CE 356 Elements of Hydraulic Engineering Specific Energy (Alternate Depths) Hydraulic Jump (Sequent Depths) Energy in Open Channels hL v2/2g h y WS EGL HGL
v Channel Bottom 2 z 1 Datum V2 Q2 Head y z y z E z 2g 2 gA2 02/03/20
Specifi c Energ 2 Specific Energy, E E = energy (head) measured with respect to the channel bottom E = V2/2g + y = q2/(2gy2) + y Multiply through by y2 and arrange to find y3 E y2 + q2/2g = 0 What kind of equation is this? How many roots? Significance of roots? 02/03/20 3 Specific Energy Diagram
10.0 Rectangular channel: E=y 8.0 Q = 600 ft3/s. Depth (ft) B = 20 ft Fr = 1 6.0 4.0
Fr = 2 Fr = V/(gy)0.5 2.0 0.0 0.0 2.0 4.0 6.0 8.0 10.0 Specific Energy (ft) 02/03/20
4 Example: Sluice Gate q = 30 ft2/s y = 5.6 ft y = 1.8 ft 02/03/20 5 figure 1 Hydraulic jump Note that there is head loss in an hydraulic jump 02/03/20 6
jump Hydraulic jump on Rattan Creek, TX. July 2, 2002 strong jump: Fr > 9.0, rough wavy surface downstream steady jump: 4.5
8 picture 02/03/20 9 figure 2 02/03/20 10 jump cv Now lets consider an hydraulic jump We know that or
1 1 gA1y1 gA 2 y 2 v x1 Q v x 2 Q 2 2 can be written as rearranging and dividing by g: 1 Q2 Q2 g A1y1 A 2 y 2 2 A1 A2 Q2 A1y1 Q2 A 2 y 2
gA1 2 gA 2 2 Using A=By for a rectangular channel Q 2 By12 Q2 By 2 2 gB1 2 gBy 2 2 Lets go back to our hydraulic jump 02/03/20
12 solvable set Q2 By12 Q2 By 2 2 gB 2 gBy 2 2 If we have an open channel where we know Q, B, and y1, we can solve for y2 02/03/20
13 rectangular Starting from Q2 By12 Q2 By 2 2 gB 2 gBy 2 2 Recalling the definition of the flow rate per unit width we can obtain
Solving for y2 Q q B y12 y 2 2 q 2 1 1 2 2 g y 2 y1 y1 8q 2 y2 1 1 3 2 gy1 y1 solution is similar (see text) 02/03/20
14 limits Now, what are the limitations of this equation? y1 8q 2 y2 1 1 3 2 gy1 shear forces are neglected shear causes smaller head loss than turbulence in the jump requires jump occurs over a short distance rectangular channel
effect of gravity downslope is neglected again requires jump to occur over a short distance neglect non-hydrostatic pressure uniform density fluid 02/03/20 15 principle and what is the fundamental principle for this equation? y1 8q 2 y2 1 1 3 2 gy1
conservation of momentum 02/03/20 16 EM graphs 02/03/20 17 head loss The more general head loss formula is V12 h L E1 E 2 y1
2g V2 2 y 2 2g Valid for any cross section 02/03/20 18
Times New Roman Arial Stencil BT Swiss924 BT Symbol Default Design Microsoft Equation 3.0 Solid State Detectors- 5 Schedule Time - the fourth coordinate Using time TOF Time of Flight TOF E896 TOF Traditional Methods Scintillation TOF technology Timing with...
Lesson Ideas and Use Teachers share at open house to see writing growth of child store anecdotal notes/observation notes share ideas and entries with other teachers in the district to collaborate reflect on their teaching use it at professional developments...
FRICTION STIR WELDING Introduction Welding using friction as the major resource No filler material involved Welds created by, a) Frictional heating b) Mechanical deformation History Invented by TWI in 1991 in England 28 organizations worldwide use FSW Friction Welding Heat...
Like a tear it falls What is Haiku 2,3 The willow is like an etching, Fine-lined against the sky. The ginkgo is like a crude sketch, Hardly worthy to be signed. The willow's music is like a soprano, Delicate and...
The Coast Guard critical information list is accessible from CG portal. A threat is an adversary with intent and capability to target our critical information. A vulnerability is a weakness that provides an adversary the opportunity to exploit your critical...
Immunochromatography. Introduction. Immunochromatographic assays, also called lateral flow dipstick immunoassay or simply strip tests. Are simple devices intended to detect the presence (or absence) of a target analyte in sample (matrix) without the need for specialized and costly equipment. ...
Natural Resource-based Interactions Organizational Interaction NGOs and IPOs CDP 532: Unit 1 (e) NGOs Emergence after 1945, became prominent on various issues including environment after 1990s (so is in Nepal) Environment as a major theme of NGO world (along with...
Ready to download the document? Go ahead and hit continue!