Fluid Mechanics

FLUID MECHANICSCHAPTER 1INTRODUCTIONTO FLUID MECHNICS

J. Berlin P. Juanzon CE, MBA, MSCMFluid MechanicsFluids are substances that are capable of flowing and conform to the shape of containing vessels.When in equilibrium, fluids cannot sustain tangential or shear forces.All fluids have some degree of compressibility and offer resistance to change of formFluids can be classified as liquids or gas.

DensityRegardless of form (solid, liquid, gas) we can define how much mass is squeezed into a particular space

PressureA measure of the amount of force exerted on a surface area

Pressure in a FluidThe pressure is just the weight of all the fluid above youAtmospheric pressure is just the weight of all the air above on area on the surface of the earthIn a swimming pool the pressure on your body surface is just the weight of the water above you (plus the air pressure above the water)Pressure in a FluidSo, the only thing that counts in fluid pressure is the gravitational force acting on the mass ABOVE youThe deeper you go, the more weight above you and the more pressureGo to a mountaintop and the air pressure is lowerPressure in a Fluid

Pressure acts perpendicular to the surface and increases at greater depth.Pressure in a Fluid

Buoyancy

Net upward force is called the buoyant force!!!Easier to lift a rock in water!!Displacement of Water

The amount of water displaced is equal to the volume of the rock.Archimedes PrincipleAn immersed body is buoyed up by a force equal to the weight of the fluid it displaces.If the buoyant force on an object is greater than the force of gravity acting on the object, the object will floatThe apparent weight of an object in a liquid is gravitational force (weight) minus the buoyant force

FlotationA floating object displaces a weight of fluid equal to its own weight.Flotation

GasesThe primary difference between a liquid and a gas is the distance between the moleculesIn a gas, the molecules are so widely separated, that there is little interaction between the individual moledulesIDEAL GASIndependent of what the molecules are

Boyles LawBoyles LawPressure depends on density of the gasPressure is just the force per unit area exerted by the molecules as they collide with the walls of the containerDouble the density, double the number of collisions with the wall and this doubles the pressureBoyles Law

Density is mass divided by volume.Halve the volume and you double the density and thus the pressure.Boyles LawAt a given temperature for a given quantity of gas, the product of the pressure and the volume is a constant

Atmospheric PressureJust the weight of the air above youUnlike water, the density of the air decreases with altitude since air is compressible and liquids are only very slightly compressibleAir pressure at sea level is about 105 newtons/meter2Barometers

Buoyancy in a GasAn object surrounded by air is buoyed up by a force equal to the weight of the air displace.Exactly the same concept as buoyancy in water. Just substitute air for water in the statementIf the buoyant force is greater than the weight of the object, it will rise in the airBuoyancy in a Gas

Since air gets less dense with altitude, the buoyant force decreases with altitude. So helium balloons dont rise forever!!!Bernoullis Principle

Bernoullis PrincipleFlow is faster when the pipe is narrowerPut your thumb over the end of a garden hoseEnergy conservation requires that the pressure be lower in a gas that is moving fasterHas to do with the work necessary to compress a gas (PV is energy, more later)Bernoullis PrincipleWhen the speed of a fluid increases, internal pressure in the fluid decreases.

Bernoullis Principle

Bernoullis Principle

Why the streamlines are compressed is quite complicated and relates to the air boundary layer, friction and turbulence.