The mass conservation implies that the same amount of water flows through the narrow and large tubes. In particular the same mass of water enters and leaves.

Slides:



Advertisements
Similar presentations
web notes: lect5.ppt flow1.pdf flow2.pdf.
Advertisements

Chapter 11 Fluids Mass Density DEFINITION OF MASS DENSITY The mass density of a substance is the mass of a substance divided by its volume: SI Unit.
Integration Relation for Control Volume
Lecture 15: Capillary motion
Physics 101: Lecture 25, Pg 1 Physics 101: Lecture 25 Fluids in Motion: Bernoulli’s Equation l Today’s lecture will cover Textbook Sections
Fluids Gases (compressible) and liquids (incompressible) – density of gases can change dramatically, while that of liquids much less so Gels, colloids,
MASS, MOMENTUM , AND ENERGY EQUATIONS
Continuity Equation Tutorial
Short Version : 15. Fluid Motion. Fluid = matter that flows under external forces = liquid & gas. solidliquidgas inter-mol forcesstrongestmediumweakest.
Experimental Thermo and Fluid Mechanics Lab. 4. Fluid Kinematics 4.1. Velocity Field 4.2. Continuity Equation.
Conservation Vector Review Mass Balance General Statement Simplifications The Control Volume A Useable Form Problems.
Fluid Flow 1700 – 1782 Swiss physicist and mathematician. Wrote Hydrodynamica. Also did work that was the beginning of the kinetic theory of gases. Daniel.
Module 3 Fluid Flow. Lesson 20 CONTINUITY EQUATION DESCRIBE how the density of a fluid varies with temperature. DEFINE the term buoyancy. DESCRIBE the.
Chapter 15B - Fluids in Motion
Eulerian Description • A finite volume called a flow domain or control volume is defined through which fluid flows in and out. • There is no need to keep.
Momentum. NEWTON’S LAWS Newton’s laws are relations between motions of bodies and the forces acting on them. –First law: a body at rest remains at rest,
Lecture 9 (1) Physics in Life Sciences Fluid flow in human body2.
R. Field 10/29/2013 University of Florida PHY 2053Page 1 Ideal Fluids in Motion Bernoulli’s Equation: The Equation of Continuity: Steady Flow, Incompressible.
Types of fluid flow Steady (or unsteady) - velocity at any point is constant. Turbulent flow - the velocity at any particular point changes erratically.
Chapter 11 Fluids. Density and Specific Gravity The density ρ of an object is its mass per unit volume: The SI unit for density is kg/m 3. Density is.
Fluids - Dynamics Level 1 Physics. Fluid Flow So far, our discussion about fluids has been when they are at rest. We will Now talk about fluids that are.
Energy Balance Equation
Chapter 11 Fluids.
Abj 3.1: Introduction to Motion and Velocity Field: Pathlines, Streamlines, and Streaklines Geometry of Motion Pathline Streamline No flow across a.
Physics 1B03summer-Lecture 13 Final Exam April 18 2 hours long – 30 MC questions Covers all material with approximately equal weight, up to and including.
Fluid Flow Steady - velocity at any point is constant. Steady flow is called streamline flow.
AOE 5104 Class 8 Online presentations for next class: –Kinematics 2 and 3 Homework 3 (thank you) Homework 4 (6 questions, 2 graded, 2 recitations, worth.
Lecture Outline Chapter 9 College Physics, 7 th Edition Wilson / Buffa / Lou © 2010 Pearson Education, Inc.
Subdivisions of matter solidsliquidsgases rigidwill flowwill flow dense dense low density and incompressible and incompressible compressible fluids condensed.
Fluids in Motion.
Ch 4 Fluids in Motion.
NNPC FSTP ENGINEERS Physics Course Code: Lesson 7.
Ice cube in a glass of water After the piece of ice melts: Water level, h ? Barge with steel beams:
Fluids.
Physics. Session Fluid Mechanics - 2 Session Objectives.
Momentum Equation and its Applications
Pressure in Fluid A fluid exerts pressure in all directions. At any point in a fluid at rest, the pressure is the same in all direction. The force due.
Shock waves and expansion waves Rayleigh flow Fanno flow Assignment
Chapter 8 Exergy: A Measure of Work Potential Study Guide in PowerPoint to accompany Thermodynamics: An Engineering Approach, 7th edition by Yunus.
Chapter 11 Fluids.
Chapter 8 Exergy: A Measure of Work Potential Study Guide in PowerPoint to accompany Thermodynamics: An Engineering Approach, 8th edition by Yunus.
FLUID FLOW STREAMLINE – LAMINAR FLOW TURBULENT FLOW REYNOLDS NUMBER.
Continuum Mechanics (MTH487)
Continuity Equation.
MASS AND ENERGY ANALYSIS OF CONTROL VOLUMES
Physical Principles of Respiratory Care
FLUIDS Pressure (P = F/A) The relationship is → P = Po + gh
Mass and Energy Analysis of Control Volumes
Chapter 8 Exergy: A Measure of Work Potential Study Guide in PowerPoint to accompany Thermodynamics: An Engineering Approach, 5th edition by Yunus.
Different types of flows and lines In fluid flow
Chapter 11 Fluids.
Fluid Mechanics Dr. Mohsin Siddique Assistant Professor
Chapter 5 The First Law of Thermodynamics for Opened Systems
Advanced Thermodynamics Exergy / Availability:
V 1. Conservation of Mass dz dy dx
Lecture no 13 &14 Kinetics & kinematics of fluid flow
Reminder: HW #10 due Thursday, Dec 2, 11:59 p.m.
FLUID MECHANICS LAMINAR AND TURBULENT FLOW.
FLUIDS IN MOTION The equations that follow are applied when a moving fluid exhibits streamline flow. Streamline flow assumes that as each particle in the.
© Laura Fellman, PCC Rock Creek Campus
The Kinetic theory Pressure
Applications of Bernoulli Equations
Fluid Mechanics Lectures 2nd year/2nd semister/ /Al-Mustansiriyah unv
Cutnell/Johnson Physics 7th edition Reading Quiz Questions
We assume here Ideal Fluids
4 CHAPTER The First Law of Thermodynamics: Control Volumes.
Ch. 4 The first law of thermodynamics: Control Volume
Physics 2 Chapter 9 Section 4.
FLUID MECHANICS ME-10 MODULE - 2 KINEMATICS OF FLUID FLOW Presented by: Ayush Agrawal (Asst. Professor) Civil Engineering Department Jabalpur Engineering.
Presentation transcript:

