fe review course fluid mechanics - louisiana state university · 2020. 9. 28. · fe review course...
TRANSCRIPT
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FE Review Course – Fluid
Mechanics
Frank T.-C. Tsai, Ph.D., P.E.
Dept. of Civil & Environmental Engineering, LSU
(O) 578-4246
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mailto:[email protected]
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Get the handbook!!
• REFERENCE HANDBOOK
• 9.4 Version for Computer-Based Testing
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Visualize questions
• Draw diagrams
• Annotate diagrams with numbers,
symbols, equations, etc.
• Find right equations from the reference
handbook
• Skip questions if you cannot quickly find
equations from the reference handbook
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Review Outline
• Basic fluid properties
• Capillary force
• Manometer
• Static pressure force
• Bouyant force
• Continuity equation
• Bernoulli equation
• Mass balance equation
• Venturi meter
• Head loss
• Forces on objects
• Fluid rotation
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CoOH
fluid
CoOH
fluidSG
4@24@2
==
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4 cosh
d
=
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Units and Scales of Pressure
Measurement
Standard atmospheric pressure
Local atmospheric pressure
Absolute zero (complete vacuum)
Absolute pressure
Gage pressure
1 std atmosphere
101.325 kPa
14.69 psi
10.34 m H20
760 mm Hg
Suction vacuum
(gage pressure)Local
barometer
reading
6894.76 Pa/psi (conversion factor)
abs gage local atmp p p= +Absolute pressures are often indicated as psia, and
gage pressure as psig. 10
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Fluid Statics•Pressure vs. elevation
•Manometers
•Force over submerged plane and
curved surfaces
•Buoyancy
P1
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1. In the following two cases, which case has higher total force acting
on the side wall?
(a) right side case (b) left side case (c) the same in both cases
d
d
1
2
d
d
2
1
(left) (right)
1
< 2
d
d
1d
2d+
1d
d
d
2d
2d+
1d
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2. What is the force at B if the tanks contain stationary oil at SG=0.7?
FA = 900 N
diameter = 20 cm
FB = ?
diameter = 30 cm
Oil
Oil1 m
3 m
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3. What is the gage pressure in the inverted jar?
50 cm
jar
air40 cm
air
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C.G. = Center of Gravity
C.P. = Center of Pressure
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12yc
bhI =
Area Moment of Inertia
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2
1
on the vertical projection
weight of fluid above W
h R
v
F F F
F F
= =
= = +
For curved surface, separate the pressure force into horizontal and
vertical part. The horizontal part becomes plane surface and the vertical
force becomes weight.
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4. The vertical force on the section ABC?
BWater
1m
A0.5m
C
1m into paper
B
A0.5m
B
1m
C
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5. Horizontal force on section ABC?
BWater
1m
A0.5m
C
1m into paper
BWater
1m
A0.5m
C
1.5m
hc
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6. What is the force on FB per 1 m into paper required to hold the gate?
B
Water2m
A
1m
FB
C (hinge)
B
0.5m
C
2m
hc
A
b
h
C.P.
C.G.
Fp
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submergedfluidbuoyancyF "= g
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7. A block-shape canoe has a 0.25 m draft shown empty. If a person of
150 kg mass is to sit inside, will the canoe (a) float (b) sink (c) neutral
(water will just reach the brim)?
2m
0.25m0.5m
1m
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The diameter of the pipe is 0.3 m.
Q=Av
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12. Calculate the density at B if the flow is steady state.
At A, diameter = 10 cm, velocity = 15 m/s, density = 1 kg/m3
At B, diameter = 18 cm, velocity = 6 m/s, density = ? kg/m3
A
B
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8. The velocity at A is 1 m/s. What is velocity at B if the flow is
incompressible and frictionless (no energy loss)?
