 Welcome to today's lecture on pneumatic circuits. We have learned a little bit about the air preparation and components. Now, contrary to the hydraulic system, pneumatic systems use pressurized compressible fluids. Air is the most common compressible fluid as you know, as it is environmental friendly, chief safe, readily available fluid media for pneumatic systems. Usually from a centralized store air, it is supplied to various locations of an entire industrial plant. Now, for the preparation of air, what we need? We need a compressor which in inlet, it accepts the air from the atmosphere, which we call standard air. And then at the inlet of the compressor, there is although a filter or strainer is there, but actual filtration is done after it is compressed. Now, that air only not only it is compressed, it needs many other preparation process before it is allowed to enter into a pneumatic system. Now, first of all this compressed air is stored which partially cleaned in a receiver or which is also simply reservoir tank. Then in compressor as you know that it cannot run for continuously or it is not desired that it would run continuously. What is there? There is a system by which the compressor is stopped when the compressed stored air reaches a certain upper level of pressure. Now, when it is stored, the compressor is stopped. Then from the compressor end or compressor head to the reservoir intake, the air is trapped with the pressure at which we have stored it. Now that we need to release before starting the compressor again. So, for that the system which we have discussed earlier, it is called starting unloader and also there is a controller. If we need better control nowadays, the electronics control system with the maybe with the hydraulic circuit can be utilized for that. Next we need a filters. That means, when the compressed air being supplied to the machines, first it is filtered. Then we need to regulate. So, there will be a regulator as well as maybe the flow control valves. Then we need a lubricator. Now why the lubricator is needed? That is needed to add some lubricant to the compressed air because it is when it is being used in the pneumatic systems, there are moving components and there are no other means to lubricate that components. So, lubricator is mixed with the air. Now we need also muffler or which is called also silencer. In case of fluid, sorry oil or liquid that is that returns to the tank and that is not that much noisy in comparison to the gases. So, when gas is released then it is released to the atmosphere air particularly in that case it makes a noise. So, essentially we need an silencer at the end, but as well we need a silencer even when it is entering to the system, I mean utilization end. That silencer is usually called online silencer. Now we need a after cooler. This after cooler is not after the utilization. In fact, before the utilization because when the air is being complex a lot of heat is generated. So, it need to be cooled before being utilized for the further work and also the air contains the water particles. So, it needs to be dried. So, we need a dryer and apart from that different sort of indicators pressure, temperature these are required. Now, this is a typical schematic or artistic view for a plant. Here what we find the compressor and usually this compressor there will be another standby compressor also. So, that if one fails another can be operated or intentionally to reduce the load of a compressor particularly from heating. We may use two compressor instead of one large compressor, but this compressor capacity by no means that this is of less capacity in pressure may be volume capacity is less. The pressure capacity it both should be same, but it can fail this tank say partially it is filled by this one then it can be filled by other one. So, in that way one can be of less capacity another can be of higher capacity, but usually both are kept of the same capacity because we can it will serve all the purposes. If one fails it will work if you want to keep one standby it will work. If you want to run say this is a and this is b a fast b or b fast then a everything will be possible if these are of same capacity. Now, as we see that this is after loader after cooler and lubricant cooler these are cooling elements here is the compressor. Now, this is control panel this is motor this is compressor air end then a lubricator or air separator may be moisture separator or lubricator separator also I do not know exactly this why this separator also used for lubricating this air this water separator is definitely is used. Now, this is the main tank and this is the dryer one dryer we need a single dryer is there then the pressure flow controller is there and this is usually you will find that each and every point the filter regulator and lubricator FRL it is called short term FRL the three elements you will find one is lubricator one is filter and another is regulator. Each and every point usually such an element will be there and these are two work station where this power is being used and this as we see that we can connect more. After such preparations then these are used, but for individual application we need to develop separate circuits this which we are talking about the air preparation filter etcetera valves etcetera that is for the common supply to the whole industry, but for any pneumatic system we need a separate circuit. Now, for designing such a circuit first of all we should consider safety of operation secondly performance of desired function thirdly efficiency of operation and last the costs all together we have to think while we are going to design any system. Suppose one of that may be not that essentials say for example, costs sometimes the costs we can of course, we will not make it of exorbitant cost, but the cost factors may not be that important. However, in every cases the safety is fast so we have to think all sorts of safety protections. Now, performance of desired function it is very important whatever may be the function we need whether it is not very precision still we need to design in such a way that we can achieve the best performance out of