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Y1 Civil Engineering > CIVE40008 Fluid Mechanics > Flashcards

CIVE40008 Fluid Mechanics Flashcards

1
Q

Describe a fluid?

A

A substance that deforms continuously under the application of a shear stress

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2
Q

continuum hypothesis?

A

You can consider the average effects of the molecules in a given volume.
Relies on no. molecules being very large & over a large scale.
A continuum prevails if the number of molecules in a given volume is sufficiently great that the average effects are constant or change smoothly with time.

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3
Q

Specific Gravity = ?

A

S=ρfluid / ρwater

Specific gravity= density of the fluid/ density of water

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4
Q

Specific weight = ?

A

γ= ρ*g

Specific weight = density * gravitational acceleration

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5
Q

describe compressibility in fluids

A

All fluids are compressible

exceptions :
- air incompressible at velocities < speed of sound
- water mostly treated as incompressible, hence constant density

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6
Q

describe normal stresses

A

Forces acting normally to the surface of the fluid particles.
- Tend to compress/ expand the fluid particle without changing its shape.

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7
Q

describe shear stresses

A

Forces that shear the particle & deform its shape without changing volume

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8
Q

what stresses act on stationary and moving fluids ?

A

normal stresses - Both stationary and moving

shear - ONLY moving fluids

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9
Q

viscosity?

A

A measure of how much resistance a fluid has to shear

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10
Q

kinematic viscosity = ?

A

ν=μ/ρ

Kinematic viscosity ( m^2/s) = dynamic viscosity (Pa s) / density

used when dealing with motion

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11
Q

describe pressure ?

A

normal force

p = F / A

due to molecules exerting an equal and opposite force onto another molecules

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12
Q

units of pressure ?

A

Pascals (1 Pa= 1N/m^2)

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13
Q

why do we assume pressure to be perpendicular to a surface ?

A

On a molecular scale the surface is never flat. By averaging over billions of collisions ( continuum approach), the resulting force will act perpendicular to the surface. Therefore we assume pressure produces a force perpendicular to the surface.

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14
Q

describe pressure transmission

A

fast but not instantaneous, dependant on speed of sound in medium & shape of container

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15
Q

absolute pressure ?

A

Pressure with respect to a vacuum

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16
Q

gauge pressure ?

A

Pressure measured relative to local atmospheric pressure

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17
Q

relationship between gauge, atmospheric and absolute pressure ?

A

p gauge = p abs - p atm

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18
Q

when is pressure constant

for hydrostatic pressure distribution

A

in horizontal planes

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19
Q

pressure equation ?

for hydrostatic pressure distribution

A

p = p0 + ∫ ρ g dz*

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20
Q

when are hydrostatic pressure changes ignored

A

in gases

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21
Q

what is a manometer ?

A
  • pressure difference between two locations in a flow
  • liquid filled U-tubes
  • Δ pressure causes liquid to sit at different levels either side of U - tube

hence height ∝ pressure differenc

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22
Q

equation for Δpressure in manometer ?

A

Δpressure = density of liquid x gravitational acceleration x difference in height of sides of mono meter

Δp = p1 - p2 = ρw * g * Δh

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23
Q

equation for fluid weight

for hydrostatic pressure distribution

A

Fv = pgV = (ρgh)(wb) = ρgh*A

density x g x height x width x depth

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24
Q

equation for net force on a surface

for hydrostatic pressure distribution

A

F h = 1/2 * ρgb*h^2
acts at z = 2h / 3

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25
Q

centre of pressure ?

A

centre of pressure is the point at which the pressure may be considered to act
-location of where pressure force acts to exert the same moment as the pressure distribution

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26
Q

how do you approach pressure calculation for submerged angled surfaces ?

for hydrostatic pressure distribution

A

consider a constant and linearly distributed load
- eg a rectangular UDL & triangular LDL

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27
Q

how do you approach pressure calculation for complex geometries ?

A

projection method : projecting horizonal & vertical planes

since locally (at infintissimaly small strips) same forces as a vertical & horizontal wall

horizontal force ~= force on equivalent vertical surface

vertical force = weight of fluid above up to free surface

LIMITATIONS : no information on centre of pressure, only relevant for forces not moments

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28
Q

buoyancy force ?

A

net upward buoyancy force = weight of displaced fluid

Fb = ρgVbody

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28
Q

One - dimensional flow ?

A

Variations only along one spatial coordinate

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29
Q

Two - dimensional flow?

