FE Review Course Fluid Mechanics - Louisiana State University · 2020. 9. 28. · FE Review Course...

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FE Review Course Fluid Mechanics Frank T.-C. Tsai, Ph.D., P.E. Dept. of Civil & Environmental Engineering, LSU [email protected] (O) 578-4246 1

Transcript of FE Review Course Fluid Mechanics - Louisiana State University · 2020. 9. 28. · FE Review Course...

  • FE Review Course – Fluid

    Mechanics

    Frank T.-C. Tsai, Ph.D., P.E.

    Dept. of Civil & Environmental Engineering, LSU

    [email protected]

    (O) 578-4246

    1

    mailto:[email protected]

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  • Get the handbook!!

    • REFERENCE HANDBOOK

    • 9.4 Version for Computer-Based Testing

    2

  • 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

    3

  • 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

    ==

    5

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  • 4 cosh

    d

    =

    6

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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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  • 12

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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

    3

    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

  • 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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  • 47

  • Dimensionless parameters

    48

  • 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

    222

    =====

    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

    49

    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

    222

    =====

    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

  • 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

    51

  • Additional Problems

    52

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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

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