Presentation is loading. Please wait.

Presentation is loading. Please wait.

Columns of fluid Density Pressure Pressure variation with depth

Published byLora Patterson Modified over 6 years ago

Similar presentations

Presentation on theme: "Columns of fluid Density Pressure Pressure variation with depth"β€” Presentation transcript:

1 Columns of fluid Density Pressure Pressure variation with depth
Pascal’s principle Absolute pressure vs. gauge pressure Columns of fluid

2 Density Density 𝜌= π‘šπ‘Žπ‘ π‘  π‘£π‘œπ‘™π‘’π‘šπ‘’ = π‘š 𝑉 Symbol β€œrho” ρ Mass kg Volume m3
Density kg/m3 Table 10-1 Example 10-1

3 Densities of materials
π‘˜π‘” π‘š 3 =1000βˆ™ 𝑔 π‘π‘š 3 Compare solids, liquids, gasses

4 Density calculation Show dimensional analysis
𝐼𝑓 𝜌= π‘šπ‘Žπ‘ π‘  π‘£π‘œπ‘™π‘’π‘šπ‘’ π‘‘β„Žπ‘’π‘› π‘šπ‘Žπ‘ π‘ =πœŒβˆ™π‘£π‘œπ‘™π‘’π‘šπ‘’ Show dimensional analysis

5 Pressure Pressure P= πΉπ‘œπ‘Ÿπ‘π‘’ π΄π‘Ÿπ‘’π‘Ž = 𝐹 𝐴 Symbol P (capital) Force Newtons
Area m2 Pressure N/m2 = Pascals = Pa (small often use kPa) Example 10-2 Same units as stress - Problem 9-39

6 Pressure variation with Depth
Weight of column of water (fluid) π‘Šπ‘’π‘–π‘”β„Žπ‘‘=π‘šπ‘”=πœŒπ‘‰π‘”=πœŒπ΄β„Žπ‘” π‘ƒπ‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’= π‘€π‘’π‘–π‘”β„Žπ‘‘ π‘Žπ‘Ÿπ‘’π‘Ž =πœŒπ‘”β„Ž Pressure increases with depth Old sub movies! (Das Boat, Red October, K-19, U-571) Always scene where they approach β€œcrush depth” A h ρghA P = ρgh

7 Properties of pressure
Pressure pushes equally all directions. Perpendicular to surface restraining it. Equal at common depth

8 Example 1– swimming pool (w/o air pressure)
Pressure at 2.0 m 𝑃=πœŒπ‘”β„Ž = (1000 π‘˜π‘” π‘š 3 )(9.8 π‘š 𝑠 2 )(2 π‘š) =19,600 π‘˜π‘” π‘š 𝑠 2 π‘š 2 =19,600 𝑁 π‘š 2 =19,600 π‘ƒπ‘Ž=19.6 π‘˜π‘ƒπ‘Ž Total Force on bottom 𝐹=π‘ƒβˆ™π΄= 19,600 𝑁 π‘š π‘š βˆ™8.5 π‘š =3.655 βˆ™ 𝑁 Same pressure on bottom and sides If you add air pressure on top of pool, both go up!

9 Absolute and gauge pressure
Add atmospheric pressure on top of water column π΄π‘π‘ π‘œπ‘™π‘’π‘‘π‘’ π‘ƒπ‘Ÿπ‘’π‘ π‘ π‘ π‘’π‘Ÿπ‘’= 𝑃 π‘Ž +πœŒπ‘”β„Ž πΊπ‘Žπ‘’π‘”π‘’ π‘ƒπ‘Ÿπ‘’π‘ π‘ π‘’π‘Ÿπ‘’=πœŒπ‘”β„Ž 𝑃 π‘Ž =1.013βˆ™ π‘ƒπ‘Ž =101.3 π‘˜π‘ƒπ‘Ž Sea level air pressure around 100 kPa Everything has kPa acting on it inside and out, we’re usually just interested in differences! Pa h ρghA + PaA P = ρgh + Pa

10 Not even half air pressure!

11 Example 2– swimming pool with air pressure
Pressure at 2.0 m 𝑃=πœŒπ‘”β„Ž = 𝑃 𝐴 +(1000 π‘˜π‘” π‘š 3 )(9.8 π‘š 𝑠 2 )(2 π‘š) =101,300 π‘ƒπ‘Ž+ 19,600 π‘˜π‘” π‘š 𝑠 2 π‘š 2 =120,090 π‘ƒπ‘Ž =121 π‘˜π‘ƒπ‘Ž Total Force on bottom 𝐹=π‘ƒβˆ™π΄= 121,090 𝑁 π‘š π‘š βˆ™8.5 π‘š =22.6 βˆ™ 𝑁

12 Various units of pressure
We always use Pascals (Pa or kPa)

13 Pascal’s Principle External pressure distributed uniformly at uniform depth. Pressure is same at common level. Thus Fin/Ain = Fout/Aout (if A small F small). Hydraulic lift. (make up example) 𝐹 𝑖𝑛 𝐴 𝑖𝑛 𝐹 π‘œπ‘’π‘‘ 𝐴 π‘œπ‘’π‘‘ Pin Pout

14 Hydraulic Lift Since Pressures are same 𝐹 𝑖𝑛 𝐴 𝑖𝑛 = 𝐹 π‘œπ‘’π‘‘ 𝐴 π‘œπ‘’π‘‘
𝐹 𝑖𝑛 𝐴 𝑖𝑛 = 𝐹 π‘œπ‘’π‘‘ 𝐴 π‘œπ‘’π‘‘ 𝐹 π‘œπ‘’π‘‘ 𝐹 𝑖𝑛 = 𝐴 π‘œπ‘’π‘‘ 𝐴 𝑖𝑛

15 Columns of fluid 𝑃 π‘π‘œπ‘‘π‘‘π‘œπ‘š = 𝑃 π‘‘π‘œπ‘ +πœŒπ‘”β„Ž 2 cases
Top pressure + pressure of column must balance bottom pressure. 𝑃 π‘π‘œπ‘‘π‘‘π‘œπ‘š = 𝑃 π‘‘π‘œπ‘ +πœŒπ‘”β„Ž 2 cases If top open 𝑃 π‘π‘œπ‘‘π‘‘π‘œπ‘š = 𝑃 π‘‘π‘œπ‘ π‘Žπ‘›π‘‘ β„Ž=0 If top closed 𝑃 π‘π‘œπ‘‘π‘‘π‘œπ‘š =πœŒπ‘”β„Ž β€œbalance” column of water Finger on the straw trick Ptop Pbottom ρgh

16 Column of water Calculate maximum height of column of water balanced in a closed straw, when bottom is open at normal air pressure 𝑃 π‘π‘œπ‘‘π‘‘π‘œπ‘š = 𝑃 π‘‘π‘œπ‘ +πœŒπ‘”β„Ž 1.013βˆ™ 𝑁 π‘š 2 =(1000 π‘˜π‘” π‘š 3 ) (9.8 π‘š 𝑠 2 ) β„Ž β„Ž= 1.013βˆ™ 𝑁 π‘š 2 (1000 π‘˜π‘” π‘š 3 ) (9.8 π‘š 𝑠 2 ) β„Ž=10.5 π‘š Ptop Pbottom ρgh

17 That’s where 760 mm mercury comes from!
Column of mercury Calculate maximum height of column of mercury (denser) balanced in a closed tube, when bottom is open at normal air pressure 𝑃 π‘π‘œπ‘‘π‘‘π‘œπ‘š = 𝑃 π‘‘π‘œπ‘ +πœŒπ‘”β„Ž 1.013βˆ™ 𝑁 π‘š 2 =( π‘˜π‘” π‘š 3 ) (9.8 π‘š 𝑠 2 ) β„Ž β„Ž= 1.013βˆ™ 𝑁 π‘š 2 ( π‘˜π‘” π‘š 3 ) (9.8 π‘š 𝑠 2 ) β„Ž=0.760 π‘š=760 π‘šπ‘š That’s where 760 mm mercury comes from! Ptop Pbottom ρgh

18 β€œBalancing” column of fluid
Balancing water with straw m Water Barometer Torricelli Mercury Barometer

19 Example – Problem 16 Equate pressure along line a---b

20 Example – Problem 16 (cont)
Pressure at (a) 𝑃 π‘Ž = 𝑃 π‘œ + 𝜌 π‘œπ‘–π‘™ 𝑔 (0.272 π‘š) Pressure at (b) 𝑃 𝑏 = 𝑃 π‘œ + 𝜌 π‘€π‘Žπ‘‘π‘’π‘Ÿ 𝑔 βˆ’ π‘š Equating 𝜌 π‘œπ‘–π‘™ 𝑔 π‘š = 𝜌 π‘€π‘Žπ‘‘π‘’π‘Ÿ 𝑔 βˆ’ π‘š 𝜌 π‘œπ‘–π‘™ = βˆ’ π‘š 𝜌 π‘€π‘Žπ‘‘π‘’π‘Ÿ 𝜌 π‘œπ‘–π‘™ = βˆ’ π‘š π‘˜π‘” π‘š 3 =654 π‘˜π‘” π‘š 3

Download ppt "Columns of fluid Density Pressure Pressure variation with depth"

Similar presentations

Chapter 12 Forces & Fluids.

