CE415L Applied Fluid Mechanics Laboratory. Experiment: No. 5 Open Channel Flow Measurements and Grade Lines

Transcription

1 CE415L pplied Fluid Mechanics Laborator Experiment: No. 5 Open Channel Flow Measurements and Grade Lines Learning Objective Following the completion of this experiment and the analsis of the data, ou should be able to 1. Explain the process used to calibrate appropriate equations to measure open channel flow using the underflow gate, rectangular weir and cutthroat flume structures.. Identif appropriate calibration equations needed to measure open channel flow using the underflow gate, rectangular weir and cutthroat flume structures based on the test conditions., 3. Compute appropriate coefficients needed to calibrate equations to measure open channel flow using the flow measurement structures studied. 4. Recommend the flow rate range over which a predefined measurement accurac ma be expected for each of the three structures studied. 5. Determine and sketch the hdraulic and energ grade lines along the channel path. Introduction There are numerous methods used to measure flow in small open channels such as irrigation ditches, drainage canals, aqueducts, or sewage treatment plant channels. Man of the flow measurement methods tpicall utilize an underflow gate, weir or flume structure. We will work with small scale versions of these three structure tpes, and estimate the hdraulic and energ grade line effects at each structure. Purpose The primar purpose of this experiment is to learn how to determine the coefficients needed to calibrate three common tpes of open channel flow measurement structures. Then the coefficients determined experimentall will be compared against published values. In addition, using some of the data recorded will provide points to plot to construct a graph illustrating hdraulic and energ grade lines of the water flow as it flows through the measurement structures. Background 1. Underflow gate. n underflow gate is positioned above the bottom of the channel and water flows under the gate. The flow is both controlled and measured b varing the height of the gate bottom above the channel. The gate can be a flat metal (vertical or sluice gate) or curved plate (radial or tainter gate) or even be a tubular shape (drum gate). Free outflow exists when the water exits the gate as a jet flow in which the flow is supercritical. Where the downstream flow is restricted, the exiting water is drowned as it enters submerged below the downstream water surface level. Figure 5.1 shows a tpical underflow gate similar to the one used for this experiment. Equations used to estimate stream flowrates tpicall include a unit-less number called a 1 of 11 8//013

2 discharge coefficient. The discharge coefficient, Cd, is used to account for several factors that are difficult to determine analticall, including the viscous and surface tension of the flow and the height of the downstream fluid level vs. the height of the gate opening. The value of the discharge coefficient is derived experimentall and is primaril dependent on the exit conditions presented b the downstream fluid level. It is crucial to recognize that the discharge coefficient ou find experimentall will probabl onl be valid for similar downstream conditions. Two general tpes of downstream conditions are denoted as follows If the fluid exits the gate as a jet and is onl subject to atmospheric pressure then a free flow condition exists. If the fluid exits the gate submerged b tail water a drowned flow condition exists. Flow b Sections of flow to be analzed 1 3 pproximate shape of surface under drowned flow conditions 1 3 g Plan View Figure Underflow Gate Section - pproximate shape of surface under free flow conditions The equation of the discharge for the gate developed from Bernoulli s energ equation, customaril used where free flow conditions exist, is: Q Cd * * b g * 1 g (Eq. 5.1) Q Flow rate (ft³/sec) Cd Discharge coefficient (dimensionless) g Height of gate above channel bottom b Width of channel (ft, assumes gate width is the channel width) g cceleration due to gravit (3. ft/sec ) Height of head upstream of the gate 1 Note that this equation is similar in form to the orifice equations used elsewhere in hdraulics engineering. n alternate method used to approximate the flow rate where drowned outflow conditions exist uses a pair of equations (Eq. 5. and Eq. 5.3) that must be solved simultaneousl for Q and : of 11 8//013

3 Flow from section 1 to 1 Q Q gb 1 gb (Eq. 5.) Flow from section to 3 where Q Q 3 gb gb 3 (Eq. 5.3) = the submerged depth immediatel downstream of the gate = the height (head) of the minimum depth of free flow immediatel downstream of the gate, estimated to be Ccg (where Cc is assumed to be 0.61 for this experiment) 3 = the height (head) downstream of the gate after the hdraulic jump NOTE: Please sure to observe the relative height relationship between and 3. You ma need to use this as a constraint when ou solve Eq. 5. and Eq. 5.3 simultaneousl. The discharge coefficient will var with the height, 3, of the downstream fluid level.. Rectangular weir. weir is an obstruction placed on the channel bottom with the top extending verticall some distance from the bottom over which the stream must flow. The shape of the flow area in the plane of the weir plate is used to determine the tpe of weir being used: rectangular, triangular, and trapezoidal. Weirs ma be sharp-edged (sharpcrested), rounded, or broad-crested. Moreover, each weir tpe will have unique features and produce effects that make it more or less suitable for specific applications. rectangular weir, like the one used in this experiment is tpicall a structure constructed of concrete or other durable material with vertical upstream and downstream faces between which a flat and level surface forms an elevated plane that the water flows over. Rectangular weirs are easil duplicated and are generall used for flow rate measurement. However, each weir must be carefull calibrated for the expected flow rates since man factors create a complex analtical problem. weir in which the crest width (transverse to the water flow) is equal to the channel width is referred to as suppressed; if the crest width is less than the channel width it is called a contracted weir. Figure 5. shows a tpical suppressed rectangular weir similar to the one used for this part of this experiment. The rectangular weir can be used to measure relativel large flow rates compared to other weir tpes such as sharp-crested weirs. However, the accurac of flow rate measurements also depends on the ratio h 1 /L as summarