Brad Peterson, P.E.

SFRIDAYS – 14:00 to 15:40

FRIDAYS – 16:10 to 17:50

CLASS INFO:CLASS INFO: Class Website: Class Website:

https://sites.google.com/site/njut2009fall/

Mr. Peterson’s Email Address: bradpeterson@engineer combradpeterson@engineer.com

CLASS SCHEDULECLASS SCHEDULE Lesson 1, Properties of Fluids, 2009 Sept 04 Lesson 2, Fluid Statics , 2009 Sept 11 Lesson 3, Hydrostatic Force on Surfaces , 2009 Sept 18 Lesson 4, Buoyancy and Flotation

L 5 T l ti d R t ti f Li id M Lesson 5, Translation and Rotation of Liquid Masses Lesson 6, Dimensional Analysis and Hydraulic Similitude Lesson 7, Fundamentals of Fluid Flow

L 8 Fl i Cl d C d it Lesson 8, Flow in Closed Conduits Lesson 9, Complex Pipeline Systems Lesson 10, Flow in Open Channels L 11 Fl f C ibl Fl id Lesson 11, Flow of Compressible Fluids Lesson 12, Measurement of Flow of Fluids Lesson 13, Forces Developed by Moving Fluids Lesson 14 Fluid Machinery Lesson 14, Fluid Machinery

Lesson 2 Fluid StaticsLesson 2, Fluid Statics1. Introduction 6. Vacuum and 1. Introduction2. Fluid Pressure3. Difference in

Atmospheric Pressure7. Absolute and Gage

PPressure4. Pressure Head

Pressure8. Barometers

Pi t d5. Pressure Variations in a Compressible Fluid

9. Piezometers and Manometers

Fluid

2 1 What is Fluid Pressure?2.1. What is Fluid Pressure?

Force acting against and distributed over a surfaceover a surface.

Force may be exerted by a solid, liquid or gasor gas.

Often, force is the weight of materialFl id i di tl b d th Fluid pressure varies directly by depth –very important consideration.

2 2 Fluid Pressure2.2. Fluid Pressure

Transmitted with equal intensity in all directionsdirections

Acts normal to any plane M d b i f f Measured by various forms of gages In this class, we refer to gage or relative

l th i t t dpressures unless otherwise stated.

2 2 Fluid Pressure (Cont)2.2. Fluid Pressure (Cont)Pressure (p) = force (F) divided by area (A)Pressure (p) force (F) divided by area (A)

2

F Np Pa 2pA m

2 3 Difference in Pressure2.3. Difference in Pressure

Difference in pressure at two points at different levels in a liquid is expresseddifferent levels in a liquid is expressed as:

2 1 2 1( )p p h h

(remember that = unit weight)

2.3. Difference in Pressure (cont)2.3. Difference in Pressure (cont)

2 1 2 1( )p p h h

If p1 is on a free surface and (h2 – h1) is

2 1 2 1( )p p h h

positive downward, then the equation becomes:

p hThese equations apply as long as γ is constant so applies to water and most ppliquids. Not to a gases.

2 4 Pressure Head2.4. Pressure Head Pressure Head (or just Head) is the Pressure Head (or just Head) is the

height of a column of fluid that will produce a given intensity of pressure, p g y p ,so:

p hp is rearranged to:

ph

2.5. Pressure Variations in a CCompressible Fluid Note that pressure variations in a Note that pressure variations in a

compressible fluid (normally a gas) are usually small because of the small unit yweight (γ)

2.6. Vacuum and Atmospheric Pressure Vacuum = space with less that atmospheric Vacuum space with less that atmospheric

pressure Atmospheric pressure refers to prevailing Atmospheric pressure refers to prevailing

pressure in the air around us At sea level standard atmospheric pressure At sea level, standard atmospheric pressure

is:101.3 , orp kPa760 of mercury, or

1 t h

ph mm1 atmosphere

Mercury BarometerMercury Barometer

Compute h for BarometerCompute h for Barometer

ph

101.3p kPa

Atmospheric pressure

2101 3 103 3 /kP kN 2101.3 103.3 /p kPa kN m

Compute h for Barometer (cont)Compute h for Barometer (cont):Compute

13.6Specific gravity of mercury = Remember,

weight of substance specific gravity = = weight of equal amount of water

= specific gravity weight of equal amount of water

313.6 9.79 /kN m = 3133.1 /kN m13.6 9.79 /kN m 133.1 /kN m

Compute h for Barometer (cont)Compute h for Barometer (cont)

ph

2

3

101.3 /p kN m3

2

133.1 /

101 3 / /

kN m

kN m

3101.3 / / 0.76 760133.1 /

kN mh m mmkN m

2 8 Barometers2.8. Barometers The device above is a basic barometer The device above is a basic barometer Measures atmospheric pressure Atmospheric pressure is sometimes Atmospheric pressure is sometimes

measured in mm of mercury and at sea level is 760mmlevel is 760mm

Varies slightly based on weather conditionsconditions

Varies inverse to elevation –atmosphereic pressure is lower at higheratmosphereic pressure is lower at higher elevations.

