 from fluid statics. Once again let us I am say I am Professor Ravek Satay from WIT Solapur. All three sessions we have learned some basic concepts of fluid statics. In the four sessions let us see what are the outcomes. At the end of this session learner will be able to define manometer, write the manometer equation and draw the pressure diagrams. Now manometers are the devices which are used for measuring the fluid pressure. In 19th the manometer equation is essential thing and drawing the pressure diagram requires a certain skill that I will explain in detail. Now let us see what is a manometer. Now as the name suggests manometer is a device which is used to measure the pressure of a liquid. Now if I take a simple manometer, simple manometer means suppose you have got a tank like this and in this suppose liquid is filled. Suppose tank is made of concrete and you want to see what is the level of the water in the tank. What you do? You have just a pipe here which is made of glass. This is a glass pipe and this pipe the level of this lab water will be equal to level of this liquid. So from this you can get an idea that exactly what is the level of the fluid present in this and we know that height is going to be a useful measure for the pressure because we know the equation p upon gamma is equal to h or p is equal to rho g into h. Now how this comes? That is very clear to you as I told in very first slide that whenever we have a column whose area is a and length is l or say h for example density is rho. So volume is area into h density is rho and g divided by area will give the pressure because it is nothing but force upon area and this force is nothing but it is the thrust. It is the thrust upon area that we have. So we can find out with the simple manometer the pressure but the problem is this simple manometer is not useful for measuring the pressure of a gas because you know that gas has got no free surface. So whenever any space is available gas expands and it reaches all corners of the particular container and because of that this is not say suitable for measuring the pressure of the gases. Second thing is if the pressure is negative because many times we have to develop vacuum and we have to go for negative pressure so this cannot measure negative pressure only positive pressure we measure and third important thing is if you want to measure very large pressures. So if a pressure is very large then we have to use a very long tube and for that see in the correct reading we have to again have some mechanism. So for this three reasons say we cannot use this particular say manometer. Now regarding manometry or pressure measurement certain things must be known to you in say before we do any calculations. First thing is there are two pressures we measure one is called as an absolute pressure absolute and second is called as a gauge pressure. Now as the name suggests gauge means it is measured with the help of a gauge and absolute pressure means it is the pressure to which we add the atmospheric pressure and it is always positive basically absolute pressure is always positive and it is never equal to zero because it cannot be zero but if you measure the gauge pressure when I measure atmospheric pressure as a reference see reference pressure above atmospheric pressure I call it a positive pressure suppose this is my atmospheric pressure above this if I measure it is positive below this I call it a negative. Now logically it is a mathematical requirement that when I move from positive to negative there must be zero. So when I measure this particular pressure I may call this as a zero pressure or I may call this an atmospheric pressure why I call this atmospheric pressure because it is present everywhere. Suppose I take this substantial box if I ask what is the atmospheric pressure acting on it net atmospheric pressure acting on this all faces is literally zero because pressure acting here is same pressure acting is here same pressure acting is here same pressure acting here is same but if inside there is vacuum inside there is a vacuum then what happens this particular pressure may have some effect on this or if inside pressure is more if this particular surface may changes shape. Now gauge pressure may be positive zero or negative as already you know and positive gauge pressure means that the pressure is more than the atmospheric pressure that we inflate our tires negative pressure means it is lower than the atmospheric pressure this you might have seen in your condensers in the boiler or a power plants we have a condenser where the pressure is less than atmospheric in the boiler pressure is more than atmospheric. So we say that gauge pressure is positive in boiler and gauge pressure is negative in condenser then practically exact value of the absolute pressure cannot be determined due to the uncertainty of the atmospheric pressure. Now always we say that if you add atmospheric pressure we will get the absolute pressure but correct value of say atmospheric pressure cannot be evaluated because it changes from location to location and other things. Now because of the restrictions of say simple manometer another device which was constructed was a U-tube manometer. Now U-tube manometer is say using two fluids and suppose see this arrangement in which here some liquid is present and even gas is also allowed not necessarily liquid and this is my manometric fluid. Suppose I take this fluid whose density is higher than this particular fluid automatically it will be held in this particular tube and because of its high density the length of the column that I require is less because finally pressure is rho g h more the value of rho I will get small value of h for the same pressure because g is constant as far as my calculations are concerned. Now what we do when the pressure inside is more what will happen this will compress this and I will get this as a manometric difference this is called as a manometric height means initially if there is no pressure or the pressure is equal to atmospheric pressure this pressure for example then both will be at same level and when the pressure inside is increased for example suppose I supply heat if I supply heat then pressure increases when the pressure increases it will start pushing this liquid down and this push liquid up means this is a shift of this column up to this height. So actually theoretically speaking it has exactly come half of the way but what is the difference now between these two it is this height. So if I know the density of this fluid and if I multiply this by h I will get the value of pressure. Now the third important thing as a analysis part of the fluid statics is drawing of pressure diagrams now here I will tell you certain things we come across two things in fluid statics one is called as the center of pressure and second is the pressure average pressure that is acting at some geometric mean of the diagram. Now see first if I have a horizontal plate if I have a horizontal plate and if on the horizontal plate some liquid is present some liquid is present. So I know that if height is same then pressure everywhere is same rho g h rho g h rho g h rho g h. So if I want to draw the pressure diagram it will be a constant line horizontal line so pressure will be constant throughout it is same pressure. But if I take this particular plate and in the liquid if I keep it in a vertical position and below the liquid surface below the liquid surface then what I do I draw a line touching the liquid surface and I know that in my previous slide we have seen that pressure increases continuously as we move onward because equation was p is equal to p naught plus rho g h. So as h increases we get increase in pressure. So now here what happens as plate is here pressure is 0 here it is a linear graph and this height is that I am getting here so pressure is increasing from this point this point this point onwards. Then what is this maximum value that I must get? So you will find that this is nothing but we have to find out the pressure triangle the pressure triangle and area of the pressure triangle area of the pressure triangle per unit width will give the force. So pressure will be shown perpendicular to the surface if the surface is inclined in this way pressure is perpendicular to this it is not horizontal because pressure always acts in the normal direction. For example if I take this geometry pressure on this surface is like this pressure on this surface is like this pressure on this surface will be like this. So this is the concept that we must know. Similarly sometimes what happens the container may have a shape like this or like this then we can show that the pressure is always perpendicular to the surface and that is why we say that whenever we compress a liquid we get the pressure perpendicular to the surface. If it is a circular geometry it is radial if it is a flat geometry perpendicular and if it is some contour like this then it will be always normal to this particular surface. So I think with this you have got an idea about the pressure diagrams for various static devices. For reference once again refer to white fluid mechanics by Tata Megahill we will stop here for today's session. Thank you.