A

Variations along the direction of the flow and across the flow, two spatial dimensions

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30
Q

Three - dimensional flow?

A

Flow varies in all three spatial directions

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31
Q

Steady flow?

A

Flow that does not change with time

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32
Q

describe a streamline ?

A

A line that is everywhere tangential to the instantaneous flow velocity (= gradient function)

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33
Q

properties of streamlines ?

A
  • streamlines cannot cross
  • fluid cannot cross a streamline
  • streamlines can meet at a point
  • locally the flow must run parallel to solid boundaries
  • two adjacent streamlines may be thought of as a ‘stream tube’
  • moving fluids cannot suddenly change direction
  • if an obstacle is not streamlined (a bluff body), the fluid will separate from the solid boundary.
  • there are separation, reattachment and recirculation zones
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34
Q

describe a vena contracta

A

stream cross-section is smallest, contraction of container leads to separation, reattachment & recirculation zones

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35
Q

define a flux

A

rate at which a substance flows through a surface

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36
Q

define volume flux

A

The volume of fluid passing through a surface per unit time

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37
Q

define mass flux

A

The mass of the fluid passing through a surface per unit time

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38
Q

define momentum flux

A

The momentum passing through a surface per unit time

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39
Q

equation for volume flux

A

Volume flux/Discharge= velocity x area

Q = ∫ u dA

Q = U*A
(where U is mean velocity)

units : m^3/s

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40
Q

equation for mass flux

A

Φρ = ∫ ρu dA (= ρQ for constant ρ)

Mass flux = density x velocity x area

units : kg/s

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41
Q

equation for momentum flux ?

A

Φρu = ∫ u(ρu) dA

units : Ns/m^3 or N

approximation : ρQU

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42
Q

define an ideal fluid

A
  • incompressible
  • no internal resistance to flow ( viscosity = 0 )
  • shear forces ignored (frictional forces)
  • only experience normal stresses
  • no boundary layers
43
Q

describe no-slip condition

A

for real fluids :
At the interface between a solid surface and a fluid, the fluid velocity and solid surface velocity are identical
(hence zero is boundary is stationary)

44
Q

describe boundary layers

A

A flow region where large differences in velocity occur, often very close to the wall ( large velocity gradient )

45
Q

define viscosity

A

measure of resistance of a fluid to shear

46
Q

equation for shear stress

A

τ = μ * du/dz
hence a Newtonian fluid

frictional stress per unit area of contact

where μ is dynamic viscosity ( Ns/m^2)

47
Q

define a newtonian fluid

A

viscosity does not change with flow rate

hence viscosity independent of shear rate

48
Q

define a laminar flow

A

Re < Recrit , viscosity dominates

τw ∝ U

Organised layered flow

49
Q

define a turbulent flow

A

Re > Recrit , viscosity negligible

τw ∝ U^2

Disorganised, random, efficient mixer causes large friction and energy loss

50
Q

describe difference between lagrangian & eulerian approaches

A

lagrangian - identifying small elements of fluid within the flow for all time, position at some instant

eulerian - bulk description of flow by defining a control volume

51
Q

mass conservation ?

A

mass flux in (Φρ in) = mass flux out (Φρ out)

ρU1A1 = ρU2A2

52
Q

volume conservation

A

U1A1 = U2A2
volume flux in (Q1) = volume flux out (Q2)

steady continuity equation

53
Q

unsteady continuity equation ?

A

dV/dt = Qin - Qout

54
Q

conservation equation expressed mathematically ?

A

d/dt ∫ XdV = Φin -Φout + S

storage = fluxes in - fluxes out + sources - sinks

55
Q

describe application of continuity equation for a leaking container

A

unsteady cont. eqn :

Qin is constant
Qout non-constant

water depth increases until Qin = Qout
system tries to equilibrize

56
Q

rate of change of momentum = ?

A

Rate of change of the momentum is equal to the sum of forces

d(mu) / dt = Σ F

57
Q

steady continuity equation for momentum

A

ρQ (Uout- Uin) = Σ Fx

58
Q

give examples of conditions for a non-zero resultant force acts on a fluid

A
  • pressure gradient
  • gravity
  • density differences
  • friction / viscosity
  • externally applied forces, eg by a solid surface
59
Q

under what conditions can we apply hydrostatic principles to hydrodynamic situations ?

A

when the vertical acceleration is negligibly small
- streamlines are nearly horizontal, with no significant curvature

60
Q

explain the pressure distribution in closed conduits

A

e.g. pipes, ducts

hydrostatic pressure distribution does not influence the net force and is thus omitted from calculation

pressure is modelled as constant

61
Q

what is the primary principle of the Bernoulli equation ? what are the assumptions ?

A

energy is constant along a streamline
assuming:
- steady flow
- constant density
- dissipationless (no friction)

62
Q

describe the components of a total energy head

A

H = p / ρg + z + U^2/ 2g

total energy head = pressure head + elevation head + velocity head

63
Q

what is the piezometric head?

A

h = p / ρg + z

potential energy of flow, due to pressure & elevation heads

constant in vertical when a hydrostatic distribution

64
Q

Describe the difference between the energy & hydraulic grade lines ?

A

EGL - H(x) energy head
HGL - h(x) piezometric head

H(x)-h(x) = U^2/ 2g
difference is the velocity head, hence associated with the kinetic energy

65
Q

what is the Bernoulli equation for curved streamlines ?

A

the centripetal force produces a pressure gradient, hence the Bernoulli equation becomes :

Δp / Δr ~ ρ*U^2 / R
(where R is the radius of curvature)

hence, if R is smaller (stronger curvature), Δp is larger

66
Q

Describe the pressure in a fluid body, using the second Bernoulli equation

A
  • pressure across straight streamlines is constant in horizontal plane, or hydrostatic in vertical plane
  • applying gravity : piezometric head across straight streamlines is constant

since straight streamline assumes R ⇒ ∞

67
Q

what are the conditions for applying the Bernoulli equation ?

A
  • converging streamlines
  • accelerating fluid
  • low energy losses (not Turbulence)
68
Q

what is the discharge formula for a draining reservoir ?

A

Q = A√(2gh)

where h is the distance from the datum (taken as centre of outflow area) to free surface

69
Q

how would you manipulate the Bernoulli equation for stagnation points ?

A

at a given point in the flow :
p = p∞, U = U∞, z = 0

at interface to surface :
p = ps , U = 0, z = 0

since energy is conserved :
p∞ + 1/2 ρU∞^2 = ps

where 1/2 ρU∞^2 is the dynamic pressure

70
Q

what is a pitot-static tube ?

A

measures stagnation & static pressure to infer the velocity of a fluid
using U = √(2g∆h)

71
Q

what is a syphon ?

A

inverted U-shaped tube which causes a liquid to flow uphill, discharging at a lower relative elevation, through a pressure gradient

72
Q

what is a venturi tube ?

A

gently converging & diverging tube to determine the volume flux in a pipe
- with a pressure tapping to identify pressure difference
- a Qideal can be found, and a correction factor can be applied to compensate for energy losses in the system

73
Q

what are major losses in pipe systems ?

A

friction with the wall

74
Q

what are minor losses in pipe systems ?

A

due to pipe entry, exit, bend, contractions

additional energy dissipation due to secondary flows induced, eg curvature or recirculation

75
Q

how do you deal with minor energy losses ?

A

apply a loss factor
- energy loss ∝ local kinetic energy of flow

∆Hlocal = ξ U^2/2g

where 0 < ξ < 1

76
Q

what is the exit loss for a pipe discharging into a reservoir ?

A

all kinetic energy is lost, hence

∆Hexit = U^2/2g

77
Q

what is the Darcy-Weisbach Friction equation ?

A

∆Hfriction = f * L/D * U^2/2g

for non circular pipes :
∆Hfriction = f * L/De * U^2/2g

where De = 4A / P (perimeter)

78
Q

Give examples of uses for pumps

A

irrigation, water supply, sewage & water control

79
Q

Give examples of uses for turbines

A

power generation, in hydro dams, or wind farms

80
Q

describe a centrifugal pump

A

centripetal accelerations induced by spinning rotor blades
- the centrifugal forces lead to a low pressure in the centre & high pressure at the outlet
- this pressure difference determines the output flow rate

81
Q

give the energy balence for a control volume with a pump or turbine

A

dEtotal / dt = (ρgHin)Q - (ρgHout)Q + P (energy added by pump per unit time)

82
Q

equation for power of a pump

A

P = ρg∆HQ in J/s

83
Q

open channel flow ?

A

flow of fluid with a free-surface that is driven along a conduit by gravity

free surface introduces new degree of freedom (flow geometry now require

84
Q

hydraulic jump ?

