welcome to lesson 2b introduction to pressure in this lesson we'll define pressure we'll discuss some types of pressure measurement we'll discuss head which is an equivalent column height and we'll do some examples here's some basic principles about pressure it's a scalar it's defined at a point in a fluid just like other scalars for example temperature are defined at a point pressure is a normal stress it has dimensions of force per unit area if this is some object in the flow pressure acts everywhere normal to that surface here are some common units of pressure atmosphere pascals kpa kilopascals bar and psi first let's talk about absolute pressure you always have to use absolute pressure which we denote by p or p abs in any equation where p stands alone in other words it's not a difference in pressure for example the ideal gas law we must use absolute pressure here just like we use absolute temperature here our notation is p by itself without any subscript is the same as p absolute when you're analyzing a change in pressure you can use either absolute or some kind of relative pressure for example delta p which is p2 minus p1 these two pressures can be absolute or relative it doesn't really matter as long as the units are consistent this is similar to delta t we can use degree c or k when we're taking a temperature difference and it doesn't matter now let's define gage pressure it's the value of pressure above local atmospheric pressure here's the equation for gage pressure from this definition p gauge is p absolute minus p atmosphere keep in mind that this is local atmospheric pressure which can change with conditions in the atmosphere let's do a quick example problem jared measures the air pressure in his car tire with the pressure gauge the reading is given the local atmospheric pressure is also known we want to calculate the absolute pressure inside the tire and give answers in several different units we use this equation solve for p abs by the way we chose to spell gauges g-a-g-e but an actual gauge that you measure with has a u in it some people put the u in gage pressure as well we plug in our atmospheric pressure and our gage pressure we get 340.92 kpa we can justify four significant digits so my first answer is 340.9 kpa to convert to these other units we use unity conversion factors we plug in our p abs using all the digits we have available to avoid round off error and then use the unity conversion factor 1 atmosphere is 101.325 kpa i'll keep four significant digits and we get 3.365 as our answer in atmospheres we do the same thing with bars one bar is defined as a hundred kpa so our answer is 3.409 bar notice that the units of atmosphere and bar are very close but they're not exact now let's do psi you can look up this unity conversion factor i get 49.45 psi note that some authors would write this as 49.45 psi a in the english system the a means absolute whereas psig has a g which means gauge this is one thing kind of nice about the english system in the metric system you simply have to say absolute or gauge now let's look at vacuum pressure pvac is the value of pressure below atmospheric pressure here's the equation if we compare with the above definition for gage pressure we see that they're the same except for a negative sign p vac is minus peak age but p-vac is used only when it's positive in other words when the pressure is less than atmospheric pressure for example in a vacuum chamber i say only because it's not proper to use a negative vacuum pressure in other words use p vac only when p vac is greater than zero when it's positive let's do another example problem here we measure the air pressure inside a vacuum chamber we give the reading and the local atmospheric pressure we need to calculate the gage pressure inside the chamber and also the absolute pressure in several units first p gauge is negative p vac so we have our answer right away for that for absolute pressure we use our equation defined above so p abs is p atmosphere minus p back we plug in the numbers both of them are in kpa and we get 1.35 kpa using proper subtraction with significant digits three significant digits is appropriate here unit conversions are similar to what we did in the previous example p abs is 1.35 kpa times a unity conversion factor giving us 0.0133 atmospheres we do the same for bars and we get a similar answer 0.0135 bar let's multiply by another conversion factor namely 1000 millibar per bar since this is such a small number low vacuum pressures like this are often given in terms of millibars i have a short youtube video called principal principles about pressure here's the url and i'll show some clips from this right now what's this talk about pressure in my class well sure we're all confused about pressure it's direction and types of measurements of pressure yeah well i'll share a short powerpoint presentation about this pressure is a scalar not a vector but it acts along the inward normal at every point along the surface of an object this holds even if the object is imaginary and inside is just the fluid pressure increases in the direction of the gravity vector which is down in this case if you shrink this object to a point it confirms that pressure is a scalar acting at that point pressure is a normal stress its dimensions are force per area or m over lt squared common units of pressure are pascals which is a newton per meter squared or an english psi a standard atmosphere is about 101.3 kpa or about 14.7 psi but pressure is often expressed as an equivalent column height of a liquid 760 millimeters of mercury is one atmosphere this means