Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Lift (force) wikipedia , lookup
Centripetal force wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Classical central-force problem wikipedia , lookup
Reynolds number wikipedia , lookup
Biofluid dynamics wikipedia , lookup
Lorentz force velocimetry wikipedia , lookup
History of fluid mechanics wikipedia , lookup
NAZARIN B. NORDIN [email protected] What you will learn: • • • • • Pascal’s law Incompressibility of fluids Pressure, force ratio Archimedes principle Density and relative density Introduction to fluids A fluid is a substance that can flow and c onfor m t o the boundaries of a n y container in which we put them. e.g. water, air, glass. • A fluid is any substance that can flow such as a liquid or a gas. • Fluids don’t have well defined shapes. • A fluid takes on any shape to fit a container. • The study of fluids can be divided into two categories : hydrostatics and hydrodynamics or fluid dynamics. Basic properties of fluids Density (mass per unit volume) - m / V Pressure (force per unit area) - P F / A Basic properties of fluids Pressure (force per unit area) - P F / A Notice that from definition, pressure may depend on direction. However, this is not the case for static fluids. (why?). Basic properties of fluids Pressure (force per unit area) - P F / A Unit of pressure: 1 pascal (Pa) = 1 Newton per square meter. 1 atm. = 1.01 x 105 Pa Fluids at rest Pressure increases when we go “deeper” into water – why? F2 F1 mg, F1 p1 A, F2 p2 A, m A( y1 y2 ) Fluids at rest Pressure of a fluid in static equilibrium depends on depth only p2 p1 g ( y1 y2 ), or p p0 gh Example Which one of the four container + fluid has highest pressure at depth h? How about if (d) is move up (down) by distance h? Pascal’s Princple • A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of the container as a direct consequence of Newton’s Law. Example: Hydraulic level • Applied force Fi change in pressure p=Fi/Ai=Fo/Ao. • Therefore output force is Fo=FiAo/Ai. • Therefore • Fo > Fi if Ao > Ai • How about work done? Archimedes’ Principle • Buoyant force – upward force in liquid because of increasing pressure in liquid as one goes down below the surface. • (a) a hole in water. Notice that the hole is in static equilibrium if it is filled with water. Archimedes’ Principle • (a) a hole in water. Notice that the hole is in static equilibrium if it is filled with water. • Therefore the upward force = mfg, mf = mass of displaced water. Archimedes’ Principle • (b) The hole in water is replaced by a solid with the same shape. • Since nothing changes in water, therefore the upward force = mfg, mf = mass of displaced water = buoyant force Archimedes’ Principle • (c) The solid in water is replaced by a piece of wood with mw < mf.. • In this case the wood float on the surface with Fb=mwg. Archimedes’ Principle • When a body is fully or partially submerged in a fluid, a buoyant force Fb from the surrounding fluid acts on the body. The force is directed upward and has a magnitude equal to the weight mfg of the fluid that has been displaced by the body. Archimedes’ Principle • Question: Imagine a large sphere of water floating in outer space. The sphere of water is formed under its own gravity. Is there any buoyant force if an object enters this sphere of fluid? PRESSURE • Pressure is the quantity that is related to the force acting on the walls of the balloon and is defined as the normal force per unit area. • If F is the force perpendicular to the surface area A, the pressure P is therefore F P A • The pressure at a point in a fluid depends on the depth. Greater depths result in greater pressures • Pascal’s Law: For a confined fluid in a container, the change in pressure will be transmitted without loss to every point of the liquid and to the walls of the container • Archimedes’ Principle: Any body that is completely or partially submerged in a fluid will experience an upthrust that is equal to the weight of the fluid displaced by the body Fluids in Motion • An ideal fluid is one that (i) flows smoothly, (ii) is non-viscuous, (iii) is incompressible, (iv) is irrotational. • The path of steady flow can be visualized using streamlines. • Under steady-state flow conditions, for a given time interval, the volume of liquid flowing into the tube must equal the volume of liquid flowing out of a tube.This is known as the Continuity Equation. Flowing liquids • The continuity equation – conservation of mass in a incompressible liquid flow. V A1v1t A2 v2 t or A1v1 A2 v2 v = velocity of fluid flowing through area A in the tube Example • What is the volume flow rate of water if Ao=1.2cm2, A=0.35cm2 and h=45mm. A0v0 Av v 2 v02 2 gh 2 ghA2 v0 28.6cm / s. 2 2 A0 A RV A0v0 34cm3 / s. Bernoulli’s Equation • Bernoulli’s Equation relates the elevation y, speed v and pressure P of a fluid at any point in a tube. • According to Bernoulli’s Equation: 1 2 P v gy constant 2 • However, Bernoulli’s Equation is not applicable to viscous fluids . Bernoulli’s Equation • Bernoulli’s Equation is a consequence of conservation of energy in steady flow. W K ; 1 1 2 K mv2 mv12 2 2 1 V (v22 v12 ) 2 Bernoulli’s Equation • Bernoulli’s Equation is a consequence of conservation of energy in steady flow. W Wg WP ; Wg ( V ) g ( y2 y1 ) W p p2 V p1V Bernoulli’s Equation • Adding together, we obtain 1 2 1 2 p1 v1 gy1 p2 v2 gy2 2 2 or 1 2 p v gy c 2 (Bernoulli’s Equation) Example • What is the speed v of the water emerging from the hole? • Show that v2=2gh (same as free fall) DENSITY •The density is an important factor that determines the behaviour of a fluid. •The density of a fluid is defined as the mass m per unit volume V: m V •The SI unit for the density is kg / m 3