it. Now, efficiency operation sometimes it can be compensated many means that we may not make the system very efficient. However, if making any system considering the best performance high efficiency and low cost that should be the motto, but it is not each and every point is the minimum or the maximum efficiency maximum cost minimum this may not be possible. So, we use the term optimum design anyway that needs I will repeat that needs may be you can follow a mathematical model to optimize everything or else that mostly depends on the experience. In case of pneumatics leakage and friction losses are the most crucial design factors that affect the above parameters most that means to minimize say for example, if I take even the cost factors to minimize this cost factors we have to make the system as much as possible it is leakage free, but in pneumatic systems that although ceilings are used, but still there is a possibility of there will be leakage say for example, a very simple example when we drive a car let us consider the car of pneumatic tire in that case car scooter everything the this is filled of to take the desired load, but what happens on the process there will be some leakage or in this pipelines this pipelines usually in plant is very big there will be several joints there will be several outlet points through which there is a whatever may be the amount there will be very small leakages that can be controlled by regular maintenance or initially selecting very good components. However, there is also a friction loss that friction loss you can say the skin friction we inside the conduit even if it is a very good finished, but when the air is flowing there will be friction between the air and the surface of the material and by no means we can neglect that one. Now, for an example leakage losses through various leakage areas with a combined area of 6.25 millimeter dia hole that means we are considering that the orifice through which the leakage is being occurred 6.25 millimeter dia. Now, this is very rough estimation because this is all area summing of all area it becomes equal to the area of 6.25 millimeter dia. Again if you consider the coefficient of discharge through this orifices of whatever may be the leakage passes may be capillary then this coefficients will be different, but roughly we can say this loss will be around 0.033 meter cube per second and this is of standard air for an operating pressure of 0.7 megapascal that is 0.7 means it is 100 psi. This may cause wastage of few lakhs of rupees in area if we calculate for pressurizing air of that amount and this is per second. So, if you consider the whole operating time for a plant this may be few lakhs of rupees in area, but anyway we can minimize that we cannot eliminate that. Such leakage losses are due to improper sealing and fittings which may not significant at the beginning, but becomes prominent after sometime. Friction losses are mainly due to undersized components and improper pipe lining. Now, you see that while we are making the pipe lining and definitely we will select the optimum size. It should be minimum leakage loss as well it should not of use volume then you will feel you will find that to feel that whole conduits if the amount of air is too high and there will be always leakage losses. So, we cannot control the leakage losses in other way. Therefore, in designing pneumatic system optimization is essential particularly in multi use pneumatic plant. Now, the energy loss due to air metal surface friction in pneumatic lines may be estimated using the Harris formula as follows where this pressure loss I mean loss in terms of pressure is expressed in this form where P f is the pressure loss in Pascal's C is coefficient which is to be determined experimentally for this coefficient is for pipe losses we are thinking of pipe losses. So, L is the length of the pipe Q is the flow rate through that conduit in meter cube per second again we call it standard air that means standard air means it is some pressure some temperature etcetera mentioned R C is the compression ratio of the system D is inside diameter of the pipe. Now, this C is to be determined considering the type of pipes type of conduits we are using. So, usually in case of pneumatic system main pipeline is of metal that is not flexible one. So, and metal means again it is steel nowadays stainless steel pipe is also being used because of the low cost production cost for the stainless steel otherwise previously this was iron steel was being steel ordinary steel was being used it is medium carbon steel not alloy steel, but again the surface preparation of such pipes even the material same may be different. So, there is some standard say in case of India we call it Indian standard according to that the C is to be determined for a range of pipe and it was found that C also depends of this diameter inside diameter D that means if we replace this C we will find a factor is coming here that numerical value something is coming here and there will be something to be added with this power subtracted or added with this power it will become in this form. So, this conversion I have not done, but as for the calculations for a compressor delivering 0.0472 meter cube per second standard of air through 2.5 centimeter standard commercial steel pipe this is just 1 inch pipe I have converted to like this length is 76.2 meter that is around 250 feet at a receiver pressure of 1.05 megapascals the pressure loss due to flow in pipe is estimated as 0.035 megapascal for this much of length this is all right this point 0.035 is not that a huge big figure, but if you reduce this pipe size just from 2.5 centimeter to 2 centimeter that means 20 millimeter it was initially 25 millimeter and then if you reduce to 2 centimeter 20 millimeter then the loss is increased by 250 percent. So, therefore, determining the size is very important now I have not calculated, but possibly we have reduced the diameter by 0.5 millimeter meter if we increase this by 0.5 millimeter it will not be that it will be very efficient we will then we will find this loss is reduced, but may be only 20 percent is reduced, but for increase in 0.5 