that the change in pressure from top to bottom of the liquid column is one atmosphere there are three common types of pressure measurement absolute pressure is pressure relative to a total vacuum we call it p or p abs this is the same p you're used to using in thermodynamics gauge pressure this is the value of pressure above local atmospheric pressure the notation is p gauge p absolute is p atmosphere plus p gauge this is what you read with a tire gauge for example this reading is a gage pressure to get the absolute pressure you take that gauge pressure and add the atmospheric pressure vacuum pressure is the value of pressure below atmospheric the notation is p-vac the relationship is p equal p atmosphere minus p-vac which is exactly the negative of peak h p-vac is a positive value used only when the pressure is below atmospheric as for example in a vacuum chamber vacuum gauges are often labeled backwards like this one a reading of 20 inches of mercury means pvac is 20 ph is negative 20 and the absolute pressure is p atmosphere minus 20 inches of mercury here's a diagram to help you understand it better suppose atmospheric pressure is 96.5 kpa and we have a gauge pressure reading of 48.3 kpa we add the two to get the absolute pressure 144.8 here we see atmospheric pressure gauge pressure and the sum which is absolute pressure since p is greater than p atmosphere we should not use vacuum pressure another example at the same atmospheric pressure suppose p-vac is 48.3 kpa the absolute pressure is the difference now which comes out to 48.2 again we have atmospheric pressure we subtract vacuum pressure and we get the absolute pressure in this case since p is less than p atmosphere we can use a vacuum pressure hey dude thanks that alleviates a lot of pressure man i didn't realize that pressure was a stress that explains why when i'm under a lot of pressure i get stressed out i think you are always stressed out little buddy here's some takeaways from the video pressure always acts inward normal and that could be on any object real or imaginary in other words even in the middle of a fluid with some imaginary surface pressure always acts inward normal we also briefly mentioned the equivalent column height of mercury or head and that's what we'll discuss next in more detail i will derive this equation in the next lesson for now if we let z be up and gravity vector be down this is a simple way to express the change of pressure with elevation p below is p above plus rho g times the absolute value of the change in height for example if z is relative to some arbitrary reference frame and g is down we're looking at a dam holding back water this symbol which we'll see a lot is the symbol for a liquid surface exposed to atmospheric pressure so the absolute pressure at this point is p atmosphere since that's the high point here we call that above and let's take a point at the bottom of the lake as below and if the depth of the water is h this equation gives us p at the bottom of the lake p below is p atmosphere that's p above plus rho g times h this is where the concept of equivalent column height comes in if we have a tube filled with water up to some level where the surface is exposed to the local atmospheric pressure and we're looking at some point here if we call this distance h the pressure at this point is p atmosphere plus rho g h just like it was in this case which we showed here the gauge pressure by definition then at this point is just rho g h we sketch gage pressure here this column height h is called the head formerly head is the column height of liquid equivalent to the pressure and it can be used for either gage pressure or absolute pressure here we're using h as a gauge pressure equivalent this is why sometimes you hear people say the pressure is 15 meters of water what does that mean pressure and height have very different units what it means is it's an equivalent column height to describe that pressure this is more easily explained using an example problem let's take the first example that we solved above we solve for absolute pressure now let's write it as an equivalent column height of mercury and water at 20 degrees c first i look up the densities of water and mercury at 20 degrees c i get 998.0 and 13 600 for water and mercury these are in units of kilogram per meter cubed and at 20 degrees c for the water we'll call h sub h2o the equivalent column height of water in this case we're using an absolute pressure a little bit different from what we did here where we used a gauge pressure as i said you can use either just make sure your reader knows which one you're using so in this case p abs is rho gh so h sub h2o is p absolute over rho h2og we plug in absolute pressure from the first example density of the water g we now plug in two unity conversion factors kilogram meter per second squared's a newton and a thousand newton per meter squared is a kpa all the units cancel except this meter in the numerator our equivalent column height of water is thus 34.83 meters we repeat for the mercury the only thing we change is this density everything else is the same and we get 2.556 meters of mercury as the equivalent column height one final comment we never said anything about the fluid in this particular flow it could be water it could be mercury it could be air could be any kind of fluid we can always pick a fluid that we express an equivalent column height or a head here we used mercury and water sometimes certain alcohol solutions are used as column heights thank you for watching this video please subscribe to my youtube channel for more videos [Music]