Section 1: fluid/sediment equations Flashcards
Reynolds number equation
Re= ρud/µ (may be l instead of d)
What does the Reynold number show
Ratio of inertial to viscous forces
What forces are represented in the Reynolds number
ρ is fluid density
u is fluid velocity
d(/l) is a length parameter such as the diameter of a pipe or length of submerged object
µ is fluid viscosity
When does the flow become turbulent, at what Reynolds number
> 2000
Features of Laminar flow
Low velocity, low Reynolds number
In linear paths generally parallel to the boundary of the flow
At constant velocity
Fluid motion is predictable
May be analysed by mathematical theory
Features of Turbulent flow
High velocity, high Reynolds number
Irregular sinuous paths
With veolicty changing (subject to accelerations/decelerations)
Fluid motion is unpredictable
Cannot be analysed with mathematical theory, requires empirical/experimental study
Froude Number equation
Fr=u/√gh
What does the Froude number show
Ratio of inertial to gravity forces
What forces are presented in the Froude number
u is fluid velocity
g is acceleration due to gravity
h is the a length parameter such as the depth of a flow or the length of an object moving on the water surface
Essential characteristics of turbulent flow
Disorder (irreproducible in detail)
Efficient mixing
Vorticity, irregularly distributed in time and space
What is the assumed acceleration due to gravity unless otherwise stated
9.81 m s-2
SI base units of ρ
kg m-3
Si base units of u
m s-1
SI base units of d and h
m
SI base units of μ
kg m-1 s-1
SI base unit of g
m s-2
Viscosity equation
τ = μ* du/dz
What forces are presented in the viscosity
τ is shear stress
μ is fluid viscosity
du/dz is rate of change of local fluid velocity (u) in the direction z normal to the shearing surfaces at any point
z is direction u is depth?
What is viscosity
A measure of the resistance of a fluid to deformation eg shearing or extension
Bernoulli Equation
p + ρu^2/2 + ρgh
What are the forces present in the Bernoulli Equation
p is static pressure (uniform in all directions) - pressure at a point on a body moving with the fluid
ρu^2/2 is dynamic pressure (pressure on surfaces perpendicular to flow) - kinetic energy per unit volume
ρgh is manometric height - gravitational potential energy per unit volume
What is the Bernoulli Equation
The sum of a pressure term, a velocity term and a gravitational/height term that remain constant
Static pressure + dynamic pressure = total pressure
What is U2 > U1
P2 < P1
Fluid velocity varies inversely with fluid pressure
If fluid has to travel through narrowing, velocity gets faster and pressure decreases
Stoke Law Equation
w = gD^2(ρs - ρl) / 18μ
What are the forces present in Stoke Law
w is settling velocity
D is grain diameter
ρs is density of solid particle
ρl is density of fluid
Fluid drag force (drag coefficient CD)
FD / ρu^2D^2
Dimensionless fluid drag force CD
CD= f (ρud/ μ)
