Eusebio Ingol Blanco, Ph.D. A.M.ASCE

Civil Engineering Program, San Ignacio de Loyola University

Universidad San Ignacio de Loyola

FC-CIV HIDRCANA: Channel Hydraulics Flow Mechanics Review

Outline

• Objective

• Motivation

• Review Fluid Mechanics

Objective

• Review the basic concepts of fluid

mechanics

• Recognize the various types of hydraulic

problems

Channel Hydraulics

Channel Hydraulics

Flow in pipes Open channel flow

Applications: Hydraulic structures design

Advance open channel flow, design of pipe

networks, etc.

Pumps

Motivation for Channel Hydraulics

• River Hydraulics and

• Water Resources

• Hydrodynamics

• Groundwater Hydraulics

• Etc.

River Hydraulics

Hydraulic Structures

Hydraulic Structures

Hydraulics and Water Resources

Hydrodynamics

Experimental Hydraulics

• Oregon State University Wave Research Laboratory

• Model-scale experimental facilities

– Tsunami Wave Basin

– Large Wave Flume

• Dimensional analysis (Chapter 7 ) is very important in designing a model experiment which represents physics of actual problem

A Review of Fluid Mechanics for Channel Hydraulics

What is a fluid?

• A fluid is a substance in the liquid or gaseous form

• Distinction between a solid and a fluid is made on the basis of the substance's ability to resist an applied shear stress that tends to change its shape. – Solid: can resist an applied shear by deforming.

Stress is proportional to strain

– Fluid: deforms continuously under applied shear. Stress is proportional to strain rate

F

A

F V

A h

Solid Fluid

Normal and Shear Stress

• Stress is defined as the force per unit area.

• Normal component called normal stress: – In a fluid at rest, the normal

stress is called pressure

• Tangential component called shear stress

dA

FsShearstres

dA

FssNormalstre

t

n

:

:

The No-Slip Condition

• No slip condition. A fluid in contact with a solid “sticks” to the surface due to viscous effects.

• The fluid property responsible for the no-slip and the development of the boundary layer condition is viscosity

• The flow region adjacent to the wall in which the viscous effects are significant is called the boundary layer.

• the no slip condition is responsible for the development of the velocity profile.

Classification of Fluid Flows

• Internal vs. External Flows

• Internal flows: flows in which the fluid is completely bounded by solid surface. e.g. flow in a pipe or duct

• Flows are dominated by the influence of viscosity throughout the flow field.

• External flows: flows in which the fluid is unbounded over solid surfaces. e.g. flow over a plate, sphere object.

• viscous effects are limited to boundary layers near solid surfaces and to wake regions downstream of bodies.

External flow over a tennis ball, and

the turbulent wake region behind.

Classification of Fluid Flows

• Compressible vs. Incompressible Flow

• Incompressible flow: density remains nearly constant throughout. The volume of each portion of fluid remains unchanged over the course of its motion.

• Liquids flows are typically incompressible

• Compressible flow: density changes of the fluid is significant

• Gas flows are often compressible, especially for high speeds

Classification of Fluid Flows

• Laminar vs. Turbulent Flow

• Laminar Flow: highly ordered fluid motion with smooth stream lines.

• Turbulent flow: highly disordered fluid motion (with high velocities characterized by velocity fluctuations and eddies.

• Transitional flow: a flow that alternates between laminar and turbulent.

Classification of Fluid Flows

• Reynolds number

DVDV

forcesVicous

forcesInertial avgavgRe

Laminar flow Re <2000

Transitional flow 2000 < Re <4000

Turbulent flowRe > 4000

1880, Osborne Reynolds

Classification of Fluid Flows

• Steady vs. Unsteady flow

• Steady Flow implies no change of properties, velocity, pressure, temperature, etc. at a point with time. Transient term in the N-S equation are zero:

• Unsteady flow fluid properties change at a point with time.

- Transient usually describes a starting, or developing flow.

- Periodic refers to a flow which oscillates about a steady

mean.

T1 = 2s

V1 = 3 m/s T2 = 5s

V2 = 3 m/s

Classification of Fluid Flows • Steady vs. Unsteady flow

• Unsteady flow fluid properties change at a point with time.

- Transient usually describes a starting, or developing

flow.

• Uniform vs. Non-Uniform flow

• Uniform flow, flow depth and velocity remain constant with location over a specific region.

• Non-Uniform flow, flow depth changes with distance in the flow direction (flow varied).

T1 = 2s

V1 = 3 m/s T2 = 5s

V2 = 4 m/s

Classification of Fluid Flows

• Steady Uniform Flow: conditions do not change with location in the stream and with time, eg. the flow of water in a pipe of constant diameter at constant velocity.

• Steady non-uniform flow: conditions change from point to point in the stream but remain constant with time

• Unsteady uniform flow: At a given instant (time), the conditions at every point are the same, but will change with time

• Unsteady non-uniform flow: Every condition of the flow changes from point to point and with time at every point.

System and Control Volume

• A system is defined as a quantity of matter or a region in space chosen for study.

• A closed system consists of a fixed amount of mass.

• An open system, or control volume, is a properly selected region in space.

• In chapeter 6, we'll discuss control volumes in more detail.

Density

• Density is defined as mass per unit volume

• In general depends on temperature and pressure.

• Liquids and solids are essentially, incompressible

substances, and the variation of its density with the

pressure is usually negligible.