A
  • rapid transition between super- and subcritical flow
  • Large amount of mixing and energy dissipation
  • Sudden step change in flow depth
85
Q

laminar flow ?

ocf

A

Re < Recrit

86
Q

turbulent flow ?

ocf

A

chaotic motion and complex flow patterns for Re&raquo_space; Recrit
** Virtually all open channel flows are turbulent **

87
Q

steady flow ?

A

no variations in time
- for example : velocity, pressure, and density remain constant at any point in space over time
- example : flow of water through a pipe with a constant velocity and pressure

88
Q

unsteady flow ?

A

variations in time :
- fluid properties are not constant at any point in space over time
- e.g. acceleration, deceleration
- flow in a river

89
Q

uniform flow ?

A

no along-channel variations in water depth, slope,
discharge etc
e.g. constant diameter pipe flow

steady uniform = equilibrated force balance, both in
space and time

90
Q

non-uniform flow ?

A

variations in one or more of the variables
e.g. changing geometry, slope
* Slowly varying flows – gradual variations; pressure is usually
hydrostatic and streamlines are straight.
* Rapidly varying flows – rapid variations; pressure is generally not
hydrostatic and streamlines are curved

usually due to hydraulic structures (weirs, dams, etc,)

91
Q

when can hydrostatic pressure distribution be introduced to OCFs?

A

if streamlines are approximately straight and parallel (uniform/slowly-varying flows)

92
Q

underlying assumtions of Bernoulli for OCFs ?

A
  1. uniform/slowly-varying flow,
  2. incompressible fluid,
  3. steady flow,
  4. friction negligible (no major energy losses).
93
Q

small slopes ?

A

apply small angle approximations :

sinθ ≈ s
cosθ ≈ 1
tanθ ≈ s

h*cosθ ≈ h

94
Q

gravity body force for OCF with small slope ?

A

F g,x = mg ≈ ρgALs

95
Q

wall shear stress for OCF ?

A

acts over the entire wetted perimeter P and length L
Ff = τwPL
(since stress = F / A)

when force balence applied in x direction with fluid body weight :

τw = ρgRs

96
Q

sub-critical ?

A

Fr < 1
upstream flow is affected (changing
h, U) by an obstacle - downstream control
U < √gh
- most rivers

‘ tranquil , slow ‘

97
Q

super-critical ?

A

Fr > 1
upstream flow is not affected by an
obstacle
U > √gh

upstream control

‘shooting, fast’

98
Q

scale - modelling ?

A

apply scale factor λ = LF /LM
- apply to Froude’s Number equation
- use dimension to identify scaling for other parameters
- e.g. velocity = L / T
- Um / √ghm = Uf / √ gλhm

99
Q

solution strategy for hydraulic jump ?

A

continuity & momentum :
ρQ(U2 -U1) = ΣF

apply Bélanger equation

or for points far enough from the control structure : apply Bernoulli

100
Q

purpose of control structures ?

A
  • Controlling water depth (ships, increasing ground water level)
  • Bed stabilization (reduced flow velocity)
  • Flood control (water storage, e.g. if located immediately after a
    lake)
  • Air entrainment etc.
101
Q

what can you obtain from an energy diagram ?

A

minimum = critical depth = Fr = 1
for each energy head : there are two intersections with the curve denoting the possible super & sub critical states

sub : piezometric head dominates
super : velocity head dominates

102
Q

assumptions for broad-crested weir w/ free outfall ?

A
  • length of weir ≫ upstream flow depth
  • free outfall (no downstream disturbance)
  • free outfall ensures discharge becomes critical
  • well-rounded/smooth weir (no major energy loss)
  • constant energy head incoming - fed from large reservoir
  • upstream velocity head is negligible’
  • streamlines ≈ parallel above weir

hence we can apply energy conservation between two points over wier

103
Q

sharp - crested weir assumptions ?

A

water level directly related to Q over weir

Assumptions :
- Downstream of weir is free jet at atmospheric pressure (broad-crested = hydrostatic)
- No losses across weir
- Upstream pressure hydrostatic
- flow over weir ≈ upstream flow depth

104
Q

poleni formula ?

A

solves bernoulli for discharge as a function of heigh & integrate over area of weir
for rectangular :

Q ideal = 2/3 * √(2g) * wh^3/2

In reality discharge will be lower due to losses and the
assumptions made ∴ correction coefficient Cd is applied:
Qreal = Cd * Qideal

Y1 Civil Engineering (7 decks)

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