6cm
7k Pa
0.5mWater
QA B
Mercury, SG=13.6
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9. The pipe centerline pressure just below the menometer (static tube) is
19k Pa (gage). How high will the liquid rise in the manometer tube?
h
density = 897 kg/m3
Q=5 m/s
A
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10. A Pitot/static tube inserted in a water flow as shown reads a static
pressure 50 mm(Hg) and a stagnation pressure 55 mm (Hg). What is
the water velocity?
QA B
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d1=5cm d2=1.8cm
Mass rate = 8 kg/sec
2 2
1 1 2 21 2
2 2
p V p Vz z
g g + + = + +
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14. A venture meter is used to measure flow velocity. Given the
manometer reading as shown below, what is the velocity at section A?
water
Diameter = 5 cmA B
70k Pa
100k Pa
Diameter = 10 cm
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zg
vp++
2
2
zp+
EGL: Energy Grade Line
(total head line)
HGL: Hydraulic Grade Line
(piezometric head line)
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Example EGL & HGL
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Moody Diagram
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13. Calculate the frictional head loss per 10 m of 30cm-diameter
concrete pipe (e = 0.5mm). The fluid is stand air at 15oC and velocity 4
m/s.
10m
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W Q h =
Turbine :
2 2
pump ,fitting turbine2 2
A A B BA B f f
p V p Vz h z h h h
g g + + + = + + + + +
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F>0 push object to right
F
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15. A horizontal nozzle sends out a water jet at 10 m/s towards the
vertical plate as shown. If the nozzle diameter is 1 cm, find the force F
required to hold the plate stationary.
F
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16. The cart is originally locked. Incompressible airflow passes through
the fixture as shown. Which way will the cart go if the wheels are
released?
(a) to the left (b) to the right (c) motionless
V2
V1
A2
A1
A1>A2
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2. Water flows at a steady rate through the horizontal shown. The following
data apply the figure. (a) What is V3? (b) What is the horizontal thrust on the
flange AB?
V1=3m/s
D1=0.5m
V3=?
D3=0.1m
V2=6m/s
D2=0.2m
p1=120kPa
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Dimensionless parameters
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Example
If a flow rate of sm /2.0 3 is measured over a 9 to1 scale model of a weir, what flow rate
can be expected on the prototype?
Flow over a weir is an openchannel flow. Use Froude number for modeling.
24332
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=====
mm
pp
m
p
m
p
m
p
p
p
m
m
lv
lv
Q
Q
l
l
v
v
gl
v
gl
v
If the model force is at 1000N, what will be the force on the prototype?
72993)(
)(22
22
22
2222===
=
m
p
m
p
pmlv
lv
F
F
lv
F
lv
F
Prototype
Model9
1
water
water
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Example
If a flow rate of sm /2.0 3 is measured over a 9 to1 scale model of a weir, what flow rate
can be expected on the prototype?
Flow over a weir is an openchannel flow. Use Froude number for modeling.
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mm
pp
m
p
m
p
m
p
p
p
m
m
lv
lv
Q
Q
l
l
v
v
gl
v
gl
v
If the model force is at 1000N, what will be the force on the prototype?
72993)(
)(22
22
22
2222===
=
m
p
m
p
pmlv
lv
F
F
lv
F
lv
F
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3. We wish to determine the wind force on a water tower when a wind normal to the
centerline of the water tower is 60 km/h. To do this we examine in a water tunnel a
geometrically similar model reduced by 1/20 scale. (a) What should the water tunnel
veoclity be if Reynolds number is used for dynamic similarity?
(b) If the force on the model is measured at 100 N, what is the projected force on
the prototype
(c) What is the expected ratio of torque about the base of the tower? i.e. prototype
torque /model torquePrototype
Model20
1
Wind
water
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17. Ignore the mass and friction of the sprinklers, which one spins
faster? The sprinkler nozzle diameters are identical. The velocity of the
jet are also identical.
(a) left one (b) right one (c) the same
left right
1m 1m 1m2m
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Additional Problems
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Structure BookmarksFE Review Course FE Review Course FE Review Course FE Review Course –Fluid Mechanics
Frank T.Frank T.Frank T.-C. Tsai, Ph.D., P.E.
