Dr. Shahid Ali

PhD Hydraulic & Water Resource Engineering (Fluid Dynamics)

Technical University Delft, the Netherlands

MSc (Nuclear Engineering), PIEAS Nilore Islamabad , Pakistan

MSc (Hydraulic & Irrigation Engineering), UET Taxila, Pakistan

BSc ( Civil Engineering), UET Taxila, Pakistan

Course OutlinesINTRODUCTION

Introduction, Basic definitions

Flow Classification, Normal flow, Velocity Distribution in open channels

Pressure Distribution (Hydrostatic and Non hydrostatic),Froude number & Reynolds

number

BASIC PRINCIPLES

Reynolds transport theorem

Conservation of Mass, Momentum and Energy

UNIFORM FLOW

Flow in rectangular and Non-rectangular channels

Critical flow, Specific energy, Flow resistance

Computation of uniform flow, Normal depth in compound channel, Channel design

GRADUALLY-VARIED FLOW

The gradually-varied-flow equation, Finding the friction slope

Profile classification, Qualitative examples of open-channel-flow behavior

Numerical solution of the GVF equation

RAPIDLY-VARIED FLOW

Hydraulic jump and energy dissipation

Specific energy, Critical-flow devices, Rapidly varied flow computation

Visualization of hydraulic jump, Characteristic of flow over weirs

Flow over spillway, ogee weir, Flow around piers

Flow in converging and diverging channel section, Forces on objects

UNSTEADY FLOW

Definitions, Height and celerity of surge waves

Derivation St. Venant equations Shallow water wave

Kinematic wave theory, Diffusion wave theory

Hydraulic flood routing, Floodway and channel improvement

Introduction to Computational Hydraulics

software’sRIC-NaysSSIIMHEC-RAS

Recommended Textbooks

1. Chaudhry, M. H., 2008, Open-Channel Flow, 2nd Edition

2. Chanson, H., 2004, Hydraulics of Open Channel Flow: An Introduction, 2nd Edition

3. Akan, A., O., 2006, Open Channel Hydraulics, 1st Edition

4. Chow, V.,T., 1959, Open Channel Hydraulics, 1st Edition

5. Chadwick, A.J., Morfett, J.C., and Borthwick, M., 2013, Hydraulics in Civil and

Environmental Engineering, 5th Edition

6. Hamill, L., 2011, Understanding Hydraulics, 3rd Edition

Open Channel Flow

Typical Open Channel Shapes

Classification Of Flow Type

Basic Principles

1.Mass Balance (Continuity Equation)

2.Momentum Balance (Force Balance)

3.Energy Balance

Physical Processes

1. Diffusion

2. Convection/Advection

Distributed Flow routing in channels

Distributed Routing

St. Venant equations

Continuity equation

Momentum Equation

0

t

A

x

Q

0)(11 2

fo SSg

x

yg

A

Q

xAt

Q

A

Assumptions for St. Venant Equations

Flow is one-dimensional

Hydrostatic pressure prevails and vertical accelerations are

negligible

Streamline curvature is small.

Bottom slope of the channel is small.

Manning’s equation is used to describe resistance effects

The fluid is incompressible

Continuity Equation

dxx

QQ

x

Q

t

Adx

)(

....

.0scvc

dAVddt

d

Q = inflow to the control volume

q = lateral inflow

Elevation View

Plan View

Rate of change of flow

with distance

Outflow from the C.V.

Change in mass

Reynolds transport theorem

Continuity Equation

0

t

A

x

Q

0)(

t

y

x

Vy

0

t

y

x

Vy

x

yV

Conservation form

Non-conservation form (velocity is dependent

variable)

Momentum Equation

From Newton’s 2nd Law:

Net force = time rate of change of momentum

....

.scvc

dAVVdVdt

dF

Sum of forces on

the C.V.

Momentum stored

within the C.V

Momentum flow

across the C. S.

Forces acting on the C.V.

Fg = Gravity force due to weight of water in the C.V.

Ff = friction force due to shear stress along the bottom and sides of the C.V.

Fe = contraction/expansion force due to abrupt changes in the channel cross-section

Fw = wind shear force due to frictional resistance of wind at the water surface

Fp = unbalanced pressure forces due to hydrostatic forces on the left and right hand side of the C.V. and pressure force exerted by banks

Elevation View

Plan View

Momentum Equation

....

.scvc

dAVVdVdt

dF

Sum of forces on

the C.V.

Momentum stored

within the C.V

Momentum flow

across the C. S.

0)(11 2

fo SSg

x

yg

A

Q

xAt

Q

A

Momentum Equation

0)(11 2

fo SSg

x

yg

A

Q

xAt

Q

A

0)(

fo SSg

x

yg

x

VV

t

V

Local

acceleration

term

Convective

acceleration

term

Pressure

force

term

Gravity

force

term

Friction

force

term

Kinematic Wave

Diffusion Wave

Dynamic Wave

Momentum Equation

fo SSx

y

x

V

g

V

t

V

g

1

Steady, uniform flow

Steady, non-uniform flow

Unsteady, non-uniform flow

Thanks