millimeter in the inside diameter the quantity of air requirement will be huge. So, just looking into this point that there will be friction loss for smaller diameter we will go for higher diameter that should not be the attitude we have to properly calculate what might be the loss and then we have to select the pipe lines that means for a plant while we are calculating the pipe lines it is impossible to calculate how much consumption will be every day and others. So, it is on the basis of average estimation and sometimes it is found that this losses is not that optimum you may need to change the whole pipe lines which is expensive, but still that means I just would like to mention we should take lot of care to select these pipe lines. Now we shall come into that a circuits so far what I have discussed that is mostly about the air preparation and what should be the line distribution line etcetera, but now let us come to the pneumatic circuits what is used for the particular operation and machines. Now this is more or less similar to the hydraulic counterpart except that there is no return line to reservoir because this is released to the air atmosphere also in most of the cases the source is a centralized preferred air supply system. In there are some machines of course which is having special even if in a plant where you will find that they are using centralized special lines, but you may find some machines which is having a special compressor attached to this machine there is really some special air preparation is required otherwise we will find normally there is a centralized system. So whatever circuit we have to think we have to think that we are tapping a air source from a centralized system this means that we have to accept that at inlet this pressure will be of a range it may not be we can have always the desired pressure. Therefore input is through a manifold normally you will find there are so many manifolds are fitted at certain distance and which is having filter regulator and lubricator unit that which I have shown it is very popularly known as FRL unit FRL unit. Now we shall look into what should be the standard structure of a pneumatic circuit and that can be realized from the following schematic view as in this figure. Now what we find that this is a pneumatic actuator this is the application end. So we shall call an actuator may be an air motor also. Now next part these two before entering into this actuator we have some control units which is we should call final control element. Now before that there are processing elements what is processing here only as a processing and elements a subtle valve is found, but it may not be subtle valve it may be regulator sorry pressure reducing valve it might be a pressure control valve it might be a flow control valve etcetera and that flow control valve again for general the any special control required for such operation will come here and processing elements may have general some control valves and these are input elements. This means from the manifold we need a regulator or valve these are these elements and finally this is our pneumatic power source. So broadly any circuit any system we can divide into few such element, but if we think of this is the utilization and this is input end that means from pneumatic power source it comes to input element and then processing elements then final control elements and then the actuator or motor etcetera. Now what is this structure which I have discussed. Now what we can do that we can designate this items by two numbers here what we can find two numbers in between that one dot this is two digit number considering a dot. Now let us first one is the x and second one is the y then a x designates working group and y designates type of elements. Now in this table what we find energy supply that is in working group is 0 and designation example y might be 1, 2, 3 depending on different type. So this working group when the first supply we put 0 you can see at the place of x we put 0 and this is 1 may be for general supply then 2 may be another supply. Then working group may be 1, 2, 3 or etcetera anything it can be and one working group per actuator it is then we will come to the actuator. Let us come to the actuator actuator is 1.0 that means working group is 1, 0 is the type of elements. Now here this type of elements 0 may be single acting cylinder or 0 is the type of elements. This is given for say without spring something is there then final control elements say these are 1.1 say these designations that this is for again type of elements and this is for group and here it is given 1. That means what we find except the supply this here we find this is in working group 1 all such components for a typical type of work which is in the group 1. So we have used group 1 and then as such the element say actuator of this type is designated 0 this control elements is 1 then this element as 6 and this is 4 this is 3 this is 2 etcetera. So this is just to give you an idea how these components are designated. Now again what I feel there is not much standardizations about this these are we should call a company standard a company they can designate such components for their machineries what they are manufacturing. Again such this designation is not possible if you buy a machine and in your plant where the general pneumatic system is there and utilizing this components. This is to give an idea and that is how these are components are differentiated. Now we shall come to the basic circuits now this is a operation of a single acting cylinder. Now from looking in this figure you can see this is the you have to recognize such components. So this is the cylinder what type of cylinder it is it is a single acting and what these lines means the strangles this is nothing but a spring. That means in case of single acting you have to think of how it is returning if it is a vertical one then due to self weight it can come down. But normally there is no guarantee that we can use the such a cylinder always in vertical position even if it might be in the downward directions. So looking into this all such single electric cylinders are mostly with a written