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CE 150 Fluid Mechanics

- G.A. Kallio
- Dept. of Mechanical Engineering, Mechatronic

Engineering Manufacturing Technology - California State University, Chico

Introduction

- Reading Munson, et al., Chapter 1

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)

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

Fluid Characteristics

Break-up of a liquid jet

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

Dimensions Units

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

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)

Basic Fluid Properties

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

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)

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

Temperature

- Temperature (ºC or K, ºF or R)
- measure of a bodys hotness or coldness
- indicative of a bodys internal energy
- more description in ME152, Thermodynamics
- unit conversions
- K ºC 273.15
- R ºF 459.67
- ºF 1.8 ºC 32

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

Weight Measures

- Specific Weight (N/m3, lb/ft3)
- Specific Gravity (nondimensional)

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

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 (?)

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)

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

Viscosity

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 100?C, pv 101.3 kPa (boiling)
- If the pressure of a liquid is reduced to the

vapor pressure, vapor bubbles will form, leading

to cavitation

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

Surface Tension

- Liquid droplet

Surface Tension

- Liquid in small tube