MOTION OF PARTICLES IN FLUID Flashcards
What is needed for a particle to move in a fluid?
Density difference between the particle and the fluid
If densities are equal, the buoyant force counterbalances the external force.
What are the three forces acting on a rigid particle moving in a fluid?
- Buoyant force (Fb) acting upward
- Resistance or drag force (FD) acting in the direction of particle motion
- Gravity (Fg) acting downward
What is the equation for buoyant force (Fb)?
Fb = Vp * ρ * g
Where V_p is the volume of the particle, ρ is the fluid density, and g is gravitational acceleration.
What is the equation for gravitational force (Fg)?
Fg = m * g
Where m is the mass of the particle.
What is the equation for drag force (FD)?
FD = CD * ρ * A * v^2 / 2
Where C_D is the drag coefficient, ρ is the fluid density, A is the projected area, and v is the velocity.
What is the general equation for the resultant force acting on a body under free-falling conditions?
Acceleration Force = Gravity force - Buoyancy Force - Drag Force
What are the two periods of falling for a particle released from rest?
- Period of accelerated falling
- Period of constant-velocity fall (terminal velocity)
What is terminal velocity (vt)?
The maximum settling velocity of a particle falling through a fluid.
What is the equation for terminal velocity derived from buoyant and drag forces?
vt = (2 * (ρp - ρ) * m * g) / (CD * ρ * A)
Where ρ_p is the particle density and ρ is the fluid density.
What is the relationship between Reynolds number (Re) and drag coefficient (C_D) for laminar flow?
CD = 24 / Re
Valid for Re < 1.
What is Stokes’ Law?
The equation for terminal velocity in laminar flow conditions.
What is the effect of Brownian motion on small particles?
It causes random motion that can suppress the effect of gravity, slowing or preventing settling.
What happens during hindered settling?
Surrounding particles interfere with the motion of individual particles, slowing their settling rate.
What is the equation for terminal settling velocity in hindered settling?
vt = vt0 * (1 - c)^n
Where v_t0 is the terminal velocity for free settling, c is the volume fraction, and n is an exponent.
What is the empirical correction factor in Steinour’s equation?
ψ = 10^(-L * c)
Where c is the volume fraction of the solid in suspension.
What is the significance of K in determining settling regimes?
K is a criterion that helps establish whether Stokes’ Law or Newton’s Law applies based on particle and fluid properties.
What is the effect of particle volume fraction on settling velocity according to Maude and Whitmore?
As the volume fraction increases, the terminal settling velocity decreases.
What is the typical Reynolds number range for hindered settling?
Stokes’ Law applies for Re < 0.3, Newton’s Law applies for Re > 1000.
What is the significance of a Reynolds number less than 1?
Settling is in the Stokes’ law range.
Fill in the blank: The equation for vt0 is _______.
gD² (ρp - ρ) / 18μ
True or False: The settling velocity increases with increasing particle size.
True