spring and that spring is just to overcome the friction minimum friction inside. If there is any pressure is trapped this side then this will not return we have to release this here completely and then due to the spring action spring release it will return to its original position. So this is an cylinder and from there this is if you know about the symbols what we find how many ports are there we find the three ports. So that we should call the there is a three way and what it is it is a looking like a button it is really a push button and this are usually manually operated and there what we find there is a spring what does it mean this spring always bring this push button valve to a position what position it is it will remain in this position normally. Now this is a frl unit and this is this indicates that this is from the common source. Now what happens this is a simple pneumatic system circuit consisting of three way and the two position this is called direction control valve. In hydraulics normally we use word DC and both d and c small usually there is no harm you can use capital D and c but in case of pneumatic normally it is called DCV we do not what we should not call DCV valve we call DCV that direction control valve. Now this direction control valve normally remains in this position that means the air from this piston end is going to the atmosphere. Now again what we find that there are two valves it is the name is needle valves basically this is a throttle valve which is controlling needle means there is a small needles and orifice which is controlling the area and this is usually screw type no push button type you can just simply rotate it just to reduce the orifice size and in turns it gives the flow control obviously there will be pressure drop but flow control will be there. Now we can control this flow at the entrance that means entrance means you see when it is coming to this position simply what we can do the whole valve we can push it here that means when the air is entering there is a control of the flow it is possible to control the flow even the we can also control the flow when the air is going out why we need to control the flow why it is going out that show that it does not returns suddenly say it is pushing something but it is also being released very slowly if there is no harm that it can return very fast we do not need this valve at all the three way DC valve may be manual push button most of the case it will find push button type for a single machine you are operating but in a sophisticated machine or you need very quick operations then you can use the auto actuated devices say for example solenoid valve that means here this actuation is through and solenoid. So this is a very simple single acting cylinder operation. Now if you consider the double acting cylinder in that case what we find these are actually there are five ports sometimes we can consider this is a these two are common because both are exhaust but in many cases this there might have two exhaust from a valve. So basically we should call it four way not five way because these two are exhaust how to count how many ways are there this is simply count the port in a single icon in a single block there are five ports so we may call it is a five way valve and how many positions one position and two positions. Now in this case that means this is a simply we can call in terms of hydraulics we call it four way in that case that both sides are actuated by the air flow again this might be push button and this spring and this figure indicates normally it is in this position that means it is a normal condition it is in retracted positions but if you push it this will be in the other side. So double acting operations is similar more or less similar only thing this is through a control valve. Now air pilot control of double acting cylinders the same double acting cylinders and we have the same valve but instead of push button what we find this is actuated by the air and that is called pilot. Operated now this pilot valve is named as V1 and V2 and in this pilot valve what we find this is again 3 by 2 directional control valve but if we think of the pressure this main system is working with one pressure and this system is working with another pressure. So we need to have a different sorry this is pressure regulator valve. That means main source is 100 psi whereas from the main source it is utilizing for this pilot operations there is only we are using 10 psi that is 0.07 megapascals whereas this is 0.7 megapascals. Now the operation as you see V1 and V2 are used as pilot valves to operate 4 by 2 DCV again I have made a mistake DCV valve I could have write it is DCV only pilot valves are usually operated with low pressure 0.07 megapascal whereas main operation needs and operating pressure of 0.7 megapascal. Now we are coming to a cylinder cycle timing systems in many cases we need not only the velocity control but there is some timing is there that means after doing say it is like that at certain portion with one velocity and maybe with another velocity or next operation should start after some times in that case what is done if we first of all look into the system this part is same as it is and then what we find there is a flow control valve needle valve and then there is a direction control valve and which is pilot operated. Now in this operations we find here one push button is there let us see how it is being operated employing a limit valve with a double acting cylinder operated by a pilot operated to by and a timed cycle extend and retracted are achieved. Now when the push button valve V3 is actuated this is actuated momentarily to extend the cylinder during extension. Now this is operated to extend the cylinder that means in normal condition it is like that now when we push this is connected to that then this air is allowed to come over here and this is operated this operation means then the this is being extended the air is going to this side stone head and this is being extended actuated. Now this is our limit valve this valve is before is limit valve during extension the piston rod pushes the cam to activate this limit valve. So when it is