V

m

VV

*lim

)/( 3mkgV

m

Specific Gravity

• Specific gravity (SG) or relative density is

defined as the ratio of the density of a substance

to the density of some standard substance at a

specified temperature (usually water at 4°C,

with H20= 1000 kg/m3)

SG=/H20

• SG is a dimensionless quantity

3/9790 mkgSG

liquid

water

liquidliquid

SG for water at 20 oC and 1 atm = 1

Specific Weight

• Specific Weight is defined as the weight per unit volume

• where g is the gravitational acceleration

• (e.g., @ 20 oC, 1 atm)

gwater = (998 kg/m3)(9.807 m2/s)

= 9790 N/m3

gair = (1.205 kg/m3)(9.807 m2/s)

= 11.8 N/m3

]/[]/[ 33 ftlbformNgg

?/ 3ftlbf

Density of Ideal Gases

• Equation of State equation for the relationship between pressure, temperature, and density.

• P v = R T

– Rn = universal gas constant = 8.314 kj/kmol . k

– M = molecular weight of the gas

– P is the absolute pressure, v is the specific volume, T is the thermodynamic temperature, R is the gas constant

MRRRTP n /,

Example 2-2

• Given: Natural gas

– Time 1: T1=10oC, p1=200 kPa

– Time 2: T2=10oC, p2=300 kPa

• Find: Ratio of mass at time 2 to that at time 1

– Ideal gas law (p is absolute pressure)

Source: example from lecture Dr. Daene McKinney, The University of Texas at Austin, USA

http://www.ce.utexas.edu/prof/mckinney/ce319f/assign.html

VRT

pVM

1

2

1

2

1

2

p

p

VRT

p

VRT

p

M

M

5.1200

300

1

2 kPa

kPa

M

M

Vapor Pressure and Cavitation

Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.

• Vapor Pressure, Pv , is defined as the pressure exerted by

its vapor in phase of equilibrium with its liquid at a

given temperature.

• If P drops below Pv, liquid is locally vaporized, creating

cavities of vapor.

• Vapor cavities collapse when local P rises above Pv.

• Cavitation is noisy, and can cause structural vibrations.

Coefficient of Compressibility

Universidad San Ignacio de Loyola Eusebio Ingol Blanco, Ph.D.

• The volume or density of a fluid changes with a change in its temperature or pressure.

• Fluids expand as T ↑ or P ↓

• Fluids contract as T ↓ or P ↑

• What flow properties do we need to relate volume

changes to changes in P and T?

– Coefficient of Compressibility

T T

P Pv

v

//

P

VV

Pk

For water k = 2.2 GPa,

1 MPa pressure change = 0.05%

volume change

Water is relatively incompressible In term of finite changes:

Example 2-3

• Given: Pressure of 2 MPa is

applied to a mass of water that

initially filled 1000-cm3 volume.

Take a K = 5x 109 Pa

• Find: Volume after the pressure is

applied.

• Solution:

3

3

3

9

6

600.999

400.01000

400.0

1000105

102

/

cmV

VVV

cm

cmPax

Pax

VK

pV

VV

pK

final

final

Coefficient of Compressibility

• What flow properties do we need to relate volume

changes to changes in P and T?

– Coefficient of Compressibility

– Coefficient of volume expansion

– Combined effects of P and T can be written as

1 1

P P

v

v T T

P T

v vdv dT dP

T P

In term of finite changes:

TT

VVB

// (at P constant)

Viscosity

• Viscosity of a fluid is measure of its resistance to motion. The tangential force per unit area is called shear stress, and is expressed for simple shear flow between plates (1D) as:

• Drag force is the force a flowing

fluid exerts on a body in the flow

direction. The magnitude of this

force depends, in part, on

viscosity

dy

du

Viscosity Newtonian fluids: Fluids for

which the rate of deformation

is proportional to the shear

stress.

Shear

stress

Shear force

coefficient of viscosity

Dynamic (absolute) viscosity

kg/m s or N s/m2 or Pa s

1 poise = 0.1 Pa s

The behavior of a fluid in laminar flow between two

parallel plates when the upper plate moves with a constant

velocity.

Viscosity

The rate of deformation (velocity gradient) of a

Newtonian fluid is proportional to shear stress, and

the constant of proportionality is the viscosity.

Variation of shear stress with the rate of

deformation for Newtonian and non-Newtonian

fluids (the slope of a curve at a point is the

apparent viscosity of the fluid at that point).

Kinematic Viscosity

m2/s or stoke

1 stoke = 1 cm2/s

Dynamic viscosity, in general,

does not depend on pressure, but

kinematic viscosity does.

For gases:

For liquids

Surface Tension

• Liquid droplets behave like small balloons

filled with the liquid on a solid surface, and the

surface of the liquid acts like a stretched elastic

membrane under tension.

• The pulling force that causes this tension acts

parallel to the surface and is due to the

attractive forces between the molecules of the

liquid.

• The magnitude of this force per unit length is

called surface tension (or coefficient of surface

tension) and is usually expressed in the unit

N/m.

• This effect is also called surface energy [per

unit area] and is expressed in the equivalent

unit of N m/m2.

Attractive forces acting on a liquid molecule at the

surface and deep inside the liquid.

Surface Tension

Stretching a liquid film with a U-shaped

wire, and the forces acting on the movable

wire of length b.

W = The work done during this stretching process

Capillary Effects

Capillary effect: The rise or fall of a liquid in a small-diameter tube inserted

into the liquid.

Capillaries: Such narrow tubes or confined flow channels.

The capillary effect is partially responsible for the rise of water to the top of tall

trees.

Meniscus: The curved free surface of a liquid in a capillary tube.

The contact angle for wetting and

nonwetting fluids.

Capillary Effects

The capillary rise of water and the

capillary fall of mercury in a small-

diameter glass tube.

The forces acting on a liquid column that

has risen in a tube due to the capillary

effect.

Capillary rise is inversely proportional to the

radius of the tube and density of the liquid.