Fluid Motion

Question 1

What is steady flow?

Answer 1

Flow that does not change with time (velocity field stays the same)

Question 2

What is plug flow?

Answer 2

Plug flow is a simple model where the velocity profile of the fluid is assumed to be constant across any cross-section of the pipe perpendicular to the axis of the pipe

i.e. ignoring shear stress from surface and fluid friction (no boundary layer)

Question 3

What is flux?

Answer 3

The rate at which a substance flows through a surface

Question 4

One of the key features of fluids in motion is their ability to transport substances such as volume, mass momentum, energy., heat, contaminant…

Answer 4

One of the key features of fluids in motion is their ability to transport substances such as volume, mass momentum, energy., heat, contaminant…

Question 5

What are the assumptions made when performing integral approximations of fluid property fluxes?

Answer 5

Rather than considering u as another function of z as it should be, the average velocity U (Q/A) is used to simplify the integral

This approximation only works well when the velocity profile is quite uniform over A i.e. for turbulent rather than laminar flows

Question 6

What is a streamline?

Answer 6

A streamline is defined as a line that is everywhere tangential to the instantaneous flow velocity

Question 7

What is the relationship between U and streamline spacing?

Answer 7

U is proportional to 1/streamline spacing

Conventionally, identical discharges pass through each stream tube

Question 8

Why does flow separation happen?

Answer 8

Moving fluids have inertia, if they move in one direction, they cannot instantaneously change direction. Thus, if an obstacle is not streamlined, the fluid will separate from the solid boundary and we will observe:

1. Flow separation
2. Flow reattachment
3. Recirculation zone

Question 9

Why do recirculation zones have higher pressure?

Answer 9

Pressure is the way the fluid ‘communicates’, recirculation zones hence have higher pressures to redirect fluid flow

Question 10

What is a vena contracta?

Answer 10

The point in a fluid flow where the stream cross-section is the smallest

Question 11

In which direction does a recirculation zone recirculate?

Answer 11

A recirculation zone recirculates in the same direction as adjacent streamlines

Question 12

What is an ideal fluid?

Answer 12

A fluid that experiences only normal stresses

wide application e.g. wave prediction

shear forces are ignored which implies that the fluid has zero viscosity

when drawing streamlines, we assumed that the fluid was ideal as we ignored friction

Question 13

What are real fluids?

Answer 13

Fluids that have a viscosity that generates shear forces

real fluids experience friction and create boundary layers

Question 14

What is the no-slip condition?

Answer 14

Fluid velocity and solid surface velocity are identical at the interface between a solid surface and a fluid

This is because under real conditions, the surface is rough on a molecular level, and causes the trapping of fluid particles

Question 15

What are boundary layers?

Answer 15

The layers of fluids that are in the immediate vicinity of a boundary surface

They experience large velocity gradients as the effects of viscosity are significant

Question 16

How is the shear stress calculated?

For Newtonian fluids

Answer 16

tau (shear stress) = mu (dynamic viscosity) times du/dz (velocity gradient)

*(Rheology is the study of fluids not obeying this relationship - Non Newtonian fluids such as rubber, clay, suspensions, plastics, paints, blood)

Question 17

What are the implication of the relationship tau = (mu)(du/dz)

Answer 17

any shear stress - no matter how small - causes flow as shear stress creates a velocity gradient

Question 18

Why do we usually ignore fluid shear stress in this module?

Answer 18

since we usually assume plug flow, velocity gradient and hence shear stress = 0

Question 19

What is the relationship between dynamic viscosity mu and kinematic viscosity v?

Answer 19

kinematic viscosity v = dynamic viscosity mu / rho

Question 20

When are dynamic and kinematic viscosity used respectively?

Answer 20

dyn mu is used for calculating forces

kine v is used when dealing with motion

v is often used when density variations are small or can be neglected

Question 21

Equation of wall shear stress?

Answer 21

TAUw = (mu)(du/dz at wall)

Question 22

What are the two flow states?

Answer 22

Laminar flow - organised layered flow
e.g. ground water flow

Turbulent flow - disorganised, random flow
e.g. river flow, tidal bore, fire plume, building ventilation

Question 23

What is Reynolds’ number and how is it used to characterise flow states?

Answer 23

Re = rhoUL/mu
(inertia/viscosity)

Re &laquo_space;1 (viscosity dominates; laminar)
Re&raquo_space;1 (viscosity negligible; turbulent)

Re > 4000 for turbulent pipe flow

The magnitude of Re number is what is important, most flows encountered in CivEng are turbulent

Question 24

What is entrance length and how is it used to help with Re number calculations?

Answer 24

Entrance length is the distance a flow travels after entering a pipe before the flow becomes fully developed

In calculations, if length < entrance lenth use length

if length > entrace length use diameter

Question 25

What are the properties of a turbulent flow?

Answer 25

Turbulence is an efficient mixer (influences spreading of substances such as odours, chemicals, nutrients…)

Also mixes momentum, causing large friction:

laminar flow: Tauw ~ U
turbulent flow: Tauw ~ U^2

big implications for energy consumption

Question 26

Why do aero engineers seek to design the point at which the fluid flow over an aerofoil becomes turbulent as far back as possible?

Answer 26

Transition to turbulence over an airfoil increases friction and therefore energy consumption