extended after so position of this valve or rather to say this cam and this piston is important. So this is an with an proper fittings it is done eventually it actuate the valve V2. So when it is pushes it is pushed then it operates valve V2 to its opposite mode to retract the cylinder that means we are pushing it. So operation some operation is being done but when it touches is automatically it retracts. Now during retraction we can control this as well this means that we if we if we operate this valve V1 then this will return at a control speed. Inclusion of flow control valve V1 improves circuit with flow control and thereby speed control features. Similarly there is we can think of the another circuit which is two step speed control speed control system. In this case what we find that there is also and limit switch is there and this is the cylinder and at this stage we find one subtle valve with two needle valves or throttle valves or so called flow control valve. And here what we find that there is a direction control valve which is pilot operated and this one side is through a push button other side is from a limit switch. A subtle valve this is called subtle valve. Subtle valve means if the air is going from this side it cannot go through this it will go here whereas when the air is coming from this side it can it will go through this it will not come back to this side. This means that this in many cases this operations is depends on the pressure at these two lines. A subtle valve V5 with two different flow control valves V3 and V4 V3 and V4 at two ends is fitted to the cylinder end of a double acting cylinder. Then V3 is adjusted to allow a greater flow rate than valve V4. So V3 is having greater flow rate than V4 that means this has more resistance this has less resistance. On adjustment of valve V1 air flow passes valves V2, V3, V4 and V4. And V5 subtle valves in the extension of cylinder at high speed. Now once the valve V6 is activated by the rod end in extension at high speed the valve V2 shifts because a signal is coming from here pilot and then this shifts and then flow is diverted through V4 through this regulated at low flow rate and then V5 the cylinder continues to extend but at slower speed. That means when it reaches here then this is actuated and after this position this will move at slow speeds. So this means say for example you can have some operations that for some portion you need less force high speed and then more force low speed. So you can this might be position of this with respect to this one possibly you can adjust by adjusting this you can make this operation of the cylinder at two speeds and it might be the half the stroke length it might be this one third full high speed and two third slow speed etcetera etcetera. After full extension the retraction is done operating valve V1 manually. So this means that we just may be this push button if we release it will come back to this positions and then it will be retracted. Now it might be also as I told push button type or we can a lever type that whenever we can fix the position either of this. Now another very important operation this is usually with the pneumatic it can be with the hydraulic also. So this is called two handed safety control system. In this a two handed safety control valve system what we find we have a double acting cylinder here how many ports we have 5 ports and 3 position this is the neutral position. So this we should call 5 by 3 DCV and these are 4 by 2 push button type valve and this is the main supply source. Now for the extension of the cylinder both the push button all also called as pump button. Pump button means these are usually you will find very big size you can simply push it like this or to be pushed that means suppose you are pushing this one this pushing this one means the air is going like this. So this is going here and it is coming over here and it is trying to actuate this one, but this one you have not pushed. So in that case what is happening that this is not activated this is still in this positions. So you will find that this is not being actuated only if you push both then this will be actuated. Intention is to engage two hands of the operator. The motion will be stopped automatically if one hand is moved one or both pump button valves from one or both pump button valves. Again for retraction of the piston both hands to be removed from the valves you can study this valves very carefully then you will find that to operate this one that is for this movement from this side we need to push this one and again for moving in the opposite directions also we need to remove both the hand. Now an example good example is that before that I would like to say this is a 5 by 3 main DCV, V3 continues to be vented if both pump bottom valves are not activated simultaneously. That means in neutral positions this air is being vented. Now thus the cylinder remains locked in this position you will find that the air is coming and this is being vented and it remains locked in this positionally. This indicates that the no passage is allowed in this position, no air is allowed to through this passage when this is in this position. Example is that shear blade operation in a paper or sheet metal cutting press usually if you look into the cutting press the cutter is like that then paper is placed this paper is placed like this and we find that what where is the line for that you will find a separate lever is there usually hand wheels by which you can bring down the shear to this line just to have line. In some cases you will find that there is a the lighting arrangement very thin line is coming on the paper by which you can see that whether you have placed this one properly after that you need to shear it. Now if you you may keep your hand and try to operate this one then your hand will cut this your finger will cut so that this arrangement is that this switches are at the two ends not even at a closed place you cannot push this two by the single pump this two ends you have to push this one you have removed your hand push this one. So, it will come down and it will shear shear the papers and now to release it you have to