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
Basic Principles
1.Mass Balance (Continuity Equation)
2.Momentum Balance (Force Balance)
3.Energy Balance
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
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