 So that's far we've been talking about calculating pressure drop in pipe flow and it's due to the viscous shear along the walls of the pipe that results in this pressure drop. There are other types of losses that can occur within piping systems and we refer to these other types of losses as being minor losses. Now piping networks can be very very long and consequently the major source of pressure drop is due to viscous shear within the pipe itself and that's why we call these minor losses. But they can occur in a number of different places so we'll look at where those places are. Okay so those are the different places where we can have minor losses within piping systems so pipe entrance would be for example if you have a reservoir and you are then coming from the reservoir into the piping system that would be an entrance region and an exit region would be if you have a piping system coming along and then all of a sudden it flows into a large tank or a reservoir that would be an exit condition. A sudden expansion or contraction is just what it sounds like so a pipe changes abruptly in diameter and that would be a sudden expansion. You get large scale circulation and separation in here and consequently there's a rather high pressure drop associated with that type of a flow. Contraction just what it sounds like our pipe is coming along and then we have a reduction in diameter and again you'll get the separation zone right at the corner as you go through that contraction. Bands, elbows, tees, those are what they sound like so a pipe band where you might have a change in angle, an elbow, you would have a 90 degree band and they sometimes have short elbows and long elbows and those would have different radius of curvature and then a T would be a junction where you might have something like that and you have in a piping network so the flow is split three ways it could be coming in and going that way and then going that way. Valves, there are many, many different types of valves. There are ball valves, gate valves, many, many different types of valves that we have but whenever you have a valve in a flow field it introduces a rather severe pressure drop with the exception of a ball valve. The ball valve is pretty clean and smooth when it is fully open. Gradual expansion and contraction that could be things like nozzles or diffusers where you maybe slowly change the area. Those are a little bit more difficult to build but they as well would have a little bit of separation in this region here and consequently they do lead to a pressure drop where ever you generate turbulence that's where you're going to encounter larger and larger losses because turbulence is a way of taking our pressure energy and converting it into kinetic energy which then goes into thermal energy and it takes place at a higher rate than you would have for normal viscous losses in a pipe. So minor losses we need a way to be able to account for all these different flow fields and so what we do is we introduce a head loss associated with minor losses. So we introduce this loss coefficient k and that is the way that we are quantifying minor losses and note we have the subscript little m to denote its head drop due to a minor loss. So to define k sometimes people call them a loss coefficient H m v squared over 2g and here remember v is the average velocity in the pipe so taking volumetric flow rate divided by area. So for a typical piping system you can have total head loss and that is going to be associated with the frictional losses that we've seen so Colbrook white and the friction factor as well as the Darcy Weisbach equation for turbulent flow or the relation for laminar flow plus what we do is we sum up all of the minor losses that might exist within a piping network or within a piping system so you might have a number of valves and flanges and things like that each of those will contribute to a loss and we can rewrite that so introducing the Darcy Weisbach equation for the major losses or for the loss due to shear plus some of all of the loss coefficients that might exist within that system. Now one thing that we need to be careful with we have a velocity here applied to the loss coefficient sum if the diameter changes within our piping network then we need to sum them individually so let me just make a little comment about that so if you have a change in diameter that's going to lead to a change in velocity and you must sum those separately because the average velocity in the pipe is going to change so when we have all of this if we sum up our total head loss due to both our major losses of the frictional and the minor losses and we put this all together into the study flow energy equation and let's see what results okay so we have our kinetic energy coefficient alpha that is in there this is our major losses and that is due to turbulent shear within the pipe this is all of our minor losses and I've also added a final term here and that would be if you have a pump between points one and two because what a pump would do it would have an impact it basically adds a hydraulic head to the system and and so we introduce it on the right hand side as a minus term but that would be if we have a pump between points one and two and if you're confused as to why it's a minus just look at the fact that that is plus and that is plus and those are all removing energy from the system so if we're introducing energy it has to be the opposite sign that's why it's minus on the right hand side so that is the study flow energy equation fairly straightforward in terms of just looking what components might have within a piping system adding up the minor losses computing the friction factor for whatever flow regime you might be laminar or turbulent and you add them all up and you can then do pressure drop calculations and different things like that with the study study flow energy equation so that concludes our segment looking at minor losses in piping systems