CHAPTER 2 Fluid Mechanics FLUID MECHANICS Fluid statics

FLUID MECHANICS • Fluid statics – study of fluids at rest in equilibrium situations.

DENSITY • Important property of any material • Mass per unit volume • A

DENSITY • Two objects made of the same material have the same density even

DENSITY Densities of Some Common Substances

SPECIFIC GRAVITY • Ratio of a material’s density to the density of water at

AVERAGE DENSITY • The density of some materials varies from point to point within

EXAMPLE 1 Find the mass and weight of the air in a living room

PRESSURE IN A FLUID • Defined as the normal force per unit area at

ATMOSPHERIC PRESSURE • pa • Pressure of the earth’s atmosphere • Varies with weather

EXAMPLE 2 In the room described in Example 1, what is the total downward

PASCAL’S LAW Pressure applied to an enclosed fluid is transmitted undiminished to every portion

ABSOLUTE PRESSURE AND GAUGE PRESSURE • Gauge pressure – excess pressure above atmospheric pressure

EXAMPLE 3 A storage tank 12. 0 m deep is filled with water. The

PRESSURE GAUGES • Mercury barometer – common pressure gauge - consists of a long

BUOYANCY • Archimedes’s principle states: When a body is completely or partially immersed in

EXAMPLE 4 A 15. 0 -kg solid gold statue is being raised from a

SURFACE TENSION • The surface of a liquid behaves like a membrane under tension.

FLUID FLOW • Ideal fluid – fluid that is incompressible (density cannot change) and

FLUID FLOW • Laminar flow – adjacent layers of fluid slide smoothly past each

EXAMPLE 5 As part of a lubricating system for heavy machinery, oil of density

EXAMPLE 6 Water enters a house through a pipe with an inside diameter of

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CHAPTER 2 Fluid Mechanics

FLUID MECHANICS • Fluid statics – study of fluids at rest in equilibrium situations. • Fluid dynamics – study of fluids in motion

DENSITY • Important property of any material • Mass per unit volume • A homogeneous material has the same density throughout • SI unit: 1 kg/m 3 • CGS unit: 1 g/cm 3

DENSITY • Two objects made of the same material have the same density even though they may have different masses and different volumes

DENSITY •

DENSITY Densities of Some Common Substances

SPECIFIC GRAVITY • Ratio of a material’s density to the density of water at 4. 0°C (1000 kg/m 3) • Pure number without units

AVERAGE DENSITY • The density of some materials varies from point to point within the material. • Density of a material depends on environmental factors such as temperature and pressure.

EXAMPLE 1 Find the mass and weight of the air in a living room at 20°C with a 4. 0 m x 5. 0 m floor and a ceiling 3. 0 m high. What are the mass and weight of an equal volume of water?

PRESSURE IN A FLUID • Defined as the normal force per unit area at a point • SI unit: pascal (1 pascal = 1 Pa = N/m 2)

PRESSURE IN A FLUID •

ATMOSPHERIC PRESSURE • pa • Pressure of the earth’s atmosphere • Varies with weather changes and with elevation • 1 atmosphere (atm): normal atmospheric pressure at sea level (average value) = 101, 325 Pa

EXAMPLE 2 In the room described in Example 1, what is the total downward force on the surface of the floor due to air pressure of 1. 00 atm?

PRESSURE, DEPTH, AND PASCAL’S LAW •

PRESSURE, DEPTH, AND PASCAL’S LAW

PASCAL’S LAW Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.

ABSOLUTE PRESSURE AND GAUGE PRESSURE • Gauge pressure – excess pressure above atmospheric pressure • Absolute pressure – total pressure

EXAMPLE 3 A storage tank 12. 0 m deep is filled with water. The top of the tank is open to the air. What is the absolute pressure at the bottom of the tank? The gauge pressure?

PRESSURE GAUGES • Mercury barometer – common pressure gauge - consists of a long glass tube, closed at one end, that has been filled with mercury and then inverted in a dish of mercury.

BUOYANCY • Archimedes’s principle states: When a body is completely or partially immersed in a fluid, the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body.

EXAMPLE 4 A 15. 0 -kg solid gold statue is being raised from a sunken ship. What is the tension in the hoisting cable when the statue is (a) at rest and completely immersed; and (b) at rest and out of the water?

SURFACE TENSION • The surface of a liquid behaves like a membrane under tension. • Arises because the molecules of the liquid exert attractive forces on each other.

FLUID FLOW • Ideal fluid – fluid that is incompressible (density cannot change) and has no internal friction (viscosity) • Flow line – the path of an individual particle in a moving fluid. • Steady flow – if the overall flow pattern does not change with time. • Streamline – a curve whose tangent at any point is in the direction of the fluid velocity at that point. • Flow tube – tube formed by flow lines passing through the edge of an imaginary element of area.

FLUID FLOW • Laminar flow – adjacent layers of fluid slide smoothly past each other and the flow is steady. • Turbulent flow – no steady-state pattern; the flow pattern changes continuously.

THE CONTINUITY EQUATION •

CONTINUITY EQUATION

EXAMPLE 5 As part of a lubricating system for heavy machinery, oil of density 850 kg/m 3 is pumped through a cylindrical pipe of diameter 8. 0 cm at a rate of 9. 5 liters per second. (a) What is the speed of the oil? What is the mass flow rate? (b) If the pipe diameter is reduced to 4. 0 cm, what are the new values of the speed and volume flow rate? Assume that the oil is incompressible.

BERNOULLI’S EQUATION •

BERNOULLI’S EQUATION

EXAMPLE 6 Water enters a house through a pipe with an inside diameter of 2. 0 cm at an absolute pressure of 4. 0 x 105 Pa (about 4 atm). A 1. 0 -cm-diameter pipe leads to a second-floor bathroom 5. 0 m above. When the flow speed at the inlet pipe is 1. 5 m/s, find the flow speed, pressure, and volume flow rate in the bathroom.