CHAPTER 14
... Air is flowing over a long flat plate with a specified velocity. The distance from the leading edge of the plate where the flow becomes turbulent, and the thickness of the boundary layer at that location are to be determined. Assumptions 1 The flow is steady and incompressible. 2 The critical Reynol ...
... Air is flowing over a long flat plate with a specified velocity. The distance from the leading edge of the plate where the flow becomes turbulent, and the thickness of the boundary layer at that location are to be determined. Assumptions 1 The flow is steady and incompressible. 2 The critical Reynol ...
Three-dimensional traveling-wave solutions in
... In order to understand transition mechanisms from laminar state to turbulence for the simplest form of shear motion, plane Couette flow has been studied a great deal both theoretically @1–3# and experimentally @4–9# in the last few years. In experiments, turbulent spots are triggered by injecting a ...
... In order to understand transition mechanisms from laminar state to turbulence for the simplest form of shear motion, plane Couette flow has been studied a great deal both theoretically @1–3# and experimentally @4–9# in the last few years. In experiments, turbulent spots are triggered by injecting a ...
LECTURE 2: Stress Conditions at a Fluid-fluid Interface
... n · T: stress (force/area) exerted by + on - (will generally have both normal and tangential components) n · T̂: stress (force/area) exerted by - on + (will generally have both normal and tangential components) σn (∇ · n): normal curvature force per unit area associated with local curvature of inter ...
... n · T: stress (force/area) exerted by + on - (will generally have both normal and tangential components) n · T̂: stress (force/area) exerted by - on + (will generally have both normal and tangential components) σn (∇ · n): normal curvature force per unit area associated with local curvature of inter ...
Transport Phenomena
... That is, the functional dependence of v and P must, in general, include all the dimensionless variables and the one dimensionless group appearing in the differential equations. No additional dimensionless groups enter via the preceding boundary conditions. As a consequence, ∂vz/∂r must likewise depe ...
... That is, the functional dependence of v and P must, in general, include all the dimensionless variables and the one dimensionless group appearing in the differential equations. No additional dimensionless groups enter via the preceding boundary conditions. As a consequence, ∂vz/∂r must likewise depe ...
Lectures on Oscillations and Waves
... smooth horizontal surface, connected to an inline horizontal spring, having spring constant k, the other end of the string being attached to a wall. The spring exerts a restoring force equal to – kx on the mass when it is a distance x from the equilibrium point. By “equilibrium point” we mean the po ...
... smooth horizontal surface, connected to an inline horizontal spring, having spring constant k, the other end of the string being attached to a wall. The spring exerts a restoring force equal to – kx on the mass when it is a distance x from the equilibrium point. By “equilibrium point” we mean the po ...
Fluid Flow - Binus Repository
... The bottom plate is stationary (zero velocity) so that eventually the velocity gradient will vary from zero at the bottom to Uterm at the top which is equal to the terminal velocity of the upper plate. The velocity gradient (change in velocity between plates; du/dy) will vary linearly from zero at ...
... The bottom plate is stationary (zero velocity) so that eventually the velocity gradient will vary from zero at the bottom to Uterm at the top which is equal to the terminal velocity of the upper plate. The velocity gradient (change in velocity between plates; du/dy) will vary linearly from zero at ...
Turbulence When the Reynolds number becomes sufficiently large
... The final conclusion is that mean velocity of a turbulent flow approximately satisfies the same equation as laminar flow, but the effective (eddy) is much larger than its molecular value. When the mean velocity is zero, the momentum equation reduces to the diffusion equation with enhanced diffusivit ...
... The final conclusion is that mean velocity of a turbulent flow approximately satisfies the same equation as laminar flow, but the effective (eddy) is much larger than its molecular value. When the mean velocity is zero, the momentum equation reduces to the diffusion equation with enhanced diffusivit ...
AT Physics II. Air Resistance The motion of
... where L is a characteristic length for the object moving through a fluid (say the radius or the diameter of a sphere), v its speed, ρ the density of the liquid and η its viscosity. Generally, high Reynolds number (anything much bigger than 1) means that viscosity is negligible; low Reynolds number ( ...
... where L is a characteristic length for the object moving through a fluid (say the radius or the diameter of a sphere), v its speed, ρ the density of the liquid and η its viscosity. Generally, high Reynolds number (anything much bigger than 1) means that viscosity is negligible; low Reynolds number ( ...
Statistics --
... As we found out in Chapter 5, even though the Lagrangian framework is the most direct way to apply Newton’s laws, it is usually computationally cumbersome in most circumstances as a method of describing the overall flow field in a given domain. An alternative approach is to utilize the Eulerian fram ...
... As we found out in Chapter 5, even though the Lagrangian framework is the most direct way to apply Newton’s laws, it is usually computationally cumbersome in most circumstances as a method of describing the overall flow field in a given domain. An alternative approach is to utilize the Eulerian fram ...
Introduction to the immersed boundary method
... may be observed. In order to overcome this drawback, Wu and Shu [12] introduced an implicit IBM for rigid walls in which the forcing term is treated as an unknown. The question is: How to choose the IBM force in such a way that the velocity of the object nodes is exactly the desired velocity? This m ...
... may be observed. In order to overcome this drawback, Wu and Shu [12] introduced an implicit IBM for rigid walls in which the forcing term is treated as an unknown. The question is: How to choose the IBM force in such a way that the velocity of the object nodes is exactly the desired velocity? This m ...
Fluid Dynamics
... He following terms describe the states which are used to classify fluid flow: uniform flow: If the flow velocity is the same magnitude and direction at every point in the fluid it is said to be uniform. non-uniform: If at a given instant, the velocity is not the same at every point the flow is n ...
... He following terms describe the states which are used to classify fluid flow: uniform flow: If the flow velocity is the same magnitude and direction at every point in the fluid it is said to be uniform. non-uniform: If at a given instant, the velocity is not the same at every point the flow is n ...
Three-dimensional numerical analysis to predict behavior of driftage carried by tsunami
... fluid density ρ is 1.0 × 103 kg/m3 , kinematic viscosity ν is 1.0 × 10−6 m2 /s, density of the driftage ρd is 0.5 × 103 kg/m3 , and the reflection coefficient between the driftage and vertical wall e is 0.5. For computational purposes, the cylindrical driftage was modeled as an octagonal pillar with ...
... fluid density ρ is 1.0 × 103 kg/m3 , kinematic viscosity ν is 1.0 × 10−6 m2 /s, density of the driftage ρd is 0.5 × 103 kg/m3 , and the reflection coefficient between the driftage and vertical wall e is 0.5. For computational purposes, the cylindrical driftage was modeled as an octagonal pillar with ...
The Material Derivative The equations above apply to a fluid
... • (i) Ω×(Ω × r) = 12 ∇ (Ω × r)2 is the centripetal acceleration and can be combined with the gravitational potential to form the geo-potential ...
... • (i) Ω×(Ω × r) = 12 ∇ (Ω × r)2 is the centripetal acceleration and can be combined with the gravitational potential to form the geo-potential ...
The harmonic hydro-mechanical movement of the
... In the vibratory movement of a solid body, the concept of acoustic particle is diluted, provided that the stimulus frequency is such that the solid is moved as a whole [6]. If the value of the stimulus frequency is too high, a wave could be introduced in the system. In the H.H.M. the acoustic partic ...
... In the vibratory movement of a solid body, the concept of acoustic particle is diluted, provided that the stimulus frequency is such that the solid is moved as a whole [6]. If the value of the stimulus frequency is too high, a wave could be introduced in the system. In the H.H.M. the acoustic partic ...
McIntyre, M.E., 2102. Potential Vorticity. From the
... Note to editors: Crucial new terms are flagged up using the macro \newterm{...} in the LATEX source, defined here to print as italic. Possible cross-references to other articles are flagged \crossref{...}. For visibility, \crossref{...} is temporarily defined to print as sans-serif. Therefore, sans- ...
... Note to editors: Crucial new terms are flagged up using the macro \newterm{...} in the LATEX source, defined here to print as italic. Possible cross-references to other articles are flagged \crossref{...}. For visibility, \crossref{...} is temporarily defined to print as sans-serif. Therefore, sans- ...
Lecture Notes
... deform under the action of an external force. Specifically, a fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude. This shearing stress (force/unit area) is created whenever a tangential force acts on a surface. When metals such as steel are ...
... deform under the action of an external force. Specifically, a fluid is defined as a substance that deforms continuously when acted on by a shearing stress of any magnitude. This shearing stress (force/unit area) is created whenever a tangential force acts on a surface. When metals such as steel are ...
Continuous and Episodic Fluid Flow in Regional Metamorphism
... Continuous and Episodic Fluid Flow in Regional Metamorphism The overall pattern of fluid behaviour in regional metamorphism is controlled by large scale factors such as rate of heat input/loss, rock rheology and original lithological mix, and so cannot be considered to be independently variable, but ...
... Continuous and Episodic Fluid Flow in Regional Metamorphism The overall pattern of fluid behaviour in regional metamorphism is controlled by large scale factors such as rate of heat input/loss, rock rheology and original lithological mix, and so cannot be considered to be independently variable, but ...
Hydrostatics and Bernoulli`s Principle Slide Notes
... 4. Couple of terms and common assumptions needed for fluid analysis as opposed to solid body analysis: a. Fluid – A substance in the liquid or gas phase b. Steady – No change at a point in time i. This is important because it defines a state of consistency that allows for basic calculations und ...
... 4. Couple of terms and common assumptions needed for fluid analysis as opposed to solid body analysis: a. Fluid – A substance in the liquid or gas phase b. Steady – No change at a point in time i. This is important because it defines a state of consistency that allows for basic calculations und ...
Ch 14 Solutions Glencoe 2013
... left panel in Figure 16 with a piece of paper. The edge of the paper should be at point N, the node. Now, concentrate on the resultant wave, shown in darker blue. Note that it acts as a wave reflected from a boundary. Is the boundary a rigid wall? Repeat this exercise for the right panel in Figure 1 ...
... left panel in Figure 16 with a piece of paper. The edge of the paper should be at point N, the node. Now, concentrate on the resultant wave, shown in darker blue. Note that it acts as a wave reflected from a boundary. Is the boundary a rigid wall? Repeat this exercise for the right panel in Figure 1 ...
Stokes wave
In fluid dynamics, a Stokes wave is a non-linear and periodic surface wave on an inviscid fluid layer of constant mean depth.This type of modelling has its origins in the mid 19th century when Sir George Stokes – using a perturbation series approach, now known as the Stokes expansion – obtained approximate solutions for non-linear wave motion.Stokes' wave theory is of direct practical use for waves on intermediate and deep water. It is used in the design of coastal and offshore structures, in order to determine the wave kinematics (free surface elevation and flow velocities). The wave kinematics are subsequently needed in the design process to determine the wave loads on a structure. For long waves (as compared to depth) – and using only a few terms in the Stokes expansion – its applicability is limited to waves of small amplitude. In such shallow water, a cnoidal wave theory often provides better periodic-wave approximations.While, in the strict sense, Stokes wave refers to progressive periodic waves of permanent form, the term is also used in connection with standing waves and even for random waves.