okay um thank you guys for attending we just have a slight problem with our i had a slight challenge anyway everything is sorted right now um we are doing boilers and boiler calculations let's start thank you for for your time okay all right um this is what we are basically going to be covering only two learning outcomes um at the end of the lesson you should be able to do these calculations the boiler efficiency as well as the equivalent evaporation of a boiler if ever guys there are questions you can just post me or you can ask me to just repeat the section that you might have missed okay um what is the boiler we've discussed this before guys in our in our introduction we said a boiler is a device that is used in order to heat a water so that it changes into steam so you've got two types of boilers it's a fire tube boiler where the fire runs in the troop as you can see here here's the fire running in the tubes and then the fire is coming out today and then there is water where the fire is where the troops are located there's water so the water comes in here and then it comes out as steam in this section so it's the fire that is inside the shoe in this boiler then there's also a water tube where now the water is now that is running in the troop and the fire is just this is where the fire is so these are just examples guys so we've got water here coming in via these tubes and then it's get heated up by this water uh and then when when it's heated up when it leaves when the steam leaves or when the water leaves it leaves a steam in the outlet there so i've got two types of these boilers so we are doing calculations now relating to these particular boilers right and then uh you've got our boiler calculations now this is what is is is is um eminent or this is what we see guys that um uh water comes in and then water comes in it cut it leaves a steam so it water inlet through the boiler and then it comes out as steel even here it's water in here when that water leaves it leaves as steam here and that whatever the entire scheme may be so this is how i just decided to make a summary of this in in a in a in a in a sketch in a simple sketch h1 it is an entire puff of water going in to the boiler h2 is the enthalpy of the water leaving the boiler as i as i've written here eight one is the enthalpy of feed water and then h2 is the enthalpy of steam leaving the boiler so it is important for us to know to when the when the when the what goes into the steam is fluid that's why h1 will always be hf because it is fluid what goes into the boiler is fluid so it's water that's why it is hf remember we said hf means it's enthalpy of fluid so it is hf and we know how to find hf guys hf is always found at the temperature ts of the water or the temperature of the water given so if h1 uh that water is is is is at a temperature of 20 degrees so we must calculate how much hf is there i i told you on the introduction how to calculate hf if it's not given but if it is given you know that you go and get it on at the back of your at the because the the the steam tables so h1 is always hf because it is fluid going in at a temperature of water so you're gonna find the temperature of water but when it leaves the boiler it can either be dry wet or super heated it depends on how powerful the boiler is so it can be dry where to superheat it so when it's dry we know that they tell us that it is dry saturated when it is wet they will give us a dryness fraction when it is superheated you will know um by them giving us the temperature of the superheated steam but sometimes guys they can tell us now if you have a pen you need to write this down sometimes they can tell us calculate the dryness friction of the steam the dryness fraction of the stimulant you you or not even to say it's a calculated triness fraction of the steam let's put it like this the question can say determine the quality of the steam so we know the quality of the steam from trying this fraction now if x is equal to 1 we know that it was hg if x is um is smaller than 1 i mean if x is greater than one is this what it means uh we it's gonna be superheated but if x is smaller than one then you know that it is going to be wet so if if they say determine the dryness fraction of the steam you calculate using that the the the you you first calculate the dryness fraction the dryness friction is going to tell you whether the steam is wet dry or superheated again if x is equal to one it is dry if a if x is smaller than one it is wet it is wet but if x is greater than one it is superheated the steam so you you check from that um but i'm going to also give you this information on your in in our whatsapp group so let's go on how do we do our calculations of a boiler so we know that what goes in is h1 what goes out is h2 this is when there's only a boiler only a boiler we are going to do two examples i'm going to explain them now we said efficiency is equal to output over input what do we get out it's steam what do we put in is fuel so what is your fuel energy or your fuel power your i mean your your steam energy will be ms into h2 minus h1 which is final minus initial always a enthalpy final minus enthalpy initial that is when we are finding a efficiency then the alpha the energy of from the fuel is mass of fuel multiplied by heat value which is the current value that's how you're going to calculate the efficiency in a boiler also in a boiler you can also find the heat energy from the boiler the heat energy from the boiler it can tell you to determine the heat in the boiler the heat energy which is ms over mf into h2 minus h1 okay i'm also going to say a bit about this ms over mf in uh going forward h2 minus h2 minus h1 this is because the boiler or evaporator i also forgot to mention this a boiler is also called an evaporator it's the same thing because a boiler does what evaporates the same thing equivalent evaporation guys is ms into h2 minus h1 mf times hfg hfg being the word being the latent heat now guys someone is stabbing us kg i think okay then a hfg but hfg at 100 hfg at 100 because equivalent evaporation guys they will always tell us calculate the equivalent of operation at 100 degrees celsius so ee the formula for equivalent evaporation is that hfg at 100 degrees celsius guys it's always 2257. it's a constant so this is our formula e at 100 degrees celsius is ms into h2 minus h1 mf times 2257. it's a constant er it does not change and that's how you calculate equivalent evaporation ms is the mass of steam in kilograms per hour or in kilograms per minute whatever that it is given at mass of mf is the mass of fuel in kilogram per hour and then q evaporator is the heat absorbed by the boiler this is the one the heat absorbed by the by the boiler i'm still going to give you those these a handout i mean this information so that you will refer again back to it can i continue or should i take any questions from now any questions okay one can i get another one so that i can have two people losing at least right here is the question now guys i'm gonna do this one example there are two examples i'm gonna do the following information were recorded in a testing of a boiler the mass of steam used is a 6600 the mass of coal which is the mass of fuel again the coal is fueling is 600 the pressure in the boiler is 2000 then there is a temperature of the feed water so in other words the temperature of the water that's where we get our h1 that's where we get our h1 as hf calorific value is 32 thermal efficiency of the boiler is 80. so we've got all of this uh information let's just write it on our data we said ms is 6600 mf is 600 kilograms per hour hv or currently values 32 mega joe mega joules per kilogram efficiency is 80 percent then we draw this a guys please always try to draw this so that you you will know exactly what you are working with so we've got a h1 and h2 now you know that here there's a temperature of water which is how much 95.2 so and then we know that here this 2000 of the boiler is going to be for the h2 or it's going to be where we find our h2 so we've got temperature temperature of water 95.2 you've got a pressure 2 000 so this is how our information is done so now i just put our data like this so we can solve now ladies and gentlemen remember i said hf or h1 is equal to hf at which temperature of the water it is 399. can you please check on your steam tables this temperature here 95.2 and see if this hf is 3.99 like i've indicated just check that on the steam tables check for ts or temperature of 95.2 and check if hf is as shown it's correct yes that's correct anyone confirm yes sir it's correct okay thank you so that's how you find our hf we find hf from the temperature of the water now do you remember what we do when the temperature of the water is not on the steam table yes sir okay thank you simply multiply that simply multiply the temperature by cp of water absolutely thank you all right um moving forward now the first question here is calculator the enthalpy of the steam produced so which is the steam produced it is h2 so they wanted nh2 the first question the second one would be the dryness friction of the steam produced and then the heat quantity absorbed by the boiler so first one we need h2 dryness friction and q evaporate so to find h2 since we're already given the efficiency guys since we're already giving the efficiency then efficient is equal to ms into h2 minus h1 mf multiplied by a heat veil so we are looking for that h2 there so we we can just substitute everything we don't even have to convert our ms and mf because they are both in kilograms per hour kilograms per hour they will cancel off so six thousand six hundred and six hundred and then please pay attention here on this thirty two thousand the two mega joules do you see that i said thirty two to the power 3 not to the power 6. the reason is i'm converting it to kilojoules because 399 is in kilojoules so that our answer of h2 will also be in kilojoules i hope i'm making sense that guys i'm clear so this 32 magnitude i converted to kilojoules not joules so i don't put it to the power positive 6. so if i calculate for h2 this is the answer that i'm going to get i hope you are you are all following you are going to manipulate the way the way that you can obviously manipulate the way that you can uh to find that h2 but you're going to get 2 206 point 273 right second question find the dryness friction now we the moment they say find the transfection guide there's no other way of finding the dryness friction except for using the formula of age weight because that's the only place where you're going to get a dinosaur shield so h2 is equal to hf plus x hfg at which pressure at a pressure of two thousand at the page of two thousand so at a page of two thousand we're gonna find hf it's a pledge of two thousand we're gonna find hfg h2 we already have can you please look for hf and hfg at two thousand eight five nine zero eight it's nine zero eight yes and then hfg will be one double eight nine that's it one double eight nine so nine oh eight one double eight nine remember h two is already we already know it here's the trinus friction we are looking for now remember guys uh this dryness friction is either going to get determined to us whether the steam was wet dry or superheated but they didn't say that you must we must determine that but you know in your mind that the answer you can get can be more than one one or less than one in our case that x is equal to zero comma nine three six which means the steam was wet it is it is it is five we move on so the steam here was wet and the last question uh calculate the the last question if there is some noise i'm not sure who's dead okay um then the next question they say calculate the word we need to calculate the quantity of heat absorbed heat absorbed by by the boiler so heat absorbed by the boiler is q evaporator or cube boiler heating the point m s over m f into h2 minus a h1 guys we already have everything here so we just substitute 6600 over 600 h2 is this and h1 is this then a you get your answer which is two uh 25 600 mega juice if you want to put it in mega juice but that's how it is somebody please just divide these two for me can you please divide these two for me and give me the answer remember i've muted everyone so if you want to give me the answer just add me eleven yeah