ICNS/PY 132 : Fluid Mechanics Weerachai Siripunvaraporn Department of Physics, Faculty of Science Mahidol University email&msn : wsiripun2004@hotmail.com

States of Matter gas liquid Solid Has a definite volume and shape Liquid Has a definite volume but not a definite shape Gas – unconfined Has neither a definite volume nor shape All of these definitions are somewhat artificial. More generally, the time it takes a particular substance to change its shape in response to an external force determines whether the substance is treated as a solid, liquid or gas. A fluid is a collection of molecules that are randomly arranged and held together by weak cohesive forces and by forces exerted by the walls of a container. Both liquids and gases are fluids. solid CH14 Introduction

What do we learn in this chapter? First, we consider the mechanics of a fluid at rest—that is, fluid statics. We then treat the mechanics of fluids in motion— that is, fluid dynamics.

Pressure in a Fluid How do you feel when you are under the water? I feel that there is a force acting on me.

Where does the force come from?

Why sharp knife are better cut than dull knife? when applying same force. To describe, we need another physics term. That term is called “Pressure”.

Pressure (P) is defined as the ratio of force to area. Its unit is N/m2 or another name is pascal (Pa). Force accelerate. Pressure cut.

Can you do what I do? Lying on a bed of nails!

What if she wear a pair of sneaker What if she wear a pair of sneaker? Assumed that each sneaker has an area of 20 cm x 10 cm. What pressure does she exert on the floor?

Density Notes SI Unit: Kg/m3 CGS Unit: g/cm3 CH14 Density is defined as the mass per unit volume of the substance. The values of density for a substance vary slightly with temperature since volume is temperature dependent. The various densities indicate the average molecular spacing in a gas is much greater than that in a solid or liquid. CH14 Section 14.2

Consider a small part of fluid, How many force acting on it?

That is, the pressure P at a depth h below a point in the liquid at which the pressure is P0 is greater by an amount ρgh. If the liquid is open to the atmosphere and P0 is the pressure at the surface of the liquid, then P0 is atmospheric pressure.

Atmospheric Pressure Everyone is under a pressure! You are under a pressure due to the weight of the water. This woman is also under the pressure due to the air (has mass).

Atmospheric Pressure What would happen if you go higher? weight of air What would happen if you go deeper into the ocean? Pressure due to weight of air

This equation implies that the pressure is the same at all points having the same depth, independent of the shape of the container. Compare the pressure at red marks of all containers? The water level on both sides are different. What would happen next? The water will flow from one side to another until both side has the same pressure at the same depth.

Why the wall do not collapse?

Pascal’s Law, Other Applications In view of the fact that the pressure in a fluid depends on depth and on the value of P0, any increase in pressure at the surface must be transmitted to every other point in the fluid. This concept was first recognized by the French scientist Blaise Pascal (1623–1662) and is called Pascal’s law: a change in the pressure applied to a fluid is transmitted undiminished to every point of the fluid and to the walls of the container. Hydraulic brakes Car lifts Hydraulic jacks Forklifts Pascal’s Law, Other Applications

F1 < F2 when A1 < A2 An important application of Pascal’s law is the hydraulic press illustrated in Figure. A force of magnitude F1 is applied to a small piston of surface area A1. The pressure is transmitted through an incompressible liquid to a larger piston of surface area A2. Because the pressure must be the same on both sides, P = F1/A1 = F2/A2. Therefore, the force F2 is greater than the force F1 by a factor A2/A1. By designing a hydraulic press with appropriate areas A1 and A2, a large output force can be applied by means of a small input force. Hydraulic brakes, car lifts, hydraulic jacks, and forklifts all make use of this principle.

Absolute vs. Gauge Pressure P = P0 + r g h P is the absolute pressure. The gauge pressure is P – P0. This is also r g h. This is what you measure in your tires. If the pressure inside equal to the atmosphere pressure, tire will be flat. Therefore, pressure inside must be higher than atmospheric pressure.

A and B PB = PA (at same depth)

0.760 m = 760 mm Another unit of pressure measurement is mmHg.

sphygmomanometer Same level as heart

Buoyancy Object floats when its density less than its surrounding fluid density and sinks when it’s higher. Dead Sea, Jordan

Have you ever tried to push a beach ball under water Have you ever tried to push a beach ball under water? This is extremely difficult to do because of the large upward force exerted by the water on the ball. The upward force exerted by a fluid on any immersed object is called a buoyant force. You need more force to push the ball beneath the water surface! And once it’s under the water, it’s hard to control it.

Consider portion of “rectangular” fluid. In equilibrium, B = Fg = Mg Question: Where is B from? Higher pressure at bottom than at the top results in upward (B) force. Replace portion of fluid with any objects results the same thing.

the direction of motion of an object submerged in a fluid is determined only by the densities of the object and the fluid.

This equation tells us that the fraction of the volume of a floating object that is below the fluid surface is equal to the ratio of the density of the object to that of the fluid.

You have an object that can float in a water on Earth. Suppose you travel to a remote planet far away from the earth. This planet has water. But g (gravitational acceleration) is less than the Earth. Will your object float in the water at (a) higher, (b) lower, (c) the same level as what is happening on Earth, or (d) sink?

Answer: Volume = 0.078 m3; Density = 1.0256 x 103 kg/m3.

Steady or Laminar flow The flow is said to be steady, or laminar, if each particle of the fluid follows a smooth path, such that the paths of different particles never cross each other. In steady flow, the velocity of fluid particles passing any point remains constant in time.

Turbulent flow Above a certain critical speed, fluid flow becomes turbulent; turbulent flow is irregular flow characterized by small whirlpool-like regions. In turbulent flow, the velocity of fluid particles passing any point changes continuously.

Compressible flow Viscous flow Rotational flow

Why the cross-section area of the water tube here is smaller than that directly beneath the faucet?

A B Which point fluid has highest (and lowest) velocity? Which point fluid has highest (and lowest) pressure? A B

V1 < V2 P1 > P2

Consider the flow of a segment of an ideal fluid through a nonuniform pipe in a time interval t.

(static fluid)

When you are in a stationary car - perhaps waiting in a left-turn lane on a fast highway - and you are passed by a car or truck traveling at high speed, you find that your car tends to be "attracted" towards the other vehicle. Why is that?

What happens to the air bubbles in the fluid in this pipe as they move from the wide diameter pipe, through the narrower region and emerge into the wider region? There are two effects to consider here. The continuity equation tells us that the rate of flow of a fluid increases (decreases) as it passes from a wider (narrower) pipe to a narrower (wider) pipe. So, the buoyant air bubbles will speed up as they pass into the narrower region then slow down again as the emerge into the wider region. The Bernoulli principle tells us that the pressure in the fluid depends on the flow rate; a faster (slower) flow rate results in a smaller (larger) pressure. So, when the bubbles move into the narrower region where the fluid is traveling faster, they experience a smaller force and so they will expand. When the bubbles emerge into the wider region, the flow rate is smaller but the pressure is greater. As a result, they are compressed back to their original size.