Dept. of Civil & Environmental Engineering, LSUDept. of Civil & Environmental Engineering, LSU
[email protected]@[email protected]
(O) 578(O) 578-4246
Get the handbook!!Get the handbook!!Get the handbook!!Get the handbook!!
•••••REFERENCE HANDBOOK
•••9.4 Version for Computer-Based Testing
Figure
Visualize questionsVisualize questionsVisualize questionsVisualize questions
•••••Draw diagrams
•••Annotate diagrams with numbers, symbols, equations, etc.
•••Find right equations from the reference handbook
•••Skip questions if you cannot quickly find equations from the reference handbook
Review OutlineReview OutlineReview OutlineReview Outline
•••••Basic fluid properties
•••Capillary force
•••Manometer
•••Static pressure force
•••Bouyant force
•••Continuity equation
•••Bernoulli equation
•••Mass balance equation
•••Venturi meter
•••Head loss
•••Forces on objects
•••Fluid rotation
SectFigureFigure
SectFigureFigureFigureFigureFigure
SectFigure
SectFigure
SectFigure
Units and Scales of Pressure Units and Scales of Pressure Units and Scales of Pressure Units and Scales of Pressure Measurement
FigureFigureFigureFigureStandard atmospheric pressureStandard atmospheric pressureStandard atmospheric pressure
Local atmospheric pressureLocal atmospheric pressureLocal atmospheric pressure
Absolute zero (complete vacuum)Absolute zero (complete vacuum)Absolute zero (complete vacuum)
FigureFigureSpanAbsolute pressureAbsolute pressureAbsolute pressure
FigureFigureFigureSpanGage pressureGage pressureGage pressure
FigureFigureSpan1 1 1 stdatmosphere
101.325 101.325 kPa
14.69 psi14.69 psi
10.34 m H10.34 m H20
760 mm Hg760 mm Hg
FigureFigureFigureSpanSuction vacuumSuction vacuumSuction vacuum
(gage pressure)(gage pressure)
FigureFigureSpanLocal Local Local barometer reading
Figure6894.76 Pa/psi (conversion factor)6894.76 Pa/psi (conversion factor)6894.76 Pa/psi (conversion factor)
FigureAbsolute Absolute Absolute pressures are often indicated as psia, and gage pressure as psig.
SectFigureFluid StaticsFluid StaticsFluid Statics
••••Pressure vs. elevation
•••Manometers
•••Force over submerged plane and curved surfaces
•••Buoyancy
FigureSpanPPP1
SectFigureFigure
1. In the following two cases, which case has higher total force acting 1. In the following two cases, which case has higher total force acting 1. In the following two cases, which case has higher total force acting 1. In the following two cases, which case has higher total force acting on the side wall?(a) right side case (b) left side case(c) the same in both cases
FigureFigure
2. What is the force at B if the tanks contain stationary oil at SG=0.7?2. What is the force at B if the tanks contain stationary oil at SG=0.7?2. What is the force at B if the tanks contain stationary oil at SG=0.7?2. What is the force at B if the tanks contain stationary oil at SG=0.7?
FigureFigure
3. What is the gage pressure in the inverted jar?3. What is the gage pressure in the inverted jar?3. What is the gage pressure in the inverted jar?3. What is the gage pressure in the inverted jar?
Figure
SectFigureFigureFigure
SectFigureC.G. = Center of GravityC.G. = Center of GravityC.G. = Center of Gravity
C.P. = Center of PressureC.P. = Center of PressureC.P. = Center of Pressure
FigureArea Moment of InertiaArea Moment of InertiaArea Moment of Inertia
SectFigure
SectFigureFigureFor For For curved surfaceSpan, separate the pressure force into horizontal and vertical part. The horizontal part becomes plane surfaceand the vertical force becomes weight.
