Basic Environmental Technology Water Supply Waste Management and
Basic Environmental Technology Water Supply, Waste Management, and Pollution Control SIXTH EDITION CHAPTER 2 Hydraulics Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -1 Pressure at point A equals pressure at point E because these points are at the same depth in the water. Likewise, the hydrostatic pressures at points B, C, and D are equivalent. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -2 Pressure measured with reference to standard or normal atmospheric pressure is called gage pressure. Gage pressure can have a negative sign when it is less than atmospheric pressure. Absolute pressure is always positive. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -3 Hydrostatic pressure at a point depends on the depth of water above the point, but not on the water surface area or volume. Note that the pressure at the bottom of tank (b) is the same as the pressure at the bottom of (c). Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -4 Illustration for Example 2 -1. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -5 Illustration for Example 2 -2. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -6 Illustration for Example 2 -4. When the valve is open, the water will rise in the vertical pipe to a certain height h that depends on the pressure in the tank. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -7 A piezometer tube offers a simple means for determining pressure by direct measurement of the corresponding pressure head. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -8 A well-type mercury manometer is more practical than a piezometer tube for measuring pressures in most hydraulic systems. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -9 Simplified cutaway view of a Bourdon pressure gage; the internal hollow tube uncurls as pressure is applied, thereby moving a pointer on the scale. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -10 A schematic example of a pressure transducer that converts pressure into a proportion a electrical signal. When the reference pressure is atmospheric, a gage pressure is displayed. Pressure differences between two points in a system can also be measured. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -11 For an incompressible fluid, such as water or sewage, the volume flow rate Q is constant at any section of the pipeline. Because Q = A ✕ V, when the flow area A is constricted, the velocity V of flow must increase. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -12 Illustration for Example 2 -10. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -13 Because the velocity and kinetic energy of the water flowing in the constricted section must increase, the potential energy must decrease (from the law of energy conservation). This is observed as a pressure drop in the constriction. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -14 The hydraulic grade line, or HGL, is a graph of the pressure head above the pipe centerline. Its downward slope in the direction of flow shows pressure loss due to friction. (A free water surface is on the HGL. Note also that p 1 = ϒh 1 and p 2 = ϒh 2. ) Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -15 A nomograph that provides a graphical solution to the Hazen–Williams equation for water flowing in circular pipes under pressure, with C = 100. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -16 A venturi meter can be installed in a pipeline to measure the flow rate. The difference between the pressure in the throat of the venturi and that in the upstream section can be converted to discharge, using Bernoulli’s equation. (Reprinted with permission from Operation of Wastewater Treatment Plant, 2 nd ed. , MOP No. 11, Copyright © 1976. Water Environment Federation, Alexandria, VA. www. wef. org. ) Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -17 Schematic diagram of a Pitot tube, a simple device that can be used to measure flow velocity. The velocity is proportional to the square root of the height of water in the tube. (v = √ 2 gh and Q = A × V) Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -18 In steady uniform open channel flow, the slope of the water surface, or HGL, is equal to the slope of the channel bottom. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -19 Any flow that occurs with a free surface exposed to atmospheric pressure is open channel flow, whether it occurs in a surface stream or in an underground pipe. ( Note: ▽ indicates a free surface. ) Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
TABLE 2 -1 Manning Roughness Coefficients Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -20 Illustration for Example 2 -16. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -21 Manning’s nomograph for circular pipes flowing full. Manning’s equation is used for open channel or gravity flow, whereas the Hazen–Williams equation is used for flow under pressure. (Adapted from U. S. Bureau of Public Roads. ) Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -22 crown. A partial-flow diagram for a circular pipe that carries flow with the water surface below the pipe Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -23 flow. Side view of a sharp-crested weir, a simple device used for measuring open channel or stream Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -24 notch weir. Commonly used weir shapes include (a) the contracted rectangular weir and (b) the triangular V- Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -25 Discharge nomograph for Cipoletti weirs. (Courtesy of Public Works Magazine. ) Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -26 A Parshall flume is often used to measure flow rate in an open channel that carries sewage; discharge is related to the head or depth of water just upstream of the constricted flume section. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
Figure 2 -27 A typical Palmer–Bowlus flume installation. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -28 The flow in an open channel versus the specific energy of flow. The critical depth occurs when the specific energy is minimum. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -29 critical depth. Examples of flow profile classifications. Here, ya is the actual depth and yc is the calculated Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -30 In a hydraulic jump, the flow suddenly changes from supercritical to subcritical, and the depth of flow increases over a short segment of the channel. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -31 The location of the hydraulic jump below a dam must be determined in order to design the apron. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -32 Illustration for Problem 3. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
FIGURE 2 -33 Illustration for Problem 9. Basic Environmental Technology, Sixth Edition Jerry A. Nathanson | Richard A. Schneider Copyright © 2015 by Pearson Education, Inc. All Rights Reserved
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