Real Fluids Flashcards
What is the difference between ideal and real fluids?
Ideal Fluid: No shear stress, only normal stress, slip at boundaries.
Real Fluid: Supports both shear and normal stresses, no slip at boundaries.
How do solids respond to stress?
Solids: Support all stress components (tension, compression, shear) in static equilibrium.
How do fluids respond to stress?
Fluids: Do not support tension, compression is supported, shear stress leads to continuous deformation (flow)
What is the mass continuity equation for fluids?
The mass conservation equation ensures that mass is conserved in any fluid element
∂ρ/∂t +∇⋅(ρv)= 0
What is the difference between unsteady and convective acceleration in fluid flow?
Unsteady acceleration: Change in velocity with respect to time at a point.
Convective acceleration: Change in velocity due to spatial variations as fluid moves through different areas.
What is the significance of viscosity in real fluids?
Viscosity describes a fluid’s resistance to shear and its dependence on the velocity gradient. For Newtonian fluids, viscosity is constant regardless of the rate of shear
What does it mean a fluid is incompressible?
Cannot squeeze more/less fluid into our element
What factors affect viscosity in real fluids?
Temperature: Viscosity decreases with increasing temperature for most fluids.
Pressure: For incompressible fluids like water, pressure has little effect on viscosity
How are stress components related to fluid motion in real fluids?
Stress in real fluids is related to the rate of strain. Shear stresses act on fluid particles and vary based on the velocity gradients within the fluid. Linear relationship
What is pressure per unit volume?
∂P/∂x,y,z
How is fluid driven through an area?
From high to low pressure
What is pressure per unit mass?
1/ρ*∂p/∂x,y,z
What is a body force?
All external forces -> f_x,y,z or g_x,y,z
What does Euler’s equations describe?
The dynamics of an inviscid and incompressible flow. Viscosity not included
How is kinematic viscosity related to dynamic viscosity?
v = mu/rho
What is the level of molecular activity dependent on?
- Pressure
- Temp
- Chemical composition
How is Euler equation related to Navier-Stokes equation?
For inviscid flows the NSE is reduced to the EE as mu = 0
Where can NSE be applied?
Turbulent and laminar
What assumptions are made in the NSE?
- Steady flow
- Flow fully developed
- Two large plates
- No flow in z direction
- Mass continuity
- Impermeable plates
- v = 0
What happens to the maximum velocity when mu is large?
Decreases
What happens to the maximum velocity when B is large?
Increases
How do larger gradients and slope affect max velocity?
Increase
What happens to a dye streak in a pipe at low velocities according to Reynolds’ experiment?
The dye streak remains a thin, straight line — indicating laminar flow.
The Reynolds number (Re) is the ratio of ______ forces to ______ forces.
Inertial forces to viscous forces.
What is the critical Reynolds number for laminar to turbulent transition in a pipe?
Approximately 2300
Which geometry has a critical Reynolds number of around 1?
(A) Pipe
(B) Channel
(C) Flat Plate
(D) Sphere
(D) Sphere
State two key characteristics of laminar flow.
- Flow in smooth, parallel layers (no mixing between layers).
- No velocity component transverse to streamlines.
At low Reynolds numbers, the drag force on a sphere moving through a fluid is given by ______ law.
Stokes’ Law
Formula for Stokes’ Law?
F_S =3πμDu
In a viscosity measurement using a sinking sphere, what must be true for the flow around the sphere?
The flow must be laminar (Re < 0.5)
What major change happens in turbulent flow compared to laminar flow?
Random fluctuations are superimposed on the mean flow, dramatically increasing apparent viscosity.
What is meant by the “apparent viscosity” in turbulent flows?
The effect of turbulent mixing mimics an increase in the fluid’s viscosity.
In Reynolds decomposition, the velocity u(t) is split into a mean part and a ______.
Fluctuation
After averaging turbulent flow equations, additional terms appear, representing the effects of ______.
Turbulent fluctuations
In the averaged Navier-Stokes equations, what extra stresses appear due to turbulence?
(A) Viscous stresses
(B) Reynolds stresses
(C) Gravitational stresses
(D) Elastic stresses
(B) Reynolds stresses
True or False:
Reynolds stresses act like an additional stress term in the fluid due to the presence of fluctuations.
True
Name two approaches commonly used to model turbulent flows.
- Eddy viscosity models (e.g., Boussinesq approximation)
- Reynolds stress models
What does the eddy viscosity concept assume about Reynolds stresses?
That they behave like an apparent increased viscosity acting on the mean flow.
