Fluids Flashcards
Which forces are supported in fluids?
- tension is not supported
- compression is supported and results in a small elastic deformation
- shear is supported but results in flow
du/dx + dv/dy + dw/dz = 0
all flux in all three directions must equal to zero
mass must be concerved
In which direction of pressure change is fluid driven?
From high to low pressure
τ = F/A
Shear stress= force/area
τ= μ δu/δy
Shear stress = dynamic viscosity * (velocity/ depth)
What is the shear stress in viscous flow?
No longer zero
Kinematic viscosity?
ν=μ/ρ (m^2/ s)
Dynamic viscosity?
μ (kg/ms)
What navier stokes simplification can you make by assuming the flow to be steady?
All time derivatives will be zero (d/dt)=0
What navier stokes simplification can you make by assuming the flow to be fully developed?
The velocity component in the x-direction will remain constant (du/dx = 0)
What navier stokes simplifications can you make when the sides are incredibly long. (Flow in one direction, boundaries in another)?
No flow in the the third direction and no effect by the boundaries.
W=0
d/dz=0
What simplification to navier stokes equations by assuming its laminar flow?
The gradient of v is zero and v is zero at the boundary, v must be zero everywhere. (V is in the y direction)
Re= ρUL/μ
Inertial forces/ viscous forces
Reynolds number= densityvelocity scale length scale/ dynamic viscosity
What are Reynolds numbers for laminar flow?
Re < Recrit
What Reynold numbers are turbulent flow?
Re> Recrit
Q= π/4 D^2 U
Volume flux= π/4 * diameter^2 * velocity
(Only for uniform flow)
What is Q along a pipe?
Constant
What is M along a pipe
Momentum is constant along a pipe
M= π/4 D^2 U^2 = QU
Momentum = π/4 * diameter ^2 * velocity ^2
Hydraulic grade line?
Represents piezometric head (h)
Energy grade line?
Represents total head line (H)
Piezometric head?
Pressure head + gravitational head combined
p1/ρg + z1 = p2/ρg + z2 + τ0PL/ ρgA
p= pressure
ρ= density
g= gravitational acceleration
z= height
τ0= shear stress
P= wetted perimeter
L= length
A= area
τ0= f/8 ρ U^2
where
f=f(Re,ks/D)
Shear stress = function of Reynolds and relative roughness * density * velocity^2/8
In what conditions is f= 64/Re
For laminar flow/ Re< 2300
In what condition is 1/f^(1/2) = -2log10[k/D/3.71 + 2.51/Re*f^(1/2)]
For turbulent flow/ for Re> 4000
When is 1/f^(1/2)= 2log10[Ref^(1/2)] -0.8
For turbulent flow in smooth pipes/ for Re>4000
hL = εU^2/2*g
minor head loss= loss coefficient* velocity^2/2*gravitational acceleration
ε= (1-Α1/A2)^2
Loss coefficient for sudden pipe enlargement = (1-small area before/ small area after)^2
RH= A/P
Hydraulic radius= flow area/ wetted perimeter
hf= f* L/4RH * U^2/2*g
head loss= function * length/4hydraulic radius * velocity^2/2gravitational acceleration
Entry length?
Region where boundary layer develops
Does laminar or turbulent flow boundary layers take longer to develop?
It takes longer for laminar pipe flow boundary layers to develop with longer entry lengths
Fully developed flow?
When boundary layers converges to pipe centreline
How does shear stress vary across a pipe?
Linearly with being 0 at the centreline
What effect of shear force have a long a plate?
The effect of shear force increases along a plate, increasing the thickness of fluid layer that is affected. Reynolds number also increases along a plate leading to turbulent flow conditions.
There’s a laminar region, transition region and then turbulent region
u/u* = u*y/ ν
u= velocity
u* = wall shear velocity
ν= velocity viscosity
y= depth/ distance from sublayer
This works when yu*/ν is between 0 and 3~5
Sublayer thickness = (3-5) ν/ u*
ν= velocity viscosity
u* = wall shear velocity
