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Now, what is pressure that I wrote a story about it?!! It is the perpendicular force applied per unit of area (F/A). When I press on something I am applying some force over an area. How I see the result of my pressing depends on the force I apply and the area it is applied to. An example is my weight which is a force, if I walk on a thin layer of ice over a lake, my weight is pressing on the area of my feet sole and the ice breaks and I fall, but if I move using my hands legs, and knees or even creep forward, the ice may not break. That is because my weight is applied over a larger area through my hands and legs and the ice resists the less pressure applied by my weight.
Pressure (P) is one heck of an important property for fluids. The atmosphere of earth is made of air, and air is a fluid, thus has the property of pressure. Now if we want to measure the pressure of any fluid on the surface of earth the pressure of atmosphere will be added to it. Gauge pressure is zero-referenced by the air. If we are only concerned about the pressure of the fluid, then that has to be with reference to a perfect vacuum (zero pressure), which is called Absolute Pressure. So we can say that the Pgage = Pabsolute - Patmosphere.
I already know one of the main properties of any fluid is to take the shape of its container! Another property of a fluid is that it cannot undergo shear stress and keeps deforming under any shear.
[One might say what is shear stress now?! A very legitimate question. In simple terms you may say cutting force, and by cutting we don't mean pressing or pulling, it's sideways. In a more technical term we may define a shear stress as the stress element that is applied parallel to the cross-section of a matter. More details about stresses and related topics in the subject Mechanics of Material]
One thing that I need to know is that in physics, fluids are treated as continuum. A continuum is a substance that can be divided into very tiny volumes no change in its properties, or anything that can gradually go from one to another condition with no sudden changes. For example, continuum of seasons, or experiences, or even the continuum of my progress through the FE exam material.
Density is the first property of a liquid to know, which is also known as Mass Density and is shown by Greek letter ρ. Density is mass per unit of volume presented as kg/m3 in SI system and in lbm/ft3 in English system. So the higher the density of a fluid, the denser and heavier it is (given the same volume). Specific Volume of a liquid is the reciprocal of its density, or you may say it is the volume per unit of mass, and as a result, its unit is the reciprocal of density's units :)
Specific Weight (γ), which is commonly mistaken by density, is the weight per unit of volume and one must know that weight and mass are different from each other. The nature of weight is force and hence it is shown as lbf/ft3. Since, weight is the product of mass and gravity, therefore, the specific weight is not a fixed property of a fluid or any other substance and is dependent on the gravitational force. That means, 1 kg of candy is still exactly 1 kg of candy on the Moon or Jupiter but 10 N (weight) of candy is only 1.7 N on Moon and about 25.3 N on Jupiter. Now we know that the specific weight of that 1 kg of candy changes from here to other planets!
Specific Gravity (SG) is the ratio of the fluid's density to a reference density (usually water's density is used, which is equal to 62.4 lbm/ft3 or 1000 kg/m3). So It is (γfluid / γwater) and there is no unit for this dimensionless property. Here is nice video about specific gravity.
Viscosity, μ is a property of fluids that shows their strength against flow caused by an external force. which is determined by a Viscometer Test comprised of two plates, one moving above the other one and the fluid is in between. According to the Newton's Law of Viscosity, this property is used to determined shear stress in fluids: τt = μ (dv/dy) where, the (dv/dy) is known as the Rate of Strain, Shear Rate, Velocity Gradient, or Rate of Shear Formation. This is why some fluids are named Newtonian Fluids. For such fluids, the strain is proportional to the shear stress, i.e. the stress-strain line is a straight line with slope μ. If the fluid is non-newtonian, the relationship is not linear and shear stress is calculated by the Power Law, as τt = k (dv/dy)n, where k is called Consistency Index. It can be observed that the value of n, if the fluid is newtonian is equal to 1, if the fluid is Pseudo-Plastic Non-Newtonian, n is less than 1, and if it is Dilatant Non_Newtonian, n is more than 1. Some may use this concept as in Kinematic Viscosity, as if the fluid is flowing, its viscosity affects its flow. The kinematic viscosity is more like the speed of the fluid's movement (flow) with units of velocity.
Now, if we reduce the area on which we are applying a pressure, that pressure is called Stress, shown by τ. Normal stress τn is equal to the pressure and normal to the force applied, while Tangential or Shear Stress τt is parallel to the force. Ideal Fluids are not compressible due to normal stress but deform due to shear stress to minimize it as much as possible.
It is an interesting concept that when you compare this with the Hook's Law (Stress=E×Strain) in Mechanics of Material, you see a similar relationship for elastic materials that relates the stress to the strain through a constant multiplier named the modulus of elasticity, which for fluid is called viscosity. Viscosity is shown by several units such as lbf-sec/ft2 (lbm/ft-sec), Pa.s (N.sec/m2), and Poise (dyne.s/cm2). Here is a very nice video on the concept of viscosity.
Another property of liquids is the Surface Tension, σ that which is caused on the free surfaces of fluids by Intermolecular Cohesive Forces. It is the tensile force between two points on the surface that are a unit distance apart (σ = F/L). The way liquids behave in a thin-bore tube is called Capillarity, or Capillary Action, that is caused by the surface tension of the liquid and the vertical solid wall of the tube... This happens when the intermolecular forces between the liquid and the wall is higher than the forces between the liquid molecules (adhesive force domination) which results in liquid climbing up the wall and form a curved surface on top of it, which is called Meniscus. Now if the molecules of the fluid are more attracted to each other than the external wall like for mercury (cohesive force domination), then the meniscus is even lower than the general surface level (like an inverse capillary action!). The Angle of Contact between the liquid and the solid wall, shows which one of the cohesive or adhesive forces dominate.
Now that we know a little about the properties of the fluids, let's jump into the Fluid Statics.
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