it's 11. the answer is gonna be 11. all right so which means it is 11. guys please pay attention to this again these two can be given as one value like you said 11 so it's 11 kilograms of steam per kilogram of fuel they can out they can also give us like this so that so so once they give us that then you know that they've already divided it for you so you're just going to use 11 for these two ms over mf is equal to 11 because it they will say the mass of steam produced per kilogram of a a few n so it will be 11 in this case so they can give us also like that all right now let me move on guys i want to do something now which is a bit okay do i have questions on this one before i continue um there's no one example which can do the whole concept that's why i'm trying to cover as much as i can like by giving you extra information like this trying to have as much as i can like again what i said about this value that they can ask you to determine the quality of of steam uh if they can ask you right now you can say the the the quality of the steam produce will be weight because yes so i have a question yes so i didn't get the part where you said if you are not given the temperature of what yeah that's the one i i i i explained in class so when i said uh it is going to be just check those notes the the the last time we met in class uh where we said it's going to be a temperature that is there that you are given multiplied by cp of water which is 4 comma 187 okay yeah just re refer back again to those notes thank you any other questions all right now i want to take your fair a little bit further now uh to where by now a steam boiler is is now a steam plant in other words it's not just a boiler alone it's a boiler with another mechanism so a feed water enters an economizer so there's an economizer now now remember what we said on our introduction we said an economizer warms up the water before it goes into the boiler so it warms the water up before the water is sent into the boiler so the economizer is at a temperature of 32 so the water goes into the economies at 32 but when it leaves the economizer it will be at a higher temperature remember we said we want the water to be as high as possible in temperature so that we can save in cold all right so feed water enters the economizer at a temperature of 32.9 in a steam boiler plant now it's a plant because it consists of more than one a am a component the boiler has a pressure of 2500 mass of steam used and then there's a catalytic value given of 33 point mega joules the feed water from economizer enters the boiler at 90 so in other words the inlet of the economizer is 32 the outlet of the economizer is 90. these are all temperatures of water because the economizer does not boil but it only increases the temperature of water so it enters at 90. i'm going to show you how to draw that then you're going to have 5 000 kilograms of wet steam so it's steam per hour with a dryness friction so this one is already given which is going to be wet our data will be ms 5000 mf 6500 i mean 650 kilograms per hour a heat value is 33 mega joules per kg then the dryness friction is zero comma nine five and then now this is how our our our diagram is going to look like our flow of water until it becomes deep so it becomes h1 h2 as well as h3 so it now goes from one to three meaning now our efficiency now i said our efficiency is always what uh the exit minus the inlet so our our h our efficiency is now gonna be h3 minus h2 instead of h2 minus h1 because this is the whole c and then the heat in the um boiler i'm just giving you i'm not answering this question i'm just making this thing to be a bit broader so that you can also be able to do other questions now the heat in the boiler uh the heat absorbed by the boiler is no longer going to be h2 minus h1 but it's going to be h3 minus h2 the heating the economizer is the one that is going to be h2 minus h1 so those h2s and h1 they depend on whether there is any other component added so but you just need to know the concept because there can also be a super heater here guys it can also be a super heater here so in other words you're gonna have h4 if there is a super heater i'm trying to i'm trying to cover like like i said where your efficiency will now be h4 minus h1 and then the heat in the economizer would be h2 minus h1 don't forget the ms over mf in the boiler it will be h3 minus h2 in the superheat it will be h4 minus h3 so i'm just trying to expand the question guys so that you can learn more out of it but let's answer this question now let's answer this question uh h1 the temperature of the water entering the economizer is 32 h2 will be found on the temperature of the water entering or leaving the economizer entering the boiler t2 of what these are all waters you see why i put blue guys the reason why i put blue it's because it's still liquid where i put red it's now boiling and it's become steam that's why i chose those colors then the pressure is 2500 let's take this so how much is hf at 32.9 how much is hf at 90 that's what we want because these two we can find them because it's hf1 and hf2 these are the values can you confirm them are they correct yes sir good so we have h1 we have h2 remember if you don't have them like a table was asking you can just basically multiply the temperature pi for comma 1 8 so we have h1 we have h2 then h3 we already know that h3 is going to be h weight because the steam produced was electronics friction but we are not worried about that for now let's go to our question the question says calculate the quantity of the heat absorbed by the economizer so the economizer is in between h2 and h1 in this case so the economizer the heat in the economizer will be eq economizes s over m f into h2 minus h1 h2 minus h1 you already know that h2 is e is equal to what 3 77 h1 is 188 138 so we just substitute and ms over mf we already have it there so 5 000 over 560 and then 3 77 138 when you calculate these guys you are going to get eight hundred ten thirty eight all right can i move on [Music] i think it was basic here then number b they say calculator and that that the thermal efficiency and equivalent evaporation from mf 100 so guys this doesn't mean anything it only it only tells us of that constant of 2257 is 100 degrees celsius so the thermal efficiency guys so we already have this so for thermal efficiency remember i said efficiency is always ms into h3 minus h1 final enthalpy minus the initial enzyme in this case because it's a plant it's h3 but h3 needs to be calculated and we know that h3 is equal to each weight it is hgf plus xf hfg and we do have the pressure for it two thousand five hundred and then if you go to the page of two thousand five hundred you will find hf and hfg to be how much can you confirm this [Music] 962 and hfg will be 1800 correct lovely then we calculate our h3 that is our h3 now we take h3 substitute it back there we already have h1 which is 138 so we just substitute h remember heat value heat value there is 33 mega joules but we are going to convert it to kilojoules so and then we multiply by 100 don't forget to multiply by 100 it is an efficient so after substituting everything you will get that the efficiency is 61.8 sa all right then a c says find equivalent evaporation e e c equivalent evaporation is ms h3 leon equivalent evaporation is always also final minus initial h3 minus h1 the only thing that changes guys from the efficient is that you no longer have one you no longer have hv but you you have two two five seven then you just substitute five thousand six fifty two thousand seven eighty nine minus one thirty eight and then that's your two two five seven there which is a constant then your answer is eight point seven six three kilograms per kilogram why kilogram per kilogram it is kilogram of steam [Music] over the kilogram of fuel kilogram per kilogram that's how it is all right um i want you i i want you to go to your textbooks guys and see something quickly i'm just asking a few people to mute okay um i'm saying textbook page number 134 example number two example number two because for my presentation i am done uh i just want to show you something there that you should see that maybe i did not cover are we there guys page 134 example two you can you cannot mute yes there we are okay yes thank you i'm interested in number three guys i'm interested in number three find the okay so number one they say find the efficiency of the boiler so they found the efficiency of a boiler the same way that we did the efficiency of a boil find the equivalent evaporation it's the same way we did it there's no difference there excuse me then number three they say find a saving in coal excuse me per hour if now you have fitted an economizer so this question started without having an economizer they're just introducing the economizer on number three whereby they say the feed water could be raised to 99.6 so in other words now h1 i mean sorry not h1 but the water that goes into the esh1 the water that goes into the boiler can now be calculated from 99.6 because it has been raised to 99.6 and then assume that everything else remains the same but the efficiency of the boiler increases by five percent in other words from that 55.89 of the boiler efficiency it will increase by five percent so you're gonna add five there that is why your efficiency when you go to the to number three it is 60.9 because that 55 was added a 55.89 they added that five because it has increased by and then the h1 is no longer going to be calculated at the previous a feed water a temperature which was given on your data or on your data which was 41.6 your feet water will now be calculated on 99.6 so those two values are going to change h1n efficient now they want us to calculate the goal savings every time you're calculating savings guys it's always how much did you spend before and then how much are you going to spend now that is what we are we you are looking at so they are calculating the new mass of fuel using the new information on number three the new mass of ua so mf there on number three you can see that it's ms it did not change 5600 h2 did not change from whatever they calculated minus h1 now h1 has changed now h1 is now 418 which is from what for 18 they're getting it from 99.6 so it has changed the efficiency there's 60.9 which which which was 55 when they added the what the five percent which is increased by which was which is 60.9 multiplied by the equity value time 10 to the power three because it must be kilo now the new mass of fuel that will be used is 5600 now how do we get savings how much mass of fuel do we use did we use before the mass of fuel before from our data it was 690 minus the new mass of fuel which is 569.4 which is going to be 126 kilograms per hour that is how we calculate the savings so you please go through that example again let's go through that example and then someone asked a question very very important question on the group i'm gonna go back to to number three on page 146 or 136 it's exercise 10.1 i see a question so can you please repeat how we use that five percent it's it says here it says here guys that um assume all other condition remains unaltered and the efficiency of the boiler increases by five percent so the efficiency increases by five percent so from the initial efficiency you have to add five the initial efficiency was 555.59 that was calculated so you just ate five that's where we are going to use this efficient all right i'm on one page 136 i hope i answered the question i'm on page one 136 activity 10.1 where it says number three on number three guys i'm gonna i i read the question and discovered which we do not have cp of superheated steam and this temperature i mean this hf i mean this h two after the boiler is super heated because i'm giving a temperature of 320 the temperature of steam i said when you are given the temperature of steam it is superheated so they didn't give us ct this is a mistake guys because we don't assume ct so you don't do number three because we do not assume cp on number one a one a the thermal efficiency is 701 it is 70.1 not 701 70 comma one then the rest is correct we are going to do number one number two number four and five we will discuss further guys on the group uh can we cut it here [Music] let's pause here we'll discuss fade on the group thank you