ce1501 ce 150 fluid mechanics g.a. kallio dept. of mechanical engineering, mechatronic engineering...
Post on 20-Dec-2015
215 views
TRANSCRIPT
CE150 1
CE 150Fluid Mechanics
G.A. Kallio
Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology
California State University, Chico
CE150 2
Introduction
Reading: Munson, et al., Chapter 1
CE150 3
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)
CE150 4
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
CE150 5
Fluid Characteristics
Break-up of a liquid jet:
CE150 6
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
CE150 7
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)
CE150 8
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
CE150 9
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)
CE150 10
Basic Fluid Properties
• Pressure• Temperature• Density• Viscosity• (Bulk Modulus)• (Speed of Sound)• Vapor Pressure• Surface Tension
CE150 11
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
CE150 12
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
CE150 13
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
CE150 14
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
CE150 15
Weight Measures
• Specific Weight (N/m3, lb/ft3):
• Specific Gravity (nondimensional)
CO@4H2
SG
g
CE150 16
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
CE150 17
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 ()
CE150 18
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
CE150 19
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
CE150 20
Viscosity
CE150 21
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
CE150 22
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
CE150 23
Surface Tension
• Liquid droplet:
Rpp ei
2
CE150 24
Surface Tension
• Liquid in small tube:
gRh
cos2