CE1501 CE 150 Fluid Mechanics G.A. Kallio Dept. of Mechanical Engineering, Mechatronic Engineering & Manufacturing Technology California State University, Chico

CE1502 Introduction Reading: Munson, et al., Chapter 1

CE1503 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)

CE1504 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

CE1505 Fluid Characteristics Break-up of a liquid jet:

CE1506 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

CE1507 Dimensions & Units

CE1508 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:

CE1509 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)

CE15010 Basic Fluid Properties Pressure Temperature Density Viscosity (Bulk Modulus) (Speed of Sound) Vapor Pressure Surface Tension

CE15011 Pressure Pressure (N/m 2, lb/ft 2 ): Other units: 1 pascal (Pa) = 1 N/m 2 1 kPa = 10 3 N/m 2 1 bar = 10 5 N/m 2 1 MPa = 10 6 N/m 2 1 atm = kPa = lb/in 2 (psi)

CE15012 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): p gage = p abs - p atm p vac = p atm - p abs

CE15013 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 R = ºF ºF = 1.8 ºC + 32

CE15014 Density Density (kg/m 3, slugs/ft 3 ): –pressure and temperature have strong influence on gas density, little effect on liquid density –in thermodynamics, specific volume (m 3 /kg, ft 3 /slug) is more often used than density:

CE15015 Weight Measures Specific Weight (N/m 3, lb/ft 3 ): Specific Gravity (nondimensional)

CE15016 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

CE15017 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 (  )

CE15018 Viscosity For Newtonian fluids,  = absolute viscosity (N-s/m 2 )  = shearing stress (N/m 2 ) 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)

CE15019 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 = N-s/m 2 –stoke = m 2 /s

CE15020 Viscosity

CE15021 Vapor Pressure Vapor pressure (p v ) 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 (p sat ) Vapor pressure is a function of T –H 2 O at 20  C, p v = 2.34 kPa –H 2 O at 100  C, p v = kPa (boiling) If the pressure of a liquid is reduced to the vapor pressure, vapor bubbles will form, leading to cavitation

CE15022 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

CE15023 Surface Tension Liquid droplet:

CE15024 Surface Tension Liquid in small tube: