into this principle you know it but basic principle is that this while it is reciprocating then there will be one is that delivery and one is the inlet and one is the delivery say it is rotating in this direction. So, only the inlet port is open and when it is rotating the other half then it is being delivered. This is the simplest form of this reciprocating system and the same thing is followed here just only suction and compression. So, in and out delivery. So, if you look in this way for one cycle only suction. So, half the cycle suction and half the cycle the delivery. So, you can put two cylinder single stage but two cylinder in such a way that is continuously it is supplying the air to dissipate a generated heat due to molecular reaction in the air being compressed. If you compress the air you will find that heat is being generated cooling system natural air draft to forced water cooling are employed. That means, for the small compressor you can simply use a fan just to cool and this reservoir as well as the compressor outside is made body is made with additional heat dissipation area. That means, fins are used even if the tank you will have you may find that additional fins may be used just to cool it. But for higher pressure may be say in case of two stage three stage and four stage you need to have forced cooling and usually cooling by water is done. Other fluid can be used in case of say refrigerator systems if some cooling is required no water is used. But in case of general compressor for big compressor which is used in industry usually you will find the oil is being used. And normally if you look into this pistons outside there are pockets these pockets are filled with water. That means, water is always flowing through these pockets that is called jacket. The piston is having the space through which the water is moving that means, while it is being compressed then itself it is being cooled to some extents. And after that also there is a separate cooler is used to cool the air. Now this is a photographic view I am not describing the components. You can understand this for the same machines these two are for first stage and this is for the second stage usually a spring is provided just for the return stroke. If you look into the geometric of this cranks after another things. So, you need to have some return. So, the springs are buffer springs are usually used. And if you look into the capacity with a 0.54 meter cube capacity reservoir storage tank you can understand this 0.54 meter cube. So, 1 meter cube is equal to how much 1000 liter. And here 0.54 means half of that 500 liters around 540 liters around this 1 meter cube the volume and compressing capacity of 1.3 meter cube per minute. So, this is called compressing capacity not the flow capacity we should call compressing capacity. At 1.23 megapascals power of the motor is 6.25 kilowatt typical. If you calculate this pressure into flow rate it will not be 6.25. But usually efficiency of compressors is relatively poor that is why at least you need 6.25 kilowatt typical. We will calculate the sizing of such in compressors. Now an air compressor is usually made auto control to start run supply pressurized air as needed. And stop when receiver is filled with maximum capacity that is pressure and be ready to start again when the pressure reaches at its lower limit. A few methods are employed for such control. Pressure switch control is one of them. Once a pressure is established after first start up a starting unloader look at this term it is called starting unloader is required to prevent the established air pressure from pushing back against the compressor preventing it from coming up to speed. The meaning of the sentence is that you have compressed the air and the compressor is stopped. Now if you look into this line from the where the rotary piston rotating piston is compressing the air from that point to compressor path is completely filled with pressurized pressure. Now it is cut off from the reservoir. Resurver is supplying the air and that pressure when it is reduced then the compressor has to start but when the compressor is going to be start the trapped air to that will create a problem to start off the compressor. So you need to release that pressure within that short path that is from the compressor head to the reservoir entry point that is called starting unloader. Now we use here the pressure switched type. Now if you look into this figure 4 this is the pressure switch what is if you look into this this is the compressor head say air inlet is here. Now this air is going and here is a non-return valve connected to the reservoir receiver and then air is being compressed and forced with force it is being entered into the reservoir. Say it is 2 megapascal. Now when such pressure is this is this is the reservoir is being filled then with a set pressure this switch is there and that gradually disconnect the motor and your compressor will stop but if you look into this path then this path will remain filled with the pressurized air. Now to relive that what is there with this pressure switch there is a lever that operates another valve actually there is another valve sort of things which allowed or relive the compressed air between this path. Now here apparently it is a open path maybe here maybe some non-return sort of valve might be there which is not shown here but what happens when this machine is stopped the reservoir is having it is maximum pressure say 2 megapascal then this motor is stopped as well this path is made free. So, that next time when the