move both hands. So, it will be released and then it will become in the lock positions. Now control of air motor this is instead of actuator if you use an motor and this one is the silencer usually with the cylinders there may have silencer or the silencer is not that very I would say that very sophisticated, but in case of air motor where the continuous flow is being exhausted you need a good quality of muffler or silencers. So, that is this one and this in this air motor what we find this valve again we find that we have the 4 by 3 DCV is there and then there is one start and one stop push button type 3 by 2 valve is there. Now, in air motor control system the start push button valve V2 is actuated momentarily at first. So, we push this one once we push this one we get this positions that means this path is being connected that means this path is being connected then the air pilot valve V1 shifts and allow air to run this motor. To stop the motor the stop push button valve V3 is actuated momentarily. Then what happens the main DCV air is moved to opposite mode it moves to this mode to cut off air from the motor and in this way the stop push button valve is this running and say it is what we could do that we could have only this valve with some push button actuation by the main from the main source, but using this to switch what we do if we put the start and then we leave it this motor will continue to running ok. In case of using one single valve with a push button we have to keep it pushed and then it will run, but with this system what we do simply like a switch as if a on switch we do it and then motor is running until we move this one this will not be stopped. Sorry there was an additional flow control valve which was being used to control the flow rate that means you can control the speed of the motor by controlling the flow rate. Now this shows a circuit that provides an adjustable disceleration air cushion at both ends. In many cases particularly where the heavy load is there we need a cushioning effect at the end of the cylinders. The cushioning effect is also used in case of hydraulic cylinder in that case the system is like that when the cylinder is reaching towards the end of the stroke then the outlet port through which the oil is going out that port is controlled the area of that port is controlled and there a cushioning effect. In case of air how it is done? Let us see pneumatic systems. The valve v 1 supplies air to the rod end of the cylinder and to the pilot of valve v 5 through the flow control valve v 3. So the valve v 1 supplies air to the rod end side. As well it supplies to the pilot size of this ok piston retracts fast due to free air exhaust from the from this end until v 5 is activated until this one is activated due to increase pressure at its pilot. Then cylinder blank end exhaust is restricted this side is restricted by valve v 7. The resulting pressure build up in the blank ends acts as an air cushion ok. So operation is like that the valve v 1 supplies air to the rod end this side ok and to the pilot size pilot side of this valve v 5 through a flow control valve v 3. Piston retracts fast it is retracting very fast from blank end until the air is activated. V 5 is activated due to the increase pressure this pressure increases due to this restrictions and due to this increase in pressure this when this actuates then v 7 become activated and due to that the air flow will be restricted and there will be cushioning effect. And the similar is achieved when it is moving from the other side also. So I suggest that you should study this valve to understand how this operation is being done. It is it will not be difficult to understand but you have to keep in mind that when it is moving towards the end automatically there is a pressure is being increased to operate this one. Possibly we can adjust this. Now say if you look into the valves these are we have not studied the valves in details. So this is a typical flow control valve and practically this is a throttle type of things. When we rotate this one gradually this passage is decreased that means the annular space is decreased and in that way the pressure flow rate is controlled. Say such applications application of such valve is seen say for example this is an schematic arrangement for the clamping of work space. Say this this is air is flowing and we are not complete if you completely trap suppose if you try to hold something trapping the fluid you will find that after sometimes the pressure is reduced and the clamp is not working. So usually what is done the flow is always there with a pressure drop that means inside the valve the pressure cylinder which is clamping. There is always the pressure with a constant pressure but the flow is maintained that means it is always keeping the this cylinder filled with required volume and the clamping is done in that way. Now this is a two position of the circuit of speed control of a single acting cylinder. This is already we have discussed this is again shown in this form how the two different positions are there and then if you look into such operations we have to always keep in mind as particularly this is a compressible fluid at the beginning and at the ends. This is not neither the constant speed is possible not the full pressure is achieved or in other words this is not the desired pressure. So it might be the actual operating range from here to here say for example we are using this here for some cutting operations or something like that say we are cutting a plastic finishing a plastic sort of things very soft material with the pneumatic not hydraulic in that case say when the tool is moving we need a constant force that operating range to be within this range. So this knowing such pressure and speed characteristics is important for such circuit. In case of hydraulics this zone is very small. Now we have followed these mainly these three books especially we will find because in the figure I have given the reference number mostly we have followed these two books. These books are available in our library also. So if possible you can go through this and I will send you these notes also too. Thank you.