st venant equations l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
St Venant Equations PowerPoint Presentation
Download Presentation
St Venant Equations

Loading in 2 Seconds...

play fullscreen
1 / 13

St Venant Equations - PowerPoint PPT Presentation


  • 302 Views
  • Uploaded on

St Venant Equations. Reading: Sections 9.1 – 9.2. Types of flow routing. Lumped/hydrologic Flow is calculated as a function of time alone at a particular location Governed by continuity equation and flow/storage relationship Distributed/hydraulic

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'St Venant Equations' - bernad


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
st venant equations

St Venant Equations

Reading: Sections 9.1 – 9.2

types of flow routing
Types of flow routing
  • Lumped/hydrologic
    • Flow is calculated as a function of time alone at a particular location
    • Governed by continuity equation and flow/storage relationship
  • Distributed/hydraulic
    • Flow is calculated as a function of space and time throughout the system
    • Governed by continuity and momentum equations
distributed flow routing in channels
Distributed Flow routing in channels
  • Distributed Routing
  • St. Venant equations
    • Continuity equation
    • Momentum Equation

What are all these terms, and where are they coming from?

assumptions for st venant equations
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
Continuity Equation

Q = inflow to the control volume

q = lateral inflow

Rate of change of flow with distance

Outflow from the C.V.

Change in mass

Elevation View

Reynolds transport theorem

Plan View

continuity equation 2
Continuity Equation (2)

Conservation form

Non-conservation form (velocity is dependent variable)

momentum equation
Momentum Equation
  • From Newton’s 2nd Law:
  • Net force = time rate of change of momentum

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
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 equation11
Momentum Equation

Sum of forces on the C.V.

Momentum stored within the C.V

Momentum flow across the C. S.

momentum equation 2
Momentum Equation(2)

Local acceleration term

Convective acceleration term

Pressure force term

Gravity force term

Friction force term

Kinematic Wave

Diffusion Wave

Dynamic Wave

momentum equation 3
Momentum Equation (3)

Steady, uniform flow

Steady, non-uniform flow

Unsteady, non-uniform flow