Chapter 12 Forces & Fluids.
PHYS 1441 – Section 002 Lecture #24 Wednesday, May 1, 2013 Dr. Jaehoon Yu Fluid and Pressure Pascal’s Principle Absolute and Relative Pressure Buoyant.

PHYS 1441 – Section 002 Lecture #24 Wednesday, May 1, 2013 Dr. Jaehoon Yu Fluid and Pressure Pascal’s Principle Absolute and Relative Pressure Buoyant.
Liquid and Atmospheric

Liquid and Atmospheric
Oct. 29, 2001 Dr. Larry Dennis, FSU Department of Physics1 Physics 2053C – Fall 2001 Chapter 10 Fluids.

Oct. 29, 2001 Dr. Larry Dennis, FSU Department of Physics1 Physics 2053C – Fall 2001 Chapter 10 Fluids.
Physics 102 Part II Thermal Physics Moza M. Al-Rabban Professor of Physics Fluids.

Physics 102 Part II Thermal Physics Moza M. Al-Rabban Professor of Physics Fluids.
Pressure in Fluid Systems

Pressure in Fluid Systems
Chapter 3: Forces in Fluids

Chapter 3: Forces in Fluids
Measuring Pressure. Atmospheric Pressure Recall: Caused by the weight of the air molecules above us. Typically 101.3 kPa or 101 300 Pa Measured using.

Measuring Pressure. Atmospheric Pressure Recall: Caused by the weight of the air molecules above us. Typically kPa or Pa Measured using.
Pgs. 317 - 342.  Calculate the pressure exerted by a fluid.  Explain Pascal’s Principle.  Calculate how pressure varies with depth in a fluid.

Pgs  Calculate the pressure exerted by a fluid.  Explain Pascal’s Principle.  Calculate how pressure varies with depth in a fluid.
Chapter 10: Fluids Three (common) phases of matter: 1. Solid: Maintains shape & size (approx.), even under large forces. 2. Liquid: No fixed shape. Takes.

Chapter 10: Fluids Three (common) phases of matter: 1. Solid: Maintains shape & size (approx.), even under large forces. 2. Liquid: No fixed shape. Takes.
PRESSURE OF A FLUID Barometer air pressure pressure = height of mercury column.

PRESSURE OF A FLUID Barometer air pressure pressure = height of mercury column.
Monday, Nov. 22, 2004PHYS 1443-003, Fall 2004 Dr. Jaehoon Yu 1 1.Density and Specific Gravity 2.Fluid and Pressure 3.Absolute and Relative Pressure 4.Pascal’s.

Monday, Nov. 22, 2004PHYS , Fall 2004 Dr. Jaehoon Yu 1 1.Density and Specific Gravity 2.Fluid and Pressure 3.Absolute and Relative Pressure 4.Pascal’s.
Advanced Physics Chapter 10 Fluids. Chapter 10 Fluids 10.1 Phases of Matter 10.2 Density and Specific Gravity 10.3 Pressure in Fluids 10.4 Atmospheric.

Advanced Physics Chapter 10 Fluids. Chapter 10 Fluids 10.1 Phases of Matter 10.2 Density and Specific Gravity 10.3 Pressure in Fluids 10.4 Atmospheric.
Warm-up Pick up the free response at the door and begin working on it.

Warm-up Pick up the free response at the door and begin working on it.
Static Fluids.

Static Fluids.
Pressure; Pascal’s Principle

Pressure; Pascal’s Principle
Physics 221 Department of Physics The Citadel Lecture Notes S. Yost November 17, 2008 Hydrostatics: Pressure and Pascal’s Law.

Physics 221 Department of Physics The Citadel Lecture Notes S. Yost November 17, 2008 Hydrostatics: Pressure and Pascal’s Law.
Chapter 10 Fluids. Units of Chapter 10 Phases of Matter Density Pressure in Fluids Atmospheric Pressure and Gauge Pressure Pascal’s Principle Measurement.

Chapter 10 Fluids. Units of Chapter 10 Phases of Matter Density Pressure in Fluids Atmospheric Pressure and Gauge Pressure Pascal’s Principle Measurement.
L 13 Fluids [2]: Statics οƒ  fluids at rest  More on fluids.  How can a steel boat float.  A ship can float in a cup of water!  Today’s weather Today’s.

L 13 Fluids [2]: Statics οƒ  fluids at rest  More on fluids.  How can a steel boat float.  A ship can float in a cup of water!  Today’s weather Today’s.
Fluids.

Fluids.

Similar presentations

Ads by Google