4. The vertical force on the section ABC?4. The vertical force on the section ABC?4. The vertical force on the section ABC?4. The vertical force on the section ABC?
FigureFigure
5. Horizontal force on section ABC? 5. Horizontal force on section ABC? 5. Horizontal force on section ABC? 5. Horizontal force on section ABC?
Figure
6. What is the force on F6. What is the force on F6. What is the force on F6. What is the force on FBper 1 m into paper required to hold the gate?
FigureFigure
SectFigureFigure
SectFigureFigureFigure
7. A block7. A block7. A block7. A block-shape canoe has a 0.25 m draft shown empty. If a person of 150 kg mass is to sit inside, will the canoe (a) float (b) sink (c) neutral (water will just reach the brim)?
Figure
SectFigureFigureThe diameter of the pipe is 0.3 m.The diameter of the pipe is 0.3 m.The diameter of the pipe is 0.3 m.
FigureQ=AvQ=AvQ=Av
12. Calculate the density at B if the flow is steady state. 12. Calculate the density at B if the flow is steady state. 12. Calculate the density at B if the flow is steady state. 12. Calculate the density at B if the flow is steady state. At A, diameter = 10 cm, velocity = 15 m/s, density = 1 kg/m3At B, diameter = 18 cm, velocity = 6 m/s, density = ? kg/m3
Figure
SectFigureFigure
8. The velocity at A is 1 m/s. What is velocity at B if the flow is 8. The velocity at A is 1 m/s. What is velocity at B if the flow is 8. The velocity at A is 1 m/s. What is velocity at B if the flow is 8. The velocity at A is 1 m/s. What is velocity at B if the flow is incompressible and frictionless (no energy loss)?
Figure
9. The pipe centerline pressure just below the menometer (static tube) is 9. The pipe centerline pressure just below the menometer (static tube) is 9. The pipe centerline pressure just below the menometer (static tube) is 9. The pipe centerline pressure just below the menometer (static tube) is 19k Pa (gage). How high will the liquid rise in the manometer tube?
Figure
10. A Pitot/static tube inserted in a water flow as shown reads a static 10. A Pitot/static tube inserted in a water flow as shown reads a static 10. A Pitot/static tube inserted in a water flow as shown reads a static 10. A Pitot/static tube inserted in a water flow as shown reads a static pressure 50 mm(Hg) and a stagnation pressure 55 mm (Hg). What is the water velocity?
Figure
SectFigureFigured1=5cmd1=5cmd1=5cm
d2=1.8cmd2=1.8cmd2=1.8cm
Mass rate = 8 kg/secMass rate = 8 kg/secMass rate = 8 kg/sec
Figure
14. A venture meter is used to measure flow velocity. Given the 14. A venture meter is used to measure flow velocity. Given the 14. A venture meter is used to measure flow velocity. Given the 14. A venture meter is used to measure flow velocity. Given the manometer reading as shown below, what is the velocity at section A?
Figure
SectFigureFigureFigureFigure
SectFigureFigureEGL: Energy Grade LineEGL: Energy Grade LineEGL: Energy Grade Line
(total (total (total head line)
HGL: Hydraulic Grade LineHGL: Hydraulic Grade Line
(piezometric (piezometric (piezometric head line)
Figure
SectFigureExample EGL & HGLExample EGL & HGLExample EGL & HGL
SectFigureFigureFigure
SectFigureMoody DiagramMoody DiagramMoody Diagram
Figure
13. Calculate the frictional head loss per 10 m of 30cm13. Calculate the frictional head loss per 10 m of 30cm13. Calculate the frictional head loss per 10 m of 30cm13. Calculate the frictional head loss per 10 m of 30cm-diameter concrete pipe (e= 0.5mm). The fluid is stand air at 15oC and velocity 4 m/s.
Figure
SectFigureFigureFigureFigureFigure
SectFigureFigureFigureFigureSpan272727
SectFigure
SectFigureFigureF>0 push object to rightF>0 push object to rightF>0 push object to right
F