What is referred to as the viscous stress tensor?
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T, with components T~.
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What is referred to as the viscous stress tensor?
T, with components T~.
What is the viscosity of air at 20°C?
0.0182 mPa·s.
What is the significance of reduced temperature (T) in viscosity calculations?
Reduced temperature is defined as T = T/Tc, where Tc is the critical temperature.
What are the two contributions to the force on the shaded surface in fluid dynamics?
Pressure force and viscous forces.
What property of the fluid is defined as the constant of proportionality in the force equation?
Viscosity.
What does the good agreement between predicted and measured viscosity values indicate?
It indicates the reliability of the estimation method used.
What type of flow is characterized by orderly motion, such as syrup being poured?
Laminar flow.
What happens to the fluid between two parallel plates when the lower plate is set in motion?
The fluid gains momentum and establishes a linear steady-state velocity profile.
What is the difference between laminar and turbulent flow?
Laminar flow is orderly, while turbulent flow is irregular and chaotic.
What does the stress component T_zz represent in fluid dynamics?
The force per unit area in the z direction on a plane perpendicular to the z direction.
What is the analogy used to describe momentum transport?
Momentum goes 'downhill' from high velocity to low velocity, similar to how heat flows from high to low temperature.
What are the SI units for viscosity and pressure?
Viscosity is in N/m² (Pa) and pressure is also in N/m² (Pa).
What is the viscosity of water at 1°C?
1.787 mPa·s.
What is the flow called when adjacent layers of fluid slide past one another in an orderly fashion?
Laminar flow.
What is the force exerted by fluid in the θ direction on a surface element of a solid sphere?
It is represented as - r r o l r = R ~ 2 sin 0 d 8 d 4.
What is the relationship between viscosity and temperature for liquids?
Viscosity generally decreases with increasing temperature.
What is the measured viscosity value for NZ at the specified conditions?
The measured value is 455 X 10^-6 poise.
What are the two coefficients characterizing the fluid in the generalization of Newton's Law of Viscosity?
Viscosity (p) and dilatational viscosity (K).
What is the significance of the Navier-Stokes equations?
They describe the motion of viscous fluid substances.
What does Newton's Law of Viscosity relate to?
It relates stress and velocity gradient in fluids.
What types of fluids are described by Newton's Law of Viscosity?
Newtonian fluids, which include all gases and liquids with molecular weight less than about 5000.
What does the generalization of Newton's law of viscosity address?
It addresses arbitrary flow patterns.
What is the relationship between shear viscosity and the term 'dynamic viscosity'?
The term 'dynamic viscosity' has a specific meaning in viscoelasticity and is inappropriate for p.
What is assumed about the velocity profile vx(y) in the context of viscosity?
It is essentially linear for a distance of several mean free paths.
What are the viscosity coefficients denoted by in the equations?
The quantities pijkl.
What is the primary mechanism of momentum transport in gases?
Transport occurs by molecules in free flight between collisions.
What is the principle of corresponding states used for?
Correlating equation-of-state and thermodynamic data.
Who were the authors of the influential books on thermodynamics and kinetics?
Olaf Andreas Hougen, K. M. Watson, and R. A. Ragatz.
What is the sign convention in Eqs. 1.1-2 and 1.2-6?
It is arbitrary, and either sign convention can be used as long as the physical meaning is understood.
When is the concept of mean free path meaningful?
When A is large compared to the range of intermolecular forces.
What is the significance of the equation 1.1-2 in the context of viscosity?
It defines viscosity in terms of a simple steady-state shearing flow.
What is the molecular momentum flux tensor?
It consists of components associated with molecular motions in the fluid.
What is the advantage of the sign convention used in this book for the stress tensor?
It is consistent with Newton's law of viscosity, Fourier's law of heat conduction, and Fick's law of diffusion.
What is reduced viscosity represented as in the context of momentum transport?
It is represented as pr = p/p.
How is the frequency of molecular bombardment on a stationary surface defined?
It is defined as R, the frequency per unit area on one side of the surface exposed to the gas.
How is momentum transport predominantly achieved in liquids?
Through intermolecular forces experienced by pairs of molecules.
What notation is used to express the generalization of Newton's Law of Viscosity?
Vector-tensor notation.
Who are the key figures associated with the relations for stresses in a Newtonian fluid?
Navier, Poisson, and Stokes.
What is the purpose of Figure 1.3-1 in the context of viscosity?
It can be used for rough estimation of viscosities of mixtures.
What is the relationship between the scalar constant A and viscosity?
A must be the same as the negative of the viscosity p.
What is the low-density limit for the viscosity of a gas?
It approaches a limit as pressure becomes smaller, nearly attained at 1 atm pressure.
What are non-Newtonian fluids?
Fluids such as polymeric liquids, suspensions, pastes, and slurries that are not described by Newton's Law.
What does the equation for the net flux of x-momentum resemble?
It has the same form as Newton's law of viscosity.
What is convective momentum transport proportional to?
Fluid density.
What is the average distance between molecules in a low-density gas?
It is many times their diameter.
What is an example of a situation where normal stresses are not zero?
Flow in a converging duct.
What is the primary physical property that characterizes the resistance to flow in fluids?
Viscosity.
What are pseudocritical properties used for in viscosity estimation?
They are used for estimating viscosities of mixtures in N-component fluids.
How does the pressure force act on the exposed surface of a fluid?
It is always perpendicular to the exposed surface.
What is the steady-state momentum flux T when the lower plate velocity is 1 ft/s?
Calculated using viscosity converted to British units.
How many stress components are considered in the generalization of Newton's law of viscosity?
Nine stress components.
What is the significance of the Kronecker delta in the molecular stress definition?
It is 1 if indices are equal and 0 if they are not, helping to define normal and shear stresses.
What is the significance of the equation presented in the text?
It describes the relationship between shearing force and velocity gradient in fluids.
What assumption is made about molecular velocities in the context of viscosity?
All molecular velocities are calculated relative to the average velocity in the region of the last collision.
What is the relationship between the molecular stresses and the forces acting on a unit area?
Molecular stresses are defined as the sum of pressure and viscous stresses acting on a unit area.
What does the kinetic theory of gases predict about viscosity?
It predicts a relation similar to Newton's Law of Viscosity, but additional higher-order terms are expected.
What is the force exerted by fluid in the +θ direction on a surface element in cylindrical coordinates?
It is represented as - ~ ~ o ( ~ = R R d e d z).
How can critical pressure (pc) be calculated?
It can be calculated from p = p/pY or estimated from empirical relations if critical p-V-T data are available.
How does viscosity change with temperature?
Viscosity is a function of temperature.
How does the viscosity of a gas behave at low density with increasing temperature?
It increases with increasing temperature.
What does mPa·s stand for?
Millipascal-second, a unit of dynamic viscosity.
What is the conversion factor used to convert viscosity from cp to lbf s/ft²?
2.0886.
What is the plate separation in the given problem?
0.001 ft.
How is the flux of x-momentum calculated?
By summing the x-momenta of molecules crossing in the positive y direction and subtracting those crossing in the opposite direction.
How can the viscosities of gases be calculated?
From the kinetic theory of gases.
What is the relationship between viscosity (μ) and mean free path (A)?
Viscosity is expressed as μ = nmiiA = ipiiA.
What is the focus of the Molecular Theory of Viscosity of Gases at Low Density?
It examines molecular momentum transport in gases composed of rigid, nonattracting spherical molecules.
What is the significance of the Boltzmann constant in the context of molecular velocities?
It is used to determine the average magnitude of molecular velocities in a gas.
What is the viscosity of glycerol at 25°C?
1.412 mPa·s.
How is the force related to area, velocity, and distance between the plates?
The force is proportional to the area and velocity, and inversely proportional to the distance between the plates.
What is the viscosity of the fluid given in the problem?
0.7 cp.
What does the generalization of Newton's law of viscosity aim to address?
More complicated flows where velocity components depend on all three coordinates and possibly on time.
When do viscous forces come into play in a fluid?
Only when there are velocity gradients within the fluid.
What is the relationship between critical viscosities and empirical methods?
Critical viscosities can be computed using empirical methods as indicated in Appendix E.
What is the significance of the dilational viscosity in fluid dynamics?
It describes sound absorption in polyatomic gases and the dynamics of liquids containing gas bubbles.
What are shear stresses in fluid dynamics?
Stresses that act parallel to the surface.
What is the abbreviation for centipoise?
cp.
How does viscosity typically change with increasing temperature for liquids?
Viscosity usually decreases with increasing temperature.
What is required to maintain the motion of the lower plate in steady flow?
A constant force (F).
What is the estimated viscosity of NZ at 50°C and 854 atm using the given parameters?
The predicted viscosity is 452 X 10^-6 poise.
What is the primary focus of Chapter 1 in the context of fluid dynamics?
Viscosity and the mechanisms of momentum transport.
What is the significance of Newton's law of viscosity?
It describes molecular momentum transport in fluids.
How does the viscosity of a liquid behave with increasing temperature?
It decreases with increasing temperature.
What is a reduced quantity in the context of viscosity?
A dimensionless quantity obtained by dividing by the corresponding quantity at the critical point.
What does the velocity gradient dvx/dy represent in gas flow?
The change in velocity of the gas as it flows parallel to the m-plane.
What can be used to estimate critical viscosity when experimental values are unavailable?
Known viscosity at a given reduced pressure and temperature.
What is depicted in Fig. 1.2-1 regarding fluid mechanics?
Pressure and viscous forces acting on planes in the fluid perpendicular to the three coordinate systems.
What is kinematic viscosity?
The ratio of viscosity to the density of the fluid.
What is the viscosity of air at 20°C?
1.8 x 10^-5 Pa·s.
What is the kinematic viscosity of water at 1°C?
0.01787 cm²/s.
What must be true for viscous stresses in a state of pure rotation?
No viscous forces are present.
What happens to the normal-stress component Tzz in a converging duct?
It is nonzero and is given by Tzz = -2p (dv/dz).
What does the scalar constant B represent in the context of viscosity?
B is set equal to $p - K, where K is the dilatational viscosity.
What do the terms paij and T~~ have in common in the equations?
They have the same sign affixed.
What is the mean free path (A) in molecular transport?
The average distance traveled by a molecule between successive collisions.
Who is considered the founder of classical mechanics?
Sir Isaac Newton.
What does the symbol T represent in the context of fluid mechanics?
The force in the x direction on a unit area perpendicular to the y direction.
What is the challenge associated with generalizing Newton's law of viscosity?
It took mathematicians about a century and a half to develop the generalization.
How can momentum be interpreted in the context of Newton's Law of Viscosity?
As the flux of x-momentum transmitted through the fluid in the positive y direction.
Who received the Nobel Prize in 1962 for work related to fluid dynamics?
Lev Davydovich Landau.
Where can one find comprehensive experimental techniques for measuring transport properties?
In the book 'Measurement of the Transport Properties of Fluids' by Wakeham, Nagashima, and Sengers.
What is the SI unit for viscosity?
Pascal-second (Pa·s), which is equivalent to N·s/m².
What is the relationship between temperature and viscosity for gases at low density?
Viscosity increases with increasing temperature.
What is the force exerted by fluid in the z direction on a surface element in cylindrical coordinates?
It is represented as +To2 1 o = ( , / z I - , dr dz / I Y a k ' I.
What happens to the number of viscosity coefficients if the fluid is isotropic?
It reduces from 81 to 2.
What is the force exerted by fluid in the r direction on a surface element of a solid cone?
It is represented as - r o r ( o = a r sin ru d r d 4).
What is the significance of the values in Table 1.1-2?
They summarize the viscosities of water and air at 1 atm pressure.
What does the equation stating that shearing force per unit area is proportional to the negative of the velocity gradient represent?
Newton's law of viscosity.
Under what assumption is the dilatational viscosity (K) often considered zero for gases?
When assuming the fluid acts as an ideal monoatomic gas.
What happens to the term containing K for incompressible liquids?
It is discarded because (V . v) = 0.
What are normal stresses in fluid dynamics?
Stresses that act perpendicular to the surface.
What does the general flow pattern in the generalization of viscosity involve?
Fluid velocity may vary in different directions and depend on time.
What is discussed in relation to the viscosity of suspensions and emulsions?
The unique characteristics and behaviors of these mixtures.
