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8. Static Fluids
A fluid is a substance that has no fixed shape. Liquids and Gases can flow and are therefore called fluids. Fluids yield easily to external pressure. In this classes, we will learn about various Mechanical Properties of Fluids like Viscosity and Surface Tension.
Density is mass per unit volume, d = m/V, where d is the symbol for density (it could olfo be the Greek letter rho), m is the mass, and V is the volume occupied by the substance.
Curiosities:
- A ton of feathers and a ton of bricks have the same mass, but the feathers make a much bigger pile because they have a much lower density.
- Salt is about 25% more dense than sugar. Therefore a teaspoon of salt weighs more than a teaspoon of sugar by almost 25%.
Preassure is defined as the force devided by the area perpendicular to the force over which the force is applied, so p = F/A.
Example: While the person being poked with the finger might be irritated, the force has little lasting effect. In contrast, the same force applied to an area the size of the sharp end of a needle is great enough to break the skin.
Pressure inside tire exerts forces perpendicular to all surfaces it contacts. That static fluids do not exert shearing forces.
Pressure is exerted on all sides of swimmer during diving, since the water would flow into the space he occupies if he were not there. The forces underneath the swimmer are larger, due to greater depth, giving a net upward or buoyant force that is balanced by the weight of the swimmer.
The bottom of the container (of height h) supports the entire weight of the fluid in it. The vertical sides cannot exert an upward force on the fluid (since it cannot withstand a shearing force), and so the bottom must support it all. In that case we have that p = mgh. Atmospheric pressure is another example of pressure due to the weight of a fluid, in this case due to the weight of air above a given height. The atmospheric pressure at the Earth’s surface varies a little due to the large-scale flow of the atmosphere induced by the Earth’s rotation (this creates weather “highs” and “lows”). However, the average pressure at sea level is given by the standard atmospheric pressure Patm, measured to be 1 athmosphere (atm) = Patm = 101000 N/m2 = 101 kPa Above relationship means that, on average, at sea level, a column of air above 1.00m2 of the Earth’s surface has a weight of 1.01×105N is equivalent to 1 atm .
PASCAL’S PRINCIPLE: A change in pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and to the walls of its container.
A typical hydraulic system with two fluid-filled cylinders, capped with pistons and connected by a tube called a hydraulic line. A downward force F1 on the left piston creates a pressure that is transmitted undiminished to all parts of the enclosed fluid. This results in an upward force F2 on the right piston that is larger than F1 because the right piston has a larger area.
Gauge pressure is the pressure relative to atmospheric pressure. Gauge pressure is positive for pressures above atmospheric pressure, and negative for pressures below it.
ABSOLUTE PRESSURE: Absolute pressure is the sum of gauge pressure and atmospheric pressure.
According to this principle the buoyant force on an object equals the weight of the fluid it displaces. In equation form, Archimedes’ principle is FB=wfl, where FB is the buoyant force and wfl is the weight of the fluid displaced by the object.
BUOYANT FORCE: The buoyant force is the net upward force on any object in any fluid.
Attractive forces between molecules of the same type are called cohesive forces. Liquids can, for example, be held in open containers because cohesive forces hold the molecules together. Attractive forces between molecules of different types are called adhesive forces. Such forces cause liquid drops to cling to window panes, for example. In this section we examine effects directly attributable to cohesive and adhesive forces in liquids.
Cohesive forces between molecules cause the surface of a liquid to contract to the smallest possible surface area. This general effect is called surface tension. Molecules on the surface are pulled inward by cohesive forces, reducing the surface area. Molecules inside the liquid experience zero net force, since they have neighbors on all sides.
One important phenomenon related to the relative strength of cohesive and adhesive forces is capillary action—the tendency of a fluid to be raised or suppressed in a narrow tube, or capillary tube. This action causes blood to be drawn into a small-diameter tube when the tube touches a drop.
The contact angle θ (contact beetwen two surfaces) is directly related to the relative strength of the cohesive and adhesive forces. The larger the strength of the cohesive force relative to the adhesive force, the larger θ is, and the more the liquid tends to form a droplet. The smaller θ is, the smaller the relative strength, so that the adhesive force is able to flatten the drop.