 I am Professor Vivek Sathay of WIT Sulapur. Now today we are going to discuss on fluid statics and in session one we are going to discuss some basic concepts of fluid statics. Now before we start any session we must know what are the learning outcomes. Learning outcomes are the measurable parameters which we measure at the end of a session and for me when you complete this particular say video and go through it you will be able to define what is static pressure, you will be able to derive the expression for static pressure and you will be able to identify whether pressure is a scalar or vector. Now let us move in mechanics whether it is a fluid mechanics, whether it is applied or whether it is any other kind of say pure mechanics, we study three varieties one is called as statics, second is called kinematics and third is called as dynamics. Out of this fluid statics we are giving say first say treatment and first of all you know that fluid is a substance which consists of liquid as well as gas. Liquid is a substance in which liquid has got free surface and gas has got no free surface. So there is a different treatment for fluid and gas we are restricting our discussion to the fluids and that to liquids. Now liquid is a typical fluid which cannot sustain any shear stress means if I apply the shear force on the surface of a liquid it will start moving in the laminar linear direction. So the fluid which does not exist say contain the particular shear stress is our prime importance. Now let us see first of all we must know how to measure the atmospheric pressure because everything is related to atmospheric pressure that we are going to see in detail when we study the gauge pressure and the total pressure. Now the first important thing is if I ask the students how to measure the atmospheric pressure how to measure atmospheric pressure. The first question I ask to the students what is the unit of pressure then many students answer it correctly as they know that it is Newton per meter square when it is Newton per meter square the thing is clear it is a force per unit area. But my question is what is atmospheric pressure? So atmospheric pressure is the pressure which is exerted on a unit area on the surface of earth by the air column which is present till the atmosphere exists. Now that pressure is approximately equal to one atmosphere and that one atmosphere if you do the calculations it turns out to be 1.013251.01325 bar or it is say 10 to 5 Newton per meter square. Now the question is how to measure this if I ask what is the device that we use for measuring the atmospheric pressure can you tell me as we measure temperature with a thermometer with which device we measure the atmospheric pressure yes it is the barometer. So barometer is a simple device which is used to measure the atmospheric pressure its construction is simple functioning is very say beautiful and that will give the clear idea and feel that how atmospheric pressure acts on a particular surface. Now this particular say barometer was invented by Torricelli and let us see how it is say measure first of all take a tube of approximately one meter length take a tube of approximately one meter length. Now why one meter that I will tell you after some time if you take one meter length completely fill it with mercury completely fill it with mercury then put your thumb here then put your thumb on the top then take a bowl of mercury which is completely filled and let there be some space so that this particular mercury can be filled in this particular bowl. Now what you do now invert the particular tube and insert it into the mercury pot then as a logical of say phenomena you feel that all the mercury will come down and the entire level of the mercury will be slightly increased means generally if I ask the students what will happen to the mercury they say that if this is the tube in which it is inverted mercury will come down and all the level will be same but here is the difference that we observe in actual practice so what happens when we invert the particular tube in a mercury bath or mercury say container then mercury starts falling you can see that in this particular portion where there was previously mercury now what has happened because mercury is falling down it is entering into this particular bowl there is absolute vacuum actually it is vacuum but theoretically speaking some mercury vapors at low pressure are present but for all our practical calculations we assume that the vapor pressure exerted by this mercury on at this particular say it is a point A is approximately 0 then we know that the why this happens then so actually it is nothing but it is as if there is some membrane or a rubber membrane on this particular and that rubber membrane has pushed that particular liquid and this particular liquid layer is sustained by this force so the pressure which is acting at this point pressure which is acting at this point is one and the same so naturally the pressure at this point B must also be same so if I equate say pressure at A pressure at C equal to pressure at B now what is pressure at C and pressure at B I know that pressure at C is pressure atmospheric pressure pressure at this point is also atmospheric pressure everywhere is atmospheric but now suppose I take this tube whose cross sectional area is A cross sectional area is A then what is the volume of this part it is A into H this is my volume what is the density of mercury it is rho and what is the weight of this mass it is rho into A into H into G so I will get this quantity as A H rho G so this is a weight so weight is nothing but force divided by area divided by area so what I get rho G H so rho G H is my pressure so pressure up at this point is nothing but pressure at point A plus rho G H so I will get in simple terms pressure at B is equal to pressure at A plus rho G H now one thing is clear from this when pressure at A is 0 because I know that it is perfect vacuum pressure at B is equal to rho G H so this is if you put the appropriate values of your say density of the mercury gravitation and the height that you measure you will find that this column length is 76 centimeter and that is why we say when the pressure is 1 atmosphere it is 76 centimeter of mercury or it is 760 millimeter of mercury or if you want to call it as a 1 atmosphere or we want to convert into bar it is 1.01325 bar so this is about the first important thing about a pressure now the question comes in statics we talk about equilibrium now equilibrium is a very fundamental concept in mechanics suppose I have this particular say bench or a table on which I put some object I put some object now this object is having some weight that is mg and the surface is providing a normal reaction N so in equilibrium what I do I equate this N to mg I equate N to mg so in equilibrium for solid bodies we equate forces what we equate force now why we equate force for equilibrium for solids and why we equate pressure for equilibrium for liquids is the main thing that you must know now many students do not have idea that pressure equally say similarity of the pressure or pressure is important parameter for measuring the equivalence okay now see here for solids the surface is rough so the actual area is less than apparent area and the contact with the particular surface is such that say all area is not covered so there is no point in assuming that pressure to be considered as force upon area and that is why we take this as a force in case of a liquid the interface between this surface and this surface is approximately same and the apparent area and actual area is one and the same therefore for fluids pressure is important parameter so in fluid statics we equate the pressure on the top and at the bottom now the next question that I want to ask you about this is whether pressure is a scalar or vector many students have the confusion and they say that pressure is a vector because pressure is a different find as force upon area and many people say that force is a vector quantity and area is a scalar quantity so vector upon scalar becomes vector now about this we will see in detail in the next session before that whatever the sketch I have drawn over here you just have a thinking over it this is a balloon in which liquid is filled and there are small holes here here here I made now suppose I put the piston down what will happen the water will ooze out from all the holes look at the directions in which the water is coming out is it normal to the surface or not that is my question so for today's session we will stop over here thank you and for any reference you I advise you to refer the book by fluid mechanics by white fluid mechanics by white by Tata McRoyle publication T.M.H. thank you