Part II: Application of the mass conservation principle in an incompressible fluid.

The mass conservation implies that the same amount of water flows through the narrow and large tubes. In particular the same mass of water enters and leaves the system. If the fluid is incompressible and all thermal fluctuations are small, the density is uniform in the system, it follows:

What is the typical velocity in the lake zurich ? http://www.rivermap.ch/ small cross section https://www.hydrodaten.admin.ch/fr/2099.html https://www.google.fr/maps/@47.3411488,8.5882158,12.79z?hl=fr Large cross section

48m 1.94km Calculate the typical Average flow rate: 101 m3/s 48m Let’s assume 5m depth. small cross section You can get the measurement from googlemaps Average depth: 50m Calculate the typical lake current velocity in the Zurichsee Large cross section 1.94km

1.94km We apply the mass conservation between the river and the lake: S1=240m2 50m S2=97’000m2 48m 1940m The velocity in the Limitat is Thus the velocity in the lake is typically: Or even quicker: 1.94km

An observation The water in the Limmat flows rapidly but in the lake it looks like it does not move ! small cross section https://www.youtube.com/watch?v=GYUZcLJLDZM Large cross section

A laboratory equivalent of the system small cross section 9.5cm 1.5mm Large cross section

The streamlines are curved tangent to the velocity at all points.

Streamlines The streamlines are curves tangent to the velocity at all points. The velocity component normal to a streamline is null If two streamlines crosses, the velocity at the intersection is zero

Streamlines Seeding the fluid with reflecting particles and using a laser to produce a light sheet, one can visualize 2D flows by tacking a picture with a shutter time, dt, long enough so that particles leaves a streak that represents a small displacement, dl, parallel to the local velocity. The exposure time has to be short enough so that the velocity remained constant both in direction and amplitude.

Streamtubes Streamtubes are volumes enclosed by the streamlines originating from an arbitrary surface. Since the walls of a streamtube are formed by streamlines, no particles can cross the wall.

Assuming we know Ua, Ub can be deduced from the mass conservation: Streamtubes Let’s choose a small dt over which the flow is quasi-steady, all the mass dm entering the tube during the time dt must exit the tube at the other end. It follows that for an incompressible fluid, the volume entering and living the tube must be the same. Assuming we know Ua, Ub can be deduced from the mass conservation: For an incompressible fluid, the velocity increases inversely proportional to the cross-section of a stream tube.

Blood flows

What is the flow rate of blood in the various blood vessels ? Vein system deoxygenated blood cells Artery system Oxygenised blood cells. Wikipedia Wikipedia

Can consider the blood as incompressible ?

Can consider the blood as incompressible ?

Very Large total cross section, small velocities Low velocity allow for more efficient osmosis processes, oxygen transfer!

Low velocity allow for more efficient osmosis processes, oxygen transfer!

Take away message: In an incompressible fluid the mass conservation is equivalent to volume conservation laws: