# Cee4476b Lecture 03 Annotated (2)

Description
Description:
Categories
Published

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
CEE 4476b Environmental Hydraulics Design Instructor: Dr. Andrew Binns Email: abinns2@uwo.ca Office: CMLP 1302 Phone: (519) 661-2111 ext. 88633 Week 2, Lecture 3 Monday, January 14, 2013  Alt-J CEE 4476b: Environmental hydraulics design Teaching assistants and office hours: ã   Phil Spencer: pspence3@uwo.ca   –   Office hours: Friday from 1-2pm (CMLP 1316) ã   Nadeem Ahmad: nahmad33@uwo.ca ã   Zoheb Nasir: znasir@uwo.ca  My office hours: ã   Tuesday from 12:30-1:30pm (CMLP 1302)  –   abinns2@uwo.ca    CEE 4476b: Environmental hydraulics design Today   s lecture ã   Specific energy  –   Definition ã   Specific energy diagram ã   Choke ã   Example Bakhmeteff (1932) ã   First introduced concept of specific energy E ã   Useful concept for solving open channel flow problems For a given approach flow ( V  1 , y  1  given), what is the depth y  2   after channel rise of ! z  ?  Specific energy Neglecting losses and applying the energy equation, we have:  z 1 +  y 1 + V  12 2 g =  z 2 +  y 2 + V  22 2 g    y 1 + V  12 2 g =  y 2 + V  22 2 g +  z Specific energy Combining the continuity equation:  y 1 + V  12 2 g =  y 2 + V  22 2 g +  z    y 1 + Q 2 2 gA 12 =  y 2 + Q 2 2 gA 22 +  z Removes an additional unknown ( V  2  ) Specific energy Combining the continuity equation:  y 1 + V  12 2 g =  y 2 + V  22 2 g +  z    y 1 + Q 2 2 gA 12 =  y 2 + Q 2 2 gA 22 +  z Removes an additional unknown ( V  2  )  y 1 ,  y 2 = discharge depths   Q =  discharge    A 1 ,  A 2 = cross-sectional area of flow  z =  z 2  #  z 1 = change in bottom elevation from section 1 to 2 Specific energy ã   From this equation, we can see that the sum of depth and velocity head must change by ! z  –   The change must result in an interchange between depth and velocity such that the energy equation is satisfied  y 1 + Q 2 2 gA 12 =  y 2 + Q 2 2 gA 22 +  z  Specific energy Definition: ã   Specific energy (E) = sum of depth and velocity head  –   Possible solutions of problem for depth depend on variation of specific energy with depth   Specific energy Definition: ã   Specific energy (E) = sum of depth and velocity head  –   There are actually two real solutions for the depth in this problem   Plot of depth ( y  ) versus specific energy ( E  ) clarifies which will prevail  Specific Energy Diagram    Specific energy ã   Specific energy can also be represented (defined) as the height of the energy grade line (EGL) as shown below  –    Above the channel bottom  –   Parallel to channel bottom in uniform flow  –   E   is constant in flow direction (until a change ! z  ) Specific energy ã   Note:  Total energy must remain constant or decrease, but specific energy E   can decrease or increase  Specific energy Definition: ã   Specific energy ( E  ) defined as:  E  =  y +   V  2 2 g    y = flow depth   V  = mean cross-sectional velocity     = kinetic energy flux correction Specific energy Assumptions: 1.   E   defined at cross-sections where flow is gradually varied  –   Free surface = Hydraulic Grade Line Specific energy Assumptions: 2.   Water surface and Energy Grade Line (EGL) are horizontal across cross-section  –   Therefore, a single value of V   corrected by !   suffices for entire cross-section Specific energy Assumptions: 3.   Slope is small such that y    !   d  –   If    (longitudinal slope of channel bed) is greater than 6 o , we have to make adjustments to our equation  p  = pressure W   = weight d   = flow depth y   = channel depth

Sep 10, 2019

#### SLB_Q311_Supp_102111

Sep 10, 2019
Search
Similar documents

View more...
Tags

## Continuum Mechanics

Related Search
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x