End of term2
At what Reynolds number (Re) does the transition from laminar to turbulent flow occur?
Re = 2300
What equations were used for the derivation of Poiseuille's resistance law?
Navier-Stokes equations
When is Poiseuille's law violated according to experience?
At high Reynolds numbers (Re)
What happens in turbulent flow conditions when Reynolds number (Re) exceeds 2300?
Different resistance laws come into play
When did the problem of turbulence emerge?
19th century
What did the theoretical law (Poiseuille) predict in terms of resistance?
Resistance proportional to the first power of velocity
What method is used to observe continuous mixing of fluid masses in turbulent flow?
Lagrangian method
What is inherently unsteady in nature in turbulent motion?
All of the above
What remains constant in turbulent motion despite apparent disorder in velocity changes?
The average value of velocity over time
What are time-averaged values of velocities or stresses commonly referred to as?
Averaged values
What is the term for the difference between the true velocity at a point and the time-averaged velocity?
Pulsational velocity
What term is used for the velocities measured at a certain point using conventional instruments, practically
not detecting pulsations?
Mean velocities
According to Reynolds, what did the idealization of fluid motion lead to?
Open system of equations
What is one of the seven Millennium Prize Problems related to in fluid dynamics?
Poincaré conjecture
What is the term for turbulence theories that are derived from experiments?
Empirical theories
What layer near the wall is assumed to exist in turbulent flow in a round-section pipe?
Laminar sublayer
How is turbulent flow in the pipe schematically represented according to the two-layer model?
Turbulent core and laminar sublayer
What phenomenon is considered impossible near the wall in turbulent flow, leading to the assumption of a
laminar sublayer?
Mixing
How many components does the two-layer model of turbulent flow consist of?
Two
What is the first component of the two-layer model of turbulent flow?
Turbulent core
What is the second component of the two-layer model of turbulent flow?
Laminar sublayer
What does Reynolds propose not to consider when looking at time-averaged idealized behavior?
Pulsations
What does Reynolds replace the actual velocity and pressure variables within the time-averaged NavierStokes equations?
Time-averaged velocities and pressures
What does the solution of the time-averaged Navier-Stokes equations represent?
Steady-state conditions
What arises due to the idealization of fluid motion, leading to the need to relate pulsations to timeaveraged quantities?
Chaos in fluid motion
What is the term for theories of turbulence that rely on new hypotheses about the mechanism of fluid
motion?
Semi-empirical theories
Which hypothesis among McCavrey, Prandtl, Karman, Taylor, Friedman, and others closes the system of
equations?
Friedman's hypothesis
How many partial differential equations does Friedman's hypothesis reduce the system to?
Twenty
What is considered impossible near the wall in turbulent flow in a round-section pipe?
Mixing
What is the term for the laminar layer near the wall in turbulent flow, as assumed in the two-layer model?
Laminar sublayer