Fluids continually deform. Deformation is the process of changing shape as a result of applied shear stress. Shear stress is a sliding force, which is parallel but not in the same line, thereby causing sliding. The ability to deform is a result of bonds that can be easily broken and reformed. Water only resists stress to a small extent, known as viscosity, a measurement of friction between fluid molecules. Viscosity in common language is known as “thickness”. For example, honey is more viscous than water. The viscosity is the shear modulus, which is shear stress rate divided by the shear strain rate [or in other words, the slope of the shear stress vs. shear strain graph] (see for more information on shear modulus, stress and strain). Whereas drag related to the friction, fluid causes on an object; viscosity relates to the friction, fluid causes on itself. Evidently, if fluid has no viscosity, there is also no drag. Alternatively, it can be said that fluids can only resist forces normal to its surface, which from , was defined as perpendicular to its surface. Ability to resist normal forces explains why fluids do take on the shape of its container.

For fluids, since density is used instead of mass, the formula can be rewritten as [mathjax]p=\rho gy[/mathjax], where [mathjax]y[/mathjax] is the vertical displacement (depth) below the fluid to a chosen point. For example, the density of water at 100m, is [mathjax]1,000\times 10\times 100=1,000,000 Pa\approx 10 atm[/mathjax]. Note that apart from volume, pressure is also unrelated to shape. This fluid pressure measurement is a gauge pressure, meaning it is absolute pressure, not including atmospheric pressure. Absolute pressure measures pressure relative to a vacuum of 0 Pa. Therefore, since there is an additional atmospheric pressure, the absolute pressure of water in the example, is in fact [mathjax]10+1=11 atm[/mathjax]. Although absolute pressure cannot be negative, gauge pressure can be negative, as it means that the pressure is less than atmospheric pressure.

A Greek king wanted to determine if a gold crown was pure gold, or if some silver has been substituted by the dishonest goldsmith. Archimedes was asked to determine this without damaging the crown. Noting that the water in the bathtub rose as he dipped in, he realized this effect could be used to determine the volume of the crown. As Archimedes knew the density of gold and the mass of the crown, using he could figure out volume of displacement, supposing the crown was pure gold. Then figuring out actual volume of displacement, he submerged the crown in water, measuring how much water spilt. The volume of fluid displaced is equal to the volume of (the submerged portion of) a submerged object. Because other metals are not as dense as gold, if the volume of water spilt is less than the hypothetical volume of displacement, impure metals have been added. Note therefore that as an object is submerged, the (displaced) fluid pushes upward against the object, a force known as buoyancy.Archimedes principle is that buoyancy, is equal to the weight of the displaced fluid. The weight of the displaced fluid is , or since fluid is measured in density, , or in-substituting, , where is the buoyancy force (per Archimedes principle, equal to the weight of the displaced fluid), is the density of the displaced fluid, is the volume of the displaced fluid, and is the gravitational constant. Keep in mind that the weight of the displaced fluid (by Archimedes principle, equivalent to buoyancy) is not necessarily the same as the weight of the object. If the object weight is greater than buoyancy, it will sink. If the object weight is less than buoyancy, it will float. Keep in mind that , meaning the statements can be restated as, if the density of the object is greater than the density of the fluid, it will sink; and if the density of the object is less than the density of the fluid, it will float. Thus, if the ratio of the density of the object to the fluid is greater than 1, will sink; and if less than 1, will float. As the density of the object decreases, the volume of the fluid displaced decreases proportionally. Note from that the volume of the submerged portion of an object is equal to the volume of the fluid displaced, meaning that the sentence can be restated as, as the density of the object decreases, the volume of the submerged portion of an object decreases proportionally. This means that the ratio of the density of an object to the fluid, is the ratio of the object that is submerged. From , since specific gravity is a density ratio to water, it is thus the proportion of an object that will be submerged if floated in water. For example, if the specific gravity of ice is 0.9, it means that 90% of an iceberg will be underwater.

An ideal fluid has non-viscous, non-compressible, non-turbulent and non-rotational flow.Turbulent flow is flow that is chaotic, and increases with increasing velocity. Laminar flow is flow at lower velocities, before the onset of turbulent flow. Rotational flow is the rotation of fluid particles, as it moves.

Note that in the mass flow rate formula [mathjax]Q=Av[/mathjax], if a pipe has the cross-sectional area of a circle [mathjax]A=\pi r^2[/mathjax], the formula becomes [mathjax]Q=\pi r^2 v[/mathjax], meaning that radius and velocity are inversely related. This means that in ideal fluids, as radius is decreased, velocity increases. Real fluids are non-ideal fluids, which have reduced flow. Deviation from ideal behavior (reduction of flow) increases in pipes with smaller diameter.

Surface tensionis the tendency of the surface of a liquid to contract, caused by intermolecular forces towards the center of the fluid. This force which causes like molecules to stick together is the cohesive force. Cohesive force is responsible for the spherical shape of liquid droplets. In contrast, adhesive force is the force which causes dissimilar molecules to stick together. Adhesive force is responsible for water droplets sticking on the walls of a glass tube. Surface tension causes meniscus, which is the curve of the liquid surface at points close to the container. Meniscus is concave for water in a test tube, because the cohesive forces (between water to each other) are stronger than the adhesive forces (between water and the container). Meniscus is convex for mercury in a test tube, because of the vice versa reason. Concave is a curve that curves inward, and convex is a curve that bulges outward. Capillary action is where the adhesive forces in a tube with sufficient small diameter, will cause the liquid to lift (against the action of gravitational force).

Gas are like liquids, but in contrast, expands to fill the entire volume available. The ability to expand is a result of very weak bonds, which are equivalent to being nonexistent.Compressibility is the ability to vary density. Gases are far more compressible than fluids.

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Maps to RK7.1

What are fluids?

2 Solids

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The atoms of solids are tightly bound to each other, and vibrate about fixed mean positions. Due to this rigidity, there is [permanent] resistance to deformation, as very strong bonds need to be broken before deformation will occur. Although rigid, solids have a small degree of elasticity.Elasticity is the property of materials to return to their original shape after deformation.

Stress is the force applied to a solid, [mathjax]\rho=\dfrac{F}{A}[/mathjax], where [mathjax]f[/mathjax] is average force, [mathjax]A[/mathjax] is area. Average force is the average of the forces not applied [and not the addition], such that a compressive force of [mathjax]10N[/mathjax] on either side has an average force of [mathjax]10N[/mathjax], not [mathjax]20N[/mathjax]. This is analogous to tension, where either end of the rope had a force [mathjax]\dfrac{1}{2}.F[/mathjax]. Stress has the units [mathjax]N/m^2[/mathjax]. Note that stress has the same formula as pressure, so can be thought of as the solid version of pressure, and has thus also has the SI units Pascal. Strain (epsilon, [mathjax]\epsilon[/mathjax]) describes the deformation, that has resulted due to the stress applied, and is defined as the change of a length, with respect to the original length. As strain is a ratio, it has no units. If stress is plotted against strain, the slope of the graph is known as the modulus of elasticity, or alternatively, [mathjax]\lambda=\dfrac{stress}{strain}[/mathjax]. For any particular metal, the modulus of elasticity is constant. There are different types of moduli of elasticity, including:

Shear modulus, which describes tendency to shear. As defined , shear is caused by two parallel forces that are not acting in the same line, thereby causing sliding. [mathjax]A[/mathjax] is the area on which the force acts, and shear strain is [mathjax]\epsilon =\dfrac{\Delta x}{l}[/mathjax], where [mathjax]\Delta x[/mathjax] is the [transverse] displacement caused due to the rectangle being slid into the shape of a rhomboid, and [mathjax]l[/mathjax] is the initial length

Bulk modulus, which describes volumetric elasticity, which is tendency of an object to resist deformation (from all directions) when uniformly compressed (from all directions). It is a 3D version of Young’s modulus. Volumetric stress is the change in pressure, and volumetric strain is [mathjax]\epsilon=\dfrac{\Delta V}{V_{0}}[/mathjax], where [mathjax]\Delta V[/mathjax] is the change in volume, and [mathjax]V_{0}[/mathjax] is the original volume. For example, the bulk modulus of diamond is much greater than the bulk modulus of air