What if the apparatus is filled with Water?

C :101 3

hp kPa

Compute Atmospheric pressure

2

101.3

101.3 103.3 /

p kPa

p kPa kN m

Atmospheric pressure

p

No Change from Mercury Example

“Water” BarometerWater Barometer

Water

Compute h for Water in B ( )Barometer (cont)

:Compute 1.0

pSpecific gravity of water = Remember,

e e be ,

weight of substance specific gravity = = weight of equal amount of water

weight of equal amount of water

= specific gravity weight of equal amount of water

31 0 9 79 / 9 79kN

specific gravity weight of equal amount of water

= 3/kN31.0 9.79 / 9.79kN m = 3/kN m

Compute h for Water in B ( )Barometer (cont)

ph

2

3

101.3 /p kN m3

2

9.79 /

101 3 / /

kN m

kN m

3101.3 / / 10.39.79 /

kN mh mkN m

“Water” BarometerWater Barometer

10 310.3 m

Water

2.7. Absolute and Gage Pressure Absolute pressure is the lowest possible Absolute pressure is the lowest possible

pressure and Gage pressure uses atmospheric Gage pressure uses atmospheric

pressure as its base

0 101.3kPa Atmospheric pressure = 101.3kPaAbsolute pressure atmospheric pressure

101.3 101.3kPa kPa Gage pressure = atmospheric pressureGage pressure = absolute pressure

2.9. Piezometers and Manometers

Simple PiezometerSimple Piezometer

1 1m1.1m

For the Simple Piezometer above, calculate pressure at A

12 34kN3

12.34Weight of glycerin kNm

3

12.34Pr essure at A 1.1kNp h m 3

13.57 13 57

mkN kP2 13.57kPa

m

Problem 1Problem 1Determine the gage pressure in kPa at aDetermine the gage pressure in kPa at a

depth of 10.0 meters below the free surface of a body of water.y

Problem 1 LayoutProblem 1, Layout

Problem 1 SolutionProblem 1, Solution

39.79 /kN m Weight of water

p h

9 79 97 9kN kN3 2

9.79 97.910.0 97.9kN kNp m kPam m

Problem 2Problem 2Find the pressure at the bottom of a tankFind the pressure at the bottom of a tank

containing glycerin under pressure as shown in following figure.g g

Problem 2 LayoutProblem 2, Layout

Problem 2 SolutionProblem 2, Solution

50p hpressure at bottom =

2

505050

p hkNkPa

pressure at bottom =

2

12.34m

kNweight of glycerin = 3mweight of glycerin =

2 3 350 12.34 74.682 74.68kN kN kNp m kPa

2 3 3m m m

Problem 3Problem 3

(a) Find the elevation of the liquid surface in Piezometer A(b) The elevation of mercury in Piezometer B(b) The elevation of mercury in Piezometer B(c) The pressure at the bottom, Elevation 0

Problem 3 SolutionProblem 3, Solution

( ) Th li id i Pi A(a) The liquid in Piezometer A ill i h l iwill rise to the same elevation

as the top of the tank.

Problem 3 Solution (cont)Problem 3, Solution (cont)9.79( ) (0 72 )(1 7 )kNb h 3( ) (0.72 )(1.7 )

11 98

Ab p h mm

kN

2

2

11.98 11.98

/

kN kPam

k

2

3

11.98 / / 0.519(2.36 9.79 / )

AkN mh p

kN m

0.3 0.519 0.819TOTALh m

Problem 3 Solution (cont)Problem 3, Solution (cont)

( ) 0

3

( ) 11 98 (2 36 9 79 / )(0 3 )

A Bc p p pkPa kN m m

11.98 (2.36 9.79 / )(0.3 )18.9

kPa kN m mkPa

CLASS SCHEDULECLASS SCHEDULE Lesson 1, Properties of Fluids, 2009 Sept 04 Lesson 2, Fluid Statics , 2009 Sept 11 Lesson 3, Hydrostatic Force on Surfaces , 2009 Sept 18 Lesson 4, Buoyancy and Flotation

L 5 T l ti d R t ti f Li id M Lesson 5, Translation and Rotation of Liquid Masses Lesson 6, Dimensional Analysis and Hydraulic Similitude Lesson 7, Fundamentals of Fluid Flow

L 8 Fl i Cl d C d it Lesson 8, Flow in Closed Conduits Lesson 9, Complex Pipeline Systems Lesson 10, Flow in Open Channels L 11 Fl f C ibl Fl id Lesson 11, Flow of Compressible Fluids Lesson 12, Measurement of Flow of Fluids Lesson 13, Forces Developed by Moving Fluids Lesson 14 Fluid Machinery Lesson 14, Fluid Machinery

Vocabulary for Next WeekVocabulary for Next Week Hydrostatic force Horizontal component Hydrostatic force Plane Magnitude

p Curved Circumferentialg

Direction Sense

Tension Longitudinal

Intensity Center of gravity

Dams Stability

Moment of inertia Centroid

Uplift Sliding Resistance