Fluids

Question 1

Which forces are supported in fluids?

Answer 1

• tension is not supported
• compression is supported and results in a small elastic deformation
• shear is supported but results in flow

Question 2

du/dx + dv/dy + dw/dz = 0

Answer 2

all flux in all three directions must equal to zero
mass must be concerved

Question 3

In which direction of pressure change is fluid driven?

Answer 3

From high to low pressure

Question 4

τ = F/A

Answer 4

Shear stress= force/area

Question 5

τ= μ δu/δy

Answer 5

Shear stress = dynamic viscosity * (velocity/ depth)

Question 6

What is the shear stress in viscous flow?

Answer 6

No longer zero

Question 7

Kinematic viscosity?

Answer 7

ν=μ/ρ (m^2/ s)

Question 8

Dynamic viscosity?

Answer 8

μ (kg/ms)

Question 9

What navier stokes simplification can you make by assuming the flow to be steady?

Answer 9

All time derivatives will be zero (d/dt)=0

Question 10

What navier stokes simplification can you make by assuming the flow to be fully developed?

Answer 10

The velocity component in the x-direction will remain constant (du/dx = 0)

Question 11

What navier stokes simplifications can you make when the sides are incredibly long. (Flow in one direction, boundaries in another)?

Answer 11

No flow in the the third direction and no effect by the boundaries.
W=0
d/dz=0

Question 12

What simplification to navier stokes equations by assuming its laminar flow?

Answer 12

The gradient of v is zero and v is zero at the boundary, v must be zero everywhere. (V is in the y direction)

Question 13

Re= ρUL/μ

Answer 13

Inertial forces/ viscous forces
Reynolds number= densityvelocity scale length scale/ dynamic viscosity

Question 14

What are Reynolds numbers for laminar flow?

Answer 14

Re < Recrit

Question 15

What Reynold numbers are turbulent flow?

Answer 15

Re> Recrit

Question 16

Q= π/4 D^2 U

Answer 16

Volume flux= π/4 * diameter^2 * velocity

(Only for uniform flow)

Question 17

What is Q along a pipe?

Answer 17

Constant

Question 18

What is M along a pipe

Answer 18

Momentum is constant along a pipe

Question 19

M= π/4 D^2 U^2 = QU

Answer 19

Momentum = π/4 * diameter ^2 * velocity ^2

Question 20

Hydraulic grade line?

Answer 20

Represents piezometric head (h)

Question 21

Energy grade line?

Answer 21

Represents total head line (H)

Question 22

Piezometric head?

Answer 22

Pressure head + gravitational head combined

Question 23

p1/ρg + z1 = p2/ρg + z2 + τ0PL/ ρgA

Answer 23

p= pressure
ρ= density
g= gravitational acceleration
z= height
τ0= shear stress
P= wetted perimeter
L= length
A= area

Question 24

τ0= f/8 ρ U^2
where
f=f(Re,ks/D)

Answer 24

Shear stress = function of Reynolds and relative roughness * density * velocity^2/8

Question 25

In what conditions is f= 64/Re

Answer 25

For laminar flow/ Re< 2300

Question 26

In what condition is 1/f^(1/2) = -2log10[k/D/3.71 + 2.51/Re*f^(1/2)]

Answer 26

For turbulent flow/ for Re> 4000

Question 27

When is 1/f^(1/2)= 2log10[Ref^(1/2)] -0.8

Answer 27

For turbulent flow in smooth pipes/ for Re>4000

Question 28

hL = εU^2/2*g

Answer 28

minor head loss= loss coefficient* velocity^2/2*gravitational acceleration

Question 29

ε= (1-Α1/A2)^2

Answer 29

Loss coefficient for sudden pipe enlargement = (1-small area before/ small area after)^2

Question 30

RH= A/P

Answer 30

Hydraulic radius= flow area/ wetted perimeter

Question 31

hf= f* L/4RH * U^2/2*g

Answer 31

head loss= function * length/4hydraulic radius * velocity^2/2gravitational acceleration

Question 32

Entry length?

Answer 32

Region where boundary layer develops

Question 33

Does laminar or turbulent flow boundary layers take longer to develop?

Answer 33

It takes longer for laminar pipe flow boundary layers to develop with longer entry lengths

Question 34

Fully developed flow?

Answer 34

When boundary layers converges to pipe centreline

Question 35

How does shear stress vary across a pipe?

Answer 35

Linearly with being 0 at the centreline

Question 36

What effect of shear force have a long a plate?

Answer 36

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

Question 37

u/u* = u*y/ ν

Answer 37

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

Question 38

Sublayer thickness = (3-5) ν/ u*

Answer 38

ν= velocity viscosity
u* = wall shear velocity