CE150 1

CE 150Fluid Mechanics

G.A. Kallio

Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology

California State University, Chico

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Introduction

Reading: Munson, et al., Chapter 1

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Fluid Mechanics

• Fluid mechanics is the study of fluids at rest (fluid statics) and in motion (fluid dynamics)

• Applications– fluid forces on structures (CE)

– open-channel flow (CE)

– water treatment (CE)

– piping systems (CE, ME)

– porous flow (CE, ME)

– air pollution control (CE, ME)

– aerodynamics (ME)

– turbomachines (ME)

– rocket propulsion/supersonic flight (ME)

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Fluid Characteristics

• Solids– molecules are very dense

– not easily deformed or compressed

• Liquids– molecules are moderately dense

– easily deformed but not compressed

• Gases– molecules are relatively sparse

– easily deformed and compressed

• Fluids include liquids and gases– substance that deforms continuously

when subjected to any shearing force

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Fluid Characteristics

Break-up of a liquid jet:

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Dimensions & Units

• Primary dimensions: length (L), time (T), mass (M), and temperature ()

• Secondary dimensions: velocity (LT-1), acceleration (LT-2), force (MLT-2), etc.

• Textbook uses the International System (SI) and British Gravitational (BG) System of units

• The English Engineering (EE) System (e.g., lbm, lbf) is still used but not emphasized here

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Dimensions & Units

Dimension SI BGmass kg sluglength m fttime s stemperature(absolute)

K R

force N(= 1 kg-m/s2)

lb(= 1 slug-ft/s2)

energy J(= 1 N-m)

Btu(= 778.169 lb-ft)

power W(= 1 J/s)

hp(= 0.7068Btu/s)

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Dimensions & Units

• All theoretically-derived equations are dimensionally homogeneous - i.e., dimensions of LHS = dimensions of RHS:

• Empirical equations are often not dimensionally homogeneous - i.e., they contain numerical constants that have dimensions and must be used with a specific system of units:

2 , mcEmaF

2127.0 VF

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Fluid Mechanics Problem Solving

• Required format for HW problems:

– Given (brief)

– Find (list items)

– Sketch (if applicable)

– Assumptions (list those not included in the problem statement)

– Analysis (show eqns. in symbolic form, then plug in values; box or highlight your answer; always include units)

– Comments (if requested)

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Basic Fluid Properties

• Pressure• Temperature• Density• Viscosity• (Bulk Modulus)• (Speed of Sound)• Vapor Pressure• Surface Tension

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Pressure

• Pressure (N/m2, lb/ft2):

• Other units:

1 pascal (Pa) = 1 N/m2

1 kPa = 103 N/m2

1 bar = 105 N/m2

1 MPa = 106 N/m2

1 atm = 101.325 kPa

= 14.696 lb/in2 (psi)

A

Fp normal

A smalllim

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Pressure

• Absolute pressure - total pressure experienced by a fluid

• Gage pressure or vacuum pressure- difference between absolute pressure and atmospheric pressure (usually indicated by a measuring device):

pgage = pabs - patm

pvac = patm - pabs

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Temperature

• Temperature (ºC or K, ºF or R)– measure of a body’s “hotness” or

“coldness”

– indicative of a body’s internal energy

– more description in ME152, Thermodynamics

unit conversions:

K = ºC + 273.15

R = ºF + 459.67

ºF = 1.8 ºC + 32

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Density

• Density (kg/m3, slugs/ft3):

– pressure and temperature have strong influence on gas density, little effect on liquid density

– in thermodynamics, specific volume (m3/kg , ft3/slug) is more often used than density:

V

m

1

m

Vv

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Weight Measures

• Specific Weight (N/m3, lb/ft3):

• Specific Gravity (nondimensional)

CO@4H2

SG

g

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Ideal Gas Law

• An ideal gas is a superheated vapor that is at a relatively low p or high T (i.e., not approaching condensation or liquefaction)

• Ideal gases obey the following equation of state, known as the ideal gas law:

– where: R = gas constant (Table 1.7, 1.8)

p = absolute pressure

T = absolute temperature

RTpvRTp or

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Viscosity

• Fluids “stick” to solid boundaries, i.e., fluid velocity is equal to the solid velocity; this is called the no-slip condition

• In Figure 1.3, a fluid velocity gradient (du/dy) exists, accompanied by a shearing stress ()

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Viscosity

• For Newtonian fluids,

= absolute viscosity (N-s/m2)

= shearing stress (N/m2)

du/dy = rate of shearing strain, or velocity gradient (1/s)

– Most common liquids and all gases are Newtonian; non-Newtonian fluids are divided into shear-thinning fluids (e.g., latex paint) and shear-thickening fluids (e.g., sand-water mixture)

dy

du

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Viscosity

• Viscosity is relatively insensitive to pressure, but can be very sensitive to temperature (see Figure 1.6 and eqns. 1.10, 1.11)

• Kinematic viscosity is the ratio of absolute viscosity to density:

• Other units:– poise = 10-1 N-s/m2

– stoke = 10-4 m2/s

)/(m / 2 s

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Viscosity

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Vapor Pressure

• Vapor pressure (pv) is the pressure that a vapor phase exerts on the liquid phase at equilibrium

• In thermodynamics, the vapor pressure at equilibrium is known as the saturation pressure (psat)

• Vapor pressure is a function of T– H2O at 20 C, pv = 2.34 kPa– H2O at 100C, pv = 101.3 kPa (boiling)

• If the pressure of a liquid is reduced to the vapor pressure, vapor bubbles will form, leading to cavitation

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Surface Tension

• Surface tension () is a force per unit length (N/m) that develops at a liquid-gas or liquid-liquid interface

• The tension is due to an imbalance of molecular forces at the liquid surface

• Surface tension is important at liquid surfaces with small radii of curvature:– liquid droplets and gas bubbles

– liquids in small tubes

– liquid jets or sprays

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Surface Tension

• Liquid droplet:

Rpp ei

2

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Surface Tension

• Liquid in small tube:

gRh

cos2