Lecture 32

Activities

• Read pages 12 to 17 from the lecture notes Lecture 32 - Flow in open channels - part IV (specific energy)
• Read pages 431 through 447 in your textbook, specifically
• Conditions for critical flow in a rectangular channel (pp. 434-435)
• Table 10.2, p. 437 - Subcritical, critical, and supercritical flow characteristics
• Section 10.13, pp. 442-444
• Sample Problem 10.8, pp. 444-446
• Table 10.3, p. 447, Occurrence of damming action

Basic Ideas

• Channel transitions occur in relatively short reaches so that energy losses are almost negligible along the transition
• Channel transitions typically occur in a flat surface, so we use the specific energy equation to solve problems (bed elevations, z, are out of the picture)
• Channel transitions include, among others:
• humps (changes in bed elevation)
• contractions or expansions (changes in bed width)
• entrance from a reservoir into a channel
• flow under gates
• Analysis presented in book and class notes applies mainly to rectangular channels - The observations shown below apply for subcritical flow upstream (section [1])
• Humps
• An local increase in bed elevation forces a dimple in the free surface
• The hump height, Δz, can increase until critical flow occurs over the hump. At this point, Δz = (Δz)_crit
• For Δz > (Δz)_crit the flow cannot be sustained at the original upstream depth, thus, the depth must increase (damming action)
• Online photographs of humps in channels
• Broad-crested weir (see photograph at bottom of page)
• Broad-crested weir in test flume (Korea)
• Small broad-crested weir in natural stream
• Large broad-crested weir near a dam (USDA)
• Contractions
• Contraction in a rectangular channel cause an increase in the unit flow rate, q = Q/b, and typically produce a drop in depth
• If the channel width continues to contract we reach critical flow for b = b_crit.
• For b < b_crit, the flow cannot be sustained at the original upstream depth, thus, the depth must increase (damming action again, also called "choking the flow")
• Online photographs of contractions in channels
• Flow around a bridge pier (channel contraction, Korea)
• Channel contractions (animations based on numerical simulations)
• Cutthroat flume (application of channel contractions in flow measurements)
• Entrance from reservoir into a channel
• Unknowns: Q (or q) and y (normal depth)
• Equations: Specific energy and Manning's
• Requires simultaneous solutions
• An example for trapezoidal cross-sections is given in Chapter 7 of the HP 49G+'s User's Guide (pdf file)
• No problems assigned for this case
• Flow under gates
• Gates are used to control flow out of canals
• Types of gates (sluice gates, tainter gates, drum gates)
• Assume no energy loss between sections upstream and downstream of the gate
• Equation can be used to solve for one of the depths or for the discharge if the depths are known
• Online photographs of gates
• Sluice gates on a river in Turkey
• Sluice gates on the River Tone -- with travelling toy monkey included
• Installing tainter gates
• Wikipedia: flood gates (includes tainter gates and drum gates)

Assignment

• See the Assignments page

Open channel flow video

• If you want to see the film of which we saw parts in the November 18 lecture visit this web site: IIHR INSTRUCTIONAL VIDEOS (from the Iowa Institute of Hydraulic Research) - Click on the link entitled Fluid Motion in a Gravitational Field.
• You can watch the video in a continuous feed when you click on the link, or you can download the video (220 MB) by following the instructions at the top of the web page (Basically, do a right click in the link and select Save Link As..).
• Be aware that downloading 220+ MB of video may take a few minutes with a high-speed connection, and an entire evening with a phone hook-up.
• There are other instructional videos in the web page that you may be interested in watching (e.g., Laminar and Turbulent Flow).
• The videos follow the book ELEMENTARY MECHANICS OF FLUIDS, by Prof. Hunter Rouse. This book, first published in 1945, and most recently reprinted by Dover Publications in 1977, is currently out of print.
• Professor Rouse also wrote books on history of hydraulics, namely:
• History of Hydraulics
• History of Hydraulics in the United States - 1776-1976

Maple applications in open channel flow

• Download a zip file with three Maple worksheets on open channel flow here
• Use Classic Worksheet Maple 10 to open these worksheets.
• Do not use the Maple 10 application.
• The worksheets were created using Maple 8. Some of the elements used in these worksheets are not supported in the new Maple 10 application. The application Classic Worksheet Maple 10 will open the worksheets without lost of content.
• The zip file contains a pdf document with simple instructions on using the Classic Worksheet Maple 10 application.
• The first worksheet deals with uniform flow in open channels
• Use of the Chezy equation combined with Coolebrook-White (borrowed from pipe flow) is presented for academic purposes
• Concentrate on the examples of Manning's equation presented in the worksheet mainly
• The second worksheet deals with specific energy applications in open channel flow (sections 10.9 - 10.13 in your textbook)
• It includes examples of gravity waves (including animations of surface waves) as presented in section 10.20 in your textbook -- we have not yet covered this section in class
• The third worksheet deals with momentum applications in open channel flow
• Forces on gates (see Chapter 6, section 6.4, in your textbook)
• Hydraulic jumps (see Section 10.18 in your textbook) -- we have not yet covered this section in class