Presentation 1

Fluids and fluid statics

Aerodynamics

The three basic states of matter are solid, liquid and gas while Plasma and Bose Einstein Condensate are rarely observed in daily life.

States of matter

A fluid is anything that would spill or float away if it weren't in a container (unless it's big enough to be held together by gravity like a star). If you can stir it up with a spoon or blow it through a straw, it's a fluid. Water is a fluid and so is air. In fact, all liquids and gases are fluids. It is defined as a substance that continually deforms (flows) under an applied shear stress.Shear stress- The component of stress that causes parallel layers of a material to move relative to each other in their own planes.

Fluids

Compressibility – refers to whether its volume can easily be increased or decreased.Gases are highly compressible while liquids are incompressible.Density- the amount of matter in a given space for that substance.It is possessed by all fluids.Pressure- the force exerted over a given area.In a liquid, the pressure comes from the weight of the fluid and the weight of the air above it, which we call the atmosphere and the same principle applies to gases.

Properties of Fluids

Buoyancy- the ability or tendency to float in a substanceBuoyancy is another common characteristic of fluids. This is the upward force from a fluid, which is usually felt by some object in that fluid. It comes from the pressure inside the fluid itself.Viscosity- the property of a liquid that describes how fast or slowly it will flow. Real fluids display viscosity and thus are capable of being subjected to low levels of shear stress.

Viscosity of liquids in general, decreases with increasing temperature while that of gases increases.Surface Tension- the elastic tendency of liquids that makes them acquire the least surface area possible.It is an important property of fluid which enables phenomenon like capillary action.Rise or fall of a liquid in a capillary tube is caused by surface tension and depends on the relative magnitude of cohesion of the liquid and the adhesion of the liquid to the walls of the containing vessel.

Fluid Statics and Fluid Dynamics form the two constituents of Fluid Mechanics. Fluid Statics deals with fluids at rest while Fluid Dynamics studies fluids in motion. A fluid at rest has no shear stress. Consequently, any force developed is only due to normal stresses i.e., pressure. Such a condition is termed the hydrostatic condition. Its importance becomes apparent when we note that the atmosphere around us can be considered to be at rest and so are the oceans. The simple theory developed here finds its application in determining pressures at different levels of atmosphere and in many pressure-measuring devices. Further, the theory is employed to calculate force on submerged objects such as ships, parts of ships and submarines. The other application of the theory is in the calculation of forces on dams and other hydraulic systems.

Fluid Statics

Pascal’s lawThe basic property of a static fluid is pressure. Pressure is familiar as a surface force exerted by a fluid against the walls of its container. Pressure also exists at every point within a volume of fluid. For a static fluid, pressure at a point is same in all directions. This is Pascal's law.

Px=Py=Ps=P

The formula that gives the pressure P on an object submerged in a fluid isP=h*ρ*gWhere ρ is the density of the fluid,g is the acceleration of gravityh is the height of the fluid above the object

Measurement of PressureOne of the direct applications of the equation of Fluid Statics we have derived is in the devices used to measure pressure. Now it is necessary to recall that we have an Absolute Pressure and a Gauge Pressure. Absolute pressure is the sum of atmospheric pressure and the gauge pressure.

Barometers

A barometer is a device for measuring atmospheric pressure. A simple barometer consists of a tube inserted in an open container of mercury with a closed and evacuated end at the top and open tube end at the bottom and with mercury extending from the container up into the tube. Strictly, the space above the liquid cannot be a true vacuum. The atmospheric pressure is calculated from the relation Patm = ρgh where ρ is the density of fluid in the barometer.

Piezometer

For measuring pressure inside a vessel or pipe in which liquid is there, a tube may be attached to the walls of the container (or pipe) in which the liquid resides so liquid can rise in the tube. By determining the height to which liquid rises and using the relation P1 = ρgh, gauge pressure of the liquid can be determined. Such a device is known as piezometer.

The “U”-Tube ManometerUsing a “U”-Tube enables the pressure of both liquids and gases to be measured with the same instrument. The “U” is connected as in the figure below and filled with a fluid called the manometric fluid. The fluid whose pressure is being measured should have a mass density less than that of the manometric fluid and the two fluids should not be able to mix readily - that is, they must be immiscible.

Archimedes' principleArchimedes' principle indicates that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.

Variation Of Pressure Vertically In A Fluid Under Gravity

p2-p1= -ρg(z2-z1)Thus in a fluid under gravity, pressure decreases with increase in height, (z2-z1)

Equality of pressure at the same level in a static fluid:

The fluid is at equilibrium so the sum of the forces acting in the x direction is zero.P1=P2

General Equation For Variation Of Pressure In A Static Fluid

dp/dz=-ρgThis equation predicts a pressure decrease in the vertically upwards direction at a rate proportional to the local density.