signal comes it starts operating without any trouble for that we need a unloader. So, this is you can say the starting unloader when motor is off by pressure switch it also bleed off it is this operation is called bleed off the trapped air between the piston head and receivers check valve this is the receivers check valve it enables the compressor to start again whenever needed. Now there is another type of unloader which is centrifugal type the basic principle is that the centrifugal mass is attached to a rotating member this is with the compressor crankshaft then when it reaches then it operates the switch in the same way the pressure switch operates. Now in such system greater production is ensured as the unloader valve is operated by the compressor itself rather than the pressure switch such normal controls described above are used where the compressor running time is 50 percent to 80 percent of total working time. Now for the compressor starting frequently say within every after 6 minutes or running time exceeds 80 percent of total time more sophisticated constant speed control is adopted that is usually nowadays with electronics control some controller is used to automatically cut off the compressor start the compressor and in between unload or the relief the trapped air between the compressor head to the reservoir inlet. Now this 6 minutes figure what I understand this is usually a figure at least you should keep a 6 minutes time off between 2 running times otherwise sufficient cooling will not be there. Now we shall consider another type of compressor which is called screw compressor. Now this is rotary positive displacement because if this is like an hydraulic screw pump here also the screw 2 screws are rotating but if you look into this this might be rotating at this 2 screws are rotating at the different speed not at the same speed and this is the entrapped volume is being compressed it is taking in and it is going out in the other side that means inlet and outlet is usually axial in case of the screw type compressor if we look into this figure then we will look into this it looks something like this these 2 profiles are not same I mean this profile and this profile are not same here is also it is not very clear from this figure but from this side view we can look into this. And what we find then there is a timing gear this is required to for inlet outlet control the cooling jackets is there and this is not symmetric asymmetric rotors anti friction and rolling bearings are used in between. Now this is the what is found that this type of compressor is having much better life and it can perform better in high pressure. So you will find that of course if you think in terms of volume that will be less in comparison to the reciprocating type. So where the moderate volume is required with very high pressure may be the screw compressor is the better than the cylindrical piston type as in screw type the entrapped volume gradually squeezed to smaller and specialized volume for to be stored in reservoir usually it is axial usually you will find the axial inlet and the outlet in the radial directions but at the other end and these are the cooling jackets. Now to assess and size of such a machine 0.7 mega meter cube per second that is the capacity of storing 0.85 mega Pascal is typical for a single stage screw compressor. So single stage screw compressor means it is not very high 0.85 mega Pascal and 0.7 meter cube per second. So this volume not that small in that way maybe this value may not be correct I have to check it 0.7 meter cube is a very big volume. Then if we look into the side view of this screws compressor you as I told these are not symmetric profiles it looks like something like this one is that thinner another is wider and here what we find this we have 4 lobes that means it might be 4 start screw and here what we find 1, 2, 3, 4, 5, 6 here 4 and here 6 that is why you will find that these two are rotating at different speed and we need a separate gear of the same ratio at the end just to match that. Now you may ask why it is different it is seen that this will give better performance as for the volume is concerned and as this is being of different size and this is the may be to optimize the capacity it is better. Suppose if we use here 4 and here 4 you may find that it is not the optimum design using 6 here and because this is the main pocket as if this pocket is being composed by this is the piston you can consider this is cylinder this is piston. So, 4 piston is compressing the air within 6 cylinder roughly you can say like that, but actual path is like that it is a helical path through which the compressed air is being moved separated by the contact at these two profiles and by the casing. It looks like Novikov gear if you look into this side view it looks like a gear not exactly Novikov gears it is different, but as if it looks like a gear. In fact gear type compressor may be regarded as short screw compressor with different inlet outlet arrangement. Now obviously if you look into this if you like to compare with this gear sorry this screw compressor with the gear type compressor definitely this is also helical that means helix gear as if, but this length of this screw cone here what is the length in this case length is very small as well you will find the inlet outlet is like that, but this is also of different profile as you can see you can compare this, but remember this one is the gear type or sometimes it is called lobe type and whereas this is the cross section of the screw type compressor. Now here