7.7-Hydraulic and Energy Grade ..

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Hydraulic and Energy Grade Lines http://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771... 7.7 Hydraulic and Energy Grade Lines This section introduces the hydraulic grade line (HGL) and the energy grade line (EGL), which are graphical representations that show head in a system. This visual approach provides insights and helps one locate and correct trouble spots in the system (usually points of low pressure). The EGL, shown in Fig. 7.7, is a line that indicates the total head at e
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  7.7 Hydraulic and Energy Grade Lines This section introduces the hydraulic grade line (HGL) and the energy grade line (EGL), which are graphicalrepresentations that show head in a system. This visual approach provides insights and helps one locate andcorrect trouble spots in the system (usually points of low pressure).The  EGL , shown in Fig. 7.7, is a line that indicates the total head at each location in a system. The  EGL is relatedto terms in the energy equation by(7.38) Notice that total head  , which characterizes the energy that is carried by a flowing fluid, is the sum of velocityhead, the pressure head, and the elevation head. Figure 7.7  EGL and HGL in a straight pipe. The  HGL, shown in Fig. 7.7, is a line that indicates the piezometric head at each location in a system:(7.39)Since the HGL gives piezometric head, the HGL will be coincident with the liquid surface in a piezometer asshown in Fig.7.7. Similarly, the EGL will be coincident with the liquid surface in a stagnation tube. Tips for Drawing HGLs and EGLs 1. In a lake or reservoir, the HGL and EGL will coincide with the liquid surface. Also, both the HGL andEGL will indicate piezometric head. For example, see Fig. 7.7.2. A pump causes an abrupt rise in the EGL and HGL by adding energy to the flow. For example, see Fig.7.8. Hydraulic and Energy Grade Lineshttp://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...1 of 61/15/2009 12:44 AM  3. For steady flow in a Pipe of constant diameter and wall roughness, the slope (∆ h  L /∆  L ) of the EGL andthe HGL will be constant. For example, see Fig. 7.74.Locate the HGL below the EGL by a distance of the velocity head (α V  2 /2  g  ).5. Height of the EGL decreases in the flow direction unless a pump is present.6. A turbine causes an abrupt drop in the EGL and HGL by removing energy from the flow. For example,see Fig. 7.9.7. Power generated by a turbine can be increased by using a gradual expansion at the turbine outlet. Asshown in Fig. 7.9, the expansion converts kinetic energy to pressure. If the outlet to a reservoir is anabrupt expansion, as in Fig. 7.11, this kinetic energy is lost.8. When a pipe discharges into the atmosphere the HGL is coincident with the system because  p /γ = 0 atthese points. For example, in Figures 7.10 and 7.12, the HGL in the liquid jet is drawn through the jetitself.9. When a flow passage changes diameter, the distance between the EGL and the HGL will change (see Fig.7.10 and Fig. 7.11) because velocity changes. In addition, the slope on the EGL will change because thehead loss per length will be larger in the conduit with the larger velocity (see Fig. 7.11).10. If the HGL falls below the pipe, then  p /γ is negative, indicating subatmospheric pressure (see Fig. 7.12)and a potential location of cavitation. Figure 7.8  Rise in EGL and HGL due to Pump. Figure 7.9  Drop in EGL and HGL due to turbine. Hydraulic and Energy Grade Lineshttp://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...2 of 61/15/2009 12:44 AM  Figure 7.10 Change in HGL and EGL due to flow through a nozzle. Figure 7.11 Change in EGL and HGL due to change in diameter of pipe. Figure 7.12 Subatmospheric pressure when pipe is above HGL. The recommended procedure for drawing an EGL and HGL is shown in Example 7.6. Notice how the tips from pp. 233–234 are applied. Hydraulic and Energy Grade Lineshttp://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...3 of 61/15/2009 12:44 AM  EXAMPLE 7.6 EGL AD HGL FOR A SYSTEM A pump draws water (50°F) from a reservoir, where the water-surface elevation is 520 ft, and forcesthe water through a pipe 5000 ft long and 1 ft in diameter. This pipe then discharges the water into areservoir with water-surface elevation of 620 ft. The flow rate is 7.85 cfs, and the head loss in the pipe is given byDetermine the head supplied by the pump, h  p , and the power supplied to the flow, and draw the HGLand EGL for the system. Assume that the pipe is horizontal and is 510 ft in elevation.  Problem Definition Situation: Water is pumped from a lower reservoir to a higher reservoir. Find: 1. Pump head (in ft).2. Power (in hp) supplied to the flow.3. Draw HGL. Draw EGL. Properties: Water (50°F), Table A.5: γ = 62.4 lbf/ft 3 . Sketch:  Plan 1. Apply the energy equation 7.29 between sections 1 and section 2.2. Calculate terms in the energy equation.3. Find the power by applying the power equation 7.30a.4. Draw the HGL and EGL by using the tips given on p. 270.  Solution 1. Energy equation (general form) Hydraulic and Energy Grade Lineshttp://edugen.wiley.com/edugen/courses/crs2436/crowe9771/crowe9771...4 of 61/15/2009 12:44 AM
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