Fluids Midterm 2 Flashcards
1
Q
External flow
A
Unbounded flow over surface (plate, ball, airplane)
2
Q
Internal flow
A
Completely bounded by a solid surface, pipe, duct.
3
Q
Incompressible flow
A
Type of flow where change and density is negligible
4
Q
Compressible flow
A
Change intensity is significant and can’t be ignored. For example, mock number qualifies compressibility.
5
Q
Mock number equation
A
Ma = speed of flow/speed of sound = v/c
(c is speed of sound)
6
Q
Speed of sound formula
A
C = sqrt( yRT )
7
Q
Incompressible flow mock number range
A
Ma < 0.3
8
Q
Compressible flow mock number range
A
Subsonic 0.3 < Ma < 1
Sonic Ma = 1
Supersonic Ma>1
9
Q
Steady flow
A
Fluid properties ( velocity, temperature temperature, pressure) do not change with time.
Example, turbines, compressors boilers, condensers, and heat exchangers
10
Q
Steady versus uniform
A
Steady is not equal to uniform.
11
Q
Uniform definition
A
Implies no change with location
12
Q
Unsteady transient flow
A
Fluid properties ( velocity temperature pressure) in the flow field change with time. Commonly found during startup and shut down.
13
Q
Multidimensional flows
A
Three dimensional velocity fairies and three dimensions XYZ or r theta Z. But can be simplified to one dimensional or two dimensional problems.
14
Q
Three types of forces and fluid flow
A
Pressure force, viscous, force, and inertia force
15
Q
Viscous flow
A
Refers to a flow in which the frictional effect is significant
16
Q
Inviscid flow
A
Refers to a float region in which the frictional effect may be negligible compared to pressure and inertia force
17
Q
Laminar flow
A
Very smooth flow patterns. A flow of high viscosity oil at low velocity is a laminar flow. Characterized by highly ordered smooth fluid layers.
18
Q
Turbulent flow
A
Highly disordered characterized by rapid fluctuations and all fluid properties typically high speed low viscosity flows. Mostly encountered flows are turbulent.
19
Q
Transitional flow
A
A flow pattern may eventually change from laminar to turbulent as velocity, increases flow patterns, alternate between laminar and turbulent
20
Q
Reynold’s number
A
Dimension this number to quantify flow regimen.
21
Q
Raynold’s number formula
A
Re = inertial force/viscous force = pVavgD/u = Vavg D/v
p- density
u -dynamic viscosities
v -kinematic viscosity
Vavg - average flow velocity
D- characteristic length
22
Q
Flows in pipes versus Reynolds number
A
Laminar: Re<2300
Transitional: 2300<Re<4000
Turbulent: Re > 4000
23
Q
Drag force
A
A fluid moving relative to a body exerts, a drag force in the same direction as the flow on the body. This is partially due to the friction caused by viscous flow.
24
Q
Viscosity
A
Viscosity is a quantitative measure of the resistance of a fluid to motion
25
Viscosity dominant flow
The flow is completely governed by viscous effects, resulting in laminar flow. Example Cuvette flow, which occurs at highly viscous fluid, flowing in a small gap between two infinitely long parallel plates.
26
Dynamic viscosity formula
τ= μ du/dy ( Si units Pas)
27
Kinematic viscosity
v = μ/p (m^2/s)
28
Viscosity versus temperature
Viscosity strongly depends on temperature and weekly depends on pressure. For liquids viscosity decreases with temperature because the cohesive intermolecular forces are weakened as the liquid molecules move and vibrate more freely at higher temperatures. For gases intermolecular forces are negligible, but collisions are not as temperature increases, gas molecules, move faster, more randomly increasing collision. That’s a greater resistance to flow and higher viscosity.
29
Sutherland correlation for gas between viscosity and temperature formula
μ = aT^1/2 /(1+b/T)
A and B are constant obtained experimentally
30
Exponential correlation for liquids between dynamic viscosity and temperature
μ = a10^ (b/T-c)
AB and C are Constance obtained experimentally
31
Drag force formula
Fdrag = -Fshear, wall = 4piuUmaxL
32
Newtonian fluid
She stress is literally proportional to the share strain rate or rate of deformation. The slope of the linear line represents the dynamic viscosity of the fluid.
33
Non-Newtonian fluid
Does not have a linear relationship between this year stress and sheer strain rate. The slope of a curve at any point is called the apparent viscosity of the fluid at that point.
34
Three classifications of non-Newtonian fluids
1) share thickening fluids. Fate increases with stress strain rate. For example, Oobleck.
2) she fitting fluids. Less viscous at higher strain rates, for example polymer, paints, and blood.
3) Bingham plastics, resist certain share stress. Beyond yield share as a liquid example toothpaste, and ketchup
35
Control volume CV
Is a selected region in space which allows both mass and energy to cross the boundary. The boundary can be real or imaginary
36
Control surface CS
the real or imaginary boundary of a control volume.
Fixed CV: if CS is fixed
Moving CV if CS is moving
37
Conservation of mass
Mass cannot be created or destroyed. The time rate of change of mass in a CUV at a certain time equals the net mass flow rate into the CV at that time.
Δ = +in -out
38
Steady flow through a CV
The properties, mass momentum and energy remain unchanged, so the sum of mass entering is equal to the sum of mass exiting the system
39
Volume flow rate
V = dV/dt = Vavg,n A = mv (m^3/s)
40
Mass flow rate
m= dm/dt = pV = pVavgA (kg/s)
41
Energy conservation
Energy is neither created nor destroyed for fluids at rest or in motion
42
Bernoulli equation energy
P + 1/2pv^2 +pgz = const
P = pressure
1/2pv^2 = kinetic energy
pgz = potential energy
43
Bernoulli equation pressure
P + 1/2 pv^2 +pgZ = const
P= static pressure
1/2pv^2 = dynamic pressure
pgz = hydrostatic pressure
44
Stagnation pressure
The sum of static and dynamic pressures
45
Berni equation pressure heads
P/pg + v^2/2g + z = const
P/pg - pressure head
v^2/2g- velocity head
z- elevation head
46
Pressure head
The height of a fluid column that produces static pressure
47
Velocity head
The height needed for fluid to reach the given velocity during frictionless freefall from rest
48
Elevation head
The height representing the potential energy
49
When is head used?
Head is used when describing energy conservation and pipe flows. It’s unit is meters.
50
When is Brandi’s equation valid?
1) steady flow
2) incompressible (Ma<0.3) the density can be assumed to be constant.
3) inviscid: the friction in the flow is negligible
4) irrotational: the velocity of the flow VxV = 0. The flow is free of eddies or swirls
5) no shaft work or heat transfer
51
Stagnation point
The point to where our flow is brought to a full stop or a zero velocity.
52
Pitot tube
One of the simplest. The tube extends into the center of the fluid channel the tip access a stag nation point. Dynamic pressure is converted to static and liquid fills the tube. You can read the stagnation pressure.
53
Pitot static tube
Similar to a regular pit tube, but it measures both static and stagnation pressure through an extra hole. The velocity can be measured using.
V = sqrt(2(Pstag-Pstatic)/P)
54
Obstruction flow meters
Orifice meter flow nozzle and venturing meter. They are contracted to develop a pressure drop as the flow passes through.
55
Average discharge coefficient
Venturi tube equals 0.95 to 0.99
Orifice meter with Reynolds number less than 30,000 is equal to 0.61
Nozzle meter with Reynolds number less than 30,000 is equal to 0.96
56
Orifice meter downsides
Highest pressure loss not suitable for high requirements on pressure recovery, and lots of friction loss
57
Entrance length
The length of the pipe entrance to where the velocity boundary layers merge at the centerline
58
Fully developed laminar or turbulent flow
The region where the velocity profile remains unchanged
59
Entrance length formula for laminar flow
Le,laminat/D = 0.5 RE
60
Turbulent flow entrance length formula
Le, turbulent/D = 1.359Re^1/4 or
Le,turbulent/D= 4.4Re^1/6
61
Fully developed laminar flows
The velocity profile is a parabola, and the max velocity occurs at the centerline
62
Fully developed turbulent flows
A velocity profile is more uniform due to rapid exchange of momentum along fluid layers
63
U formula for laminar
u(r) = umax(1-r^2/R^2)
Vavg = 1/2 umax
64
U formula for turbulent flows
u(r) = umax(1-r/R)^1/n
n = 7 for most flows
65
What do hydraulic energy grade lines show?
A graphical representation of head
66
Hydraulic grade lines HGL
Represent the sum of of pressure head and elevation head
P/pg+z
67
Energy grade line EGL
Represents the total head or total mechanical energy
P/pg + v^2/2g + z
68
What factors must be taken into account in energy conservation?
Friction losses along the pipe and fittings
Energy added to flowing fluid by pump
Energy extracted by turbine
69
Incompressible flow energy conservation
P/pg +av^2/2g + z + hpump = P/pg +av^2/2g + z + hturbine +hl
70
a for energy conservation avg values
Two for laminar
1.04 to 1.11 for turbulent
71
What causes the EGL to drop along the pipe?
The friction loss along the pipe
72
What causes HGL to rise in the diffuser?
The increase in flow velocity and the increase of pressure.
73
Why are EGL and HGL parallel in pipe section?
The pipe diameter remains constant
74
Why do both EGL and HGL rise in the pump and drop in the turbine?
Pump adds energy to the fluid, passing through it, turbine extracts energy from the fluid
75
Pump efficiency /work formulas
hpump = Wpump/mg = Wpump/pQg
Npump = Wpump/Wshaft
76
Turbine efficiency and work formulas
hturb = Wturb/mg = wturb/pQg
Nturb = Wshaft/Wturb Wshaft
77
78
The energy grade line drops in a straight constant area pipe, but why
Because of major energy losses
79
What is a loss?
The conversion of mechanical energy to internal energy i.e. temperature increases
80
Why do we have losses at the wall?
Because of the no slip condition which creates a elastic gradient that causes the fluid to rotate
81
What is a major loss?
Energy loss due to friction at the wall
82
Why do we have no slip condition?
Because fluid is viscous
83
How does rotation relate to energy loss?
It increases the area of the share layer between the fluid layers, leading to the conversion of rotational, kinetic energy into internal energy
84
85
Consider a device with one inlet and one outlet. If the volume flow rate at the inlet and the outlet are the same, is the flow through this device necessarily steady? Why?
No, a flow with the same volume flow rate at the inlet and the exit is not necessarily steady even if the density is constant. To be steady the mass flow rate through the device must remain constant in time and no variables can change with time at any specified spatial position
86
Consider a device with one inlet and one outlet. If the mass flow rate at the inlet and the outlet are the same, is the flow through this device necessarily steady? Why?
Not necessarily, Considering the steadily increasing flow of an incompressible liquid through the device. At any instant in time the mass flow rate in must equal the mass flow rate but since there is nowhere else for the liquid to go. However the mass flow rate itself is changing with time and hence the problem is unsteady
87
The water level of a tank on a building roof is 20 m above the ground. A hose leads from the tank bottun to the ground. The end of the hose has a nozzle, which is pointed straight up. What is the maximum height to which the water could rise? Which factor would reduce this height?
With no losses and a 100% effective nozzle, the water stream could reach to the water level in the tank or 20 meters. In reality the friction losses in the hose nozzle inefficiencies, orifice losses, air drag would prevent attainment to the maximum theoretical height
88
Pressure and cross section relationships
As the duct converges to a smaller cross sectional area, the velocity increases. By Bernoulli’s equation the pressure therefore decreases.
89
90
Obstruction flow meter
Measures the flow rate through a pipe bu constricting the flow and measuring the decrease in pressure due to the increase in velocity at or downstream of the constriction site.
91
Comparison of the three types of obstruction meters
Orifice is cheapest, smallest and least accurate and causes greatest head loss
Venturi is the most expensive, largest, most accurate and smallest head loss. The nozzle meter is in between in all aspects of
92
Someone claims that the average velocity in a circular pipe in fully developed laminar flow can be determined by simply measuring the velocity at R/2 (midway between the wall and centerline. Do you agree
No the average velocity in a circular pipe is fully developed laminar flow cannot be determined by simply measuring the velocity at R/2. The average velocity is Vmax/2 but ay R/2 it os 3Vmax/4
93
94
In the fully developed region of flow in a circular pipe does the velocity profile change in the flow direction
No it does not change
95
Consider fully developed laminar flow in a circular pipe. If the diameter of the pipe is reduced by half while the flow rate and pipe length are constant the head loss will..
Increase the head loss by a factor of 16
96
Consider a fully developed flow in a circular pipe with negligible entrance effects. If the length of the pipe is doubles the head loss will
Will also double
97
Relationship between head loss and pipe length
They are proportional
98
Consider fully developed laminar flow in a circular pipe. If the viscosity of the fluid is reduced by half by heating while the flow rate is held constant, how does the head loss change
The head loss is reduced by half
99