again I have shown some say this is gear type and similar is the lobe type, but in case of lobe type usually these profiles are same both the profiles are same and number of lobes will be same, but basic principle this lobes and gear are the same principle and you will find inlet outlet is like that, but remember like the gear pump this is say suppose this is rotating in this directions then this will be inlet and this will be outlet normally if it is rotating like in this directions then people confuses perhaps air is flowing like this in case of gear pump also, but it is not like that. The air is coming in then it is being trapped and it is going out if we remember recall that comparing with the gear pump here from this contact point and this three contact line or point on this plane if we consider with the rotation this area will be gradually it will reduce that means this volume will be compressed. So, this compressed air will now go inside it will be trapped and then it will be delivered in the other sides and this is the side view of this lobe type compressor. Inlet outlet as different this is completely radial in case of screw type you will find this is going like this and probably outlet will be like this. So, the length to be considered as a width of the gear in this case also the teeth may be straight and not helical say here somewhat it is helical one can use the straight teeth for the gear type compressor and lobes are always mostly you will find may be straight also here of course it is showing that as if it is helical it might be straight also. In this lobe there is no space within the lobe, but here this space is given it might be this is all can be used for cooling purpose also. However, capacity wise the screw type is superior although has more friction losses due to friction are minimized using liquid lubricant which also carry heat as well as mixed with the compressed and pre filtered air. Now, in such in such compressor you have to lubricate this. So, that lubricant is mixed with the air. So, it might be we have to reduce the air first demodernize the air before entering into such compressor and then or else the well being mixed that will not be separated we have to use the separator or filter in such way the oils are not being separated because the oil mixing is being to some extent is being done while it is being compressed. Now, this is another view of the lobe type and this is the constructional feature you can see in this case lobes are straight here as you can see and you can see these operations. How these operations is being done gradually 1, 2, 3, 4, 5 these are the 5 stage of operations. I think you can study this yourself. Now, next one is the vane type compressor. In vane type compressor this is the principle is exactly same as what is in hydraulic machines oil hydraulic machines. Now, the this is a typical capacity 2.5 meter cube per second this is very high and 0.35 megapascal in single stage. Now, if you look into this this vane are not placed exactly radial you will find that is inclined. This inclination is given is like that for this compressor you will find this is rotating in this directions not in this directions. So, that this is having the sealing effect better sealing effect. If you rotate in this direction the pressurized oil will put the pressure and to allow it to go inside and so, there will be leakage through this. Looking into this vane orientations you can find that this is the direction of that means, from this side it will rotate in the anticlockwise directions. This you can see how much this inclination is there and this is the constructional feature of the vane type compressor. And also if you look into this in this case of course, the vane are straight, but this is on what is that there is a this is shown that how the thrust pin are provided. And then and this is the packing strip this is the rotor and there is the slot veins etcetera. This is a functional feature may be this is also the straight type veins are used. Here also as you find the veins are straight now if you look into the compressor rating. The rating of compressor is usually expressed as its storage flow in flow in rate capacity of free air that is at atmospheric pressure that is 0.101 mega Pascal absolute 14.7 psi and temperature is 20 degree Celsius. The flow rate is then called standard flow rate and usually express in meter cube per second. So, this means that intake volume we call in meter cube per seconds. This that volume what we have the mention in the capacity that is the intake volume to the machine say 2.5 meter cube per second is the intake volume per seconds. Now, this gas law law is known to you. So, we can use this gas law to calculate the rating of the compressors. V P and T are the indicate the volume pressure and temperature respectively and subscript 1 and 2 represent compressors inlet and outlet parameters. Dividing both side by time q we get in terms of the flow rate. Now, if you consider a problem the a typical numerical example in a large scale system the air is used at a rate of 0.0142 meter cube per second at 0.875 mega Pascal and 32.22 degree Celsius. Celsius spelling will be S not C. Anyway, this is now this rate if you look into this rate is the delivery rate utilization rate not the compressors rate. Now, we have to estimate the free air flow capacity of the compressors. In that case the solution is like that in this equations what we put that is the q 2 is given that is the q utilization side that is the outlet of decompression. So, q 2 is this mass and pressure p 2 now this pressure whatever pressure is given here mind it we have to convert it into the absolute that means you add simply the normal absolute pressure. So, and then the temperature is we have to add 273 that is the reference temperature we have to add this and then the this to T 1 and T 2 temperature rise is from 21.11 to 32.22 and what we find the 0.132 meter cube per second of free air we need to compress. So, note absolute temperature is taken as 273 degree Celsius and this means that in order to have an air of 0.875 mega Pascal at 32.22 degree Celsius at a rate of 0.0142 meter cube per second by the reservoir of a compressor it needs a supply of 0.132 meter cube per second at 0.101 mega Pascal and 21.11 degree Celsius. Apart from the storage of air reservoir that is storage tank of a compressor dampen the pressure fluctuation and supply the pressure to utilization ends at constant pressure. In many cases among all pneumatic system at the utilization end a few may demand the higher flow rate at starting which exceeds the capacity of the compressor. A well designed reservoir is capable of handling sub transient situations that means time to time we need more excess air to flow. A reservoir size is expressed now we have to also depending on the plant we have to find out the reservoir size. This is expressed by this formula and where you will find is the time that the reservoir can supply required amount of air and then q r is the consumption rate of the pneumatic system q c is the output flow rate of the compressor and P max is the maximum pressure level in reservoir and P mean minimum pressure level in receiver and V r is the receiver size. So, again we consider another problem calculate the required size of a reservoir for a system consuming 0.1 meter cube per second standard for 6 minutes between a pressure limits 0.7 mega Pascal and 0.56 mega Pascal before the compressor resumes operations. That means this is the maximum limit where the compressor will be stopped and this is the minimum limit when again the compressor will start. What size is required if the compressor has to run and deliver air at point not not 2 meter cube per second standard. Now, simply in this to calculate the V r we consider this is the pressure and this is the 6 minutes time means this is in second and this is the difference of this pressure pressure here and this is the difference in the capacity flow capacity. So, what we find that we need the reservoir capacity of 2.6 meter cube at least, but here we have simplified the problem to arrived into this say formulation this as a requirement is this you have to exercise that really you have to make the average of total utilization compressor time how much it should be stopped etcetera. So, that becomes a little complicated not this simple, but for as a numerical example this is the way how to calculate the capacity of a compressor size of the reservoir. Pressure at numerator and denominator have the same unit that means in this case you should take care that this should be same unit even if the pressure as expressed here in PSI that is not a problem this and this and in case of B as you can see that this is the meter cube per second the standard. So, for that we need 0.208 meter cube suppose this amount of flow as intake is provided then we can reduce the capacity of the reservoir. Generally in selection of a reservoir tank size 50 percent oversize is recommended considering 25 percent for overload and 25 percent for an expansion if needed in future. Say for you are designing a certain compressor and reservoir for an industry then in that case first of all you have to consider at least 25 percent overload may be there. So, 75 percent directly coming over there and usually what happens after setting up you may need to add 1 or 2 more equipment with that. So, another 25 percent that means whatever capacity is wanted for industry usually if it is in the beginning stage and considering that is the 50 percent requirement we usually consider 100 percent and then we design the compressor. Now, power required to drive the compressor a semi empirical formula is usually is used in recommending actual motor size compressor efficiency to be considered. Then this is the semi empirical relation to calculate the power where P this is for the total of the motor and then this is ideal. So, we are calculating the ideal one and then we divided by the efficiency overall efficiency to calculate the power and Q is the flow rate standard and P in is the inlet atmospheric pressure in Pascal's and P out is the outlet pressure in Pascal's and absolute and this is the overall efficiency. And again if we consider another problem determine the motor power required to drive a compressor having overall efficiency is equal to 75 percent that delivering 0.4 not 47 meter cube per second at a pressure of 0.2 mega Pascal's. So, these are the given data considering this we can calculate this power ideal is coming 13.3 kilowatt and the efficiency is 0.75. So, 17.73 so we recommend a motor of 18 kilowatt. I think we can continue these components in the next lectures. So, now this is main portion of this is a book this is available in print is all India Indian book I do not know whether the print is still available or this is available in the market. But, this is very good book to have some basic knowledge about the pneumatics also there is another book that is by India publications and also this is print is all of India, but some practical application the second book is good and for basic knowledge the first one is very good. So, thank you.