nuum
• Atoms are widely spaced in the gas phase.
• Even though atoms in liquids are closely packed, there are also voids between molecules.
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• Enter the BG units of each term for the equation to have {lbf/ft2} = {lbf/ft2} + {slugs/ft3}{ft2/s2} + {slugs/ft3}{ft/s2}{ft} = {lbf/ft2} + {slugs/ft/s2} + {slugs/ft/s2} lbf/ft2 = {lbf/ft2}
SI unit
N
m2 m3 m/s m/s2 Pa = N/m2 s1
BG unit
lbf ft2 ft3 ft/s ft/s2 lbf/ft2
Conversion factor
1 N = 0.22481 lbf 1 m2 = 10.764 ft2 1 m3 = 35.315 ft3 1 ft/s = 0.3048 m/s 1 ft/s2 = 0.3048 m/s2 1 lbf/ft2 = 47.88 Pa 1 s1 = 1 s1 1 ftlbf = 1.3558 J 1 ftlbf/s = 1.3558 W = 1/550 hp 1 slugs/ft3 = 515.4 kg/m3
School of Engineering Mechanical Engineering
CHAPTER
01
© Tulong Zhu, All rights reserved.
ENGR 320 FLUID MECHANICS
Introduction
Solids and Fluids
Substance
Thus all terms have units of lbf/ft2. No conversion factors are needed.
01 - 10
Properties of Fluids
Velocity
• Velocity is the most important property for a fluid, since other properties follow directly from the velocity field. V (x, y, z, t) = i u(x, y, z, t) + j v(x, y, z, t) + k w(x, y, z, t) Other Properties
Mass {M} Length {L} Time {T} Temperature {Q}
SI unit
Kilogram (kg) Meter (m) Second (s) Kelvin (K)
BG unit
Slug Foot (ft) Second (s)
Conversion factor
1 slug = 14.5939 kg 1 ft = 0.3048 m 1s=1s
Angular velocity {T1}
Energy, heat, work {ML2T 2} Power {ML2T 3} Density {ML3} Viscosity {ML 1T 1}
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s1
ftlbf ftlbf/s slugs/ft3
J = Nm
W = J/s kg/m3 kg/(ms) m2/(s2K)
Primary Dimensions
• In fluid mechanics, there are only four primary dimensions from which all other dimensions can be derived: mass, length, time and temperature. Primary dimensions
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Example 1: Solution
(a) • Enter the dimensions of each term 1 p0 p V 2 gZ for the equation to have 2 {ML1T 2} = {ML1T 2} + {ML3}{L2T 2} + {ML3}{LT 2}{L} = {ML1T 2} ◄ (b) • Enter the SI units of each term for the equation to have {N/m2} = {N/m2} + {kg/m3}{m2/s2} + {kg/m3}{m/s2}{m} = {N/m2} + {kg/m/s2} + {kg/m/s2} Notice that {kg/m/s2} = kgm/s2/m2 =N/m2, we have {N/m2} = {N/m2} + {N/m2} + {N/m2}= {N/m2} Thus all terms have units of Pa. No conversion factors are needed. (c)
• In this course, we will view all fluids as a continuous, homogeneous matter with no voids, that is, a continuum.
• This assumption is valid as long as the size of the system is much larger than the distance between molecules.
• Density,
• Pressure, p
• Temperature, T
Most common
ˆ • Internal Energy, u
ˆ p/ • Enthalpy, h u
• Entropy, s
• Specific heat, cp and cv • Coefficient of viscosity, m
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Dimensions and Units
Dimension • A dimension is the measure by which a physical variable is expressed quantitatively. • A unit is a particular way of attaching a number to the quantitative dimension.
• Widely spaced.
• Strong cohesive forces. • Retains volume.
• Form a free surface in the presence of gravity
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• Weak cohesive forces. • Expands until it fills the entire available space • Cannot form a free surface
Problem • A useful theoretical equation for computing the relation between pressure, velocity, and altitude in a steady flow of a nearly inviscid, nearly incompressible fluid with negligible heat transfer and shaft work is the Bernoulli relation, named after Daniel Bernoulli:
slugs/(fts) 1 slugs/(fts) = 47.88 kg/(ms) ft2/(s2 °R) 1 m2/(s2K) = 5.980 ft2/(s2°R)
Specific heat {L2T 2Q1 }
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Example 1.1 (White 6th ed. Ex. 1.3)
1 p0 p V 2 gZ 2
where p0 = stagnation pressure p = pressure in motion fluid V = velocity = density Z = altitude g = gravitational acceleration (a) Show that this equation satisfies the principle of dimensional homogeneity. (b) Show that consistent units result without additional conversion factors in SI units. (c) Repeat (b) for BG units.
Advice
Notes
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Secondary Dimensions
• All secondary dimensions can be derived from these primary dimensions. Secondary dimensions
Force {MLT2} Area {L2} Volume {L3} Velocity {LT 1} Acceleration {LT2} Pressure or stress {ML 1T2}
Fluids
Solids
Fluids or
• A fluid is a substance that continually deforms (flows) under an applied shear stress. • A fluid is a substance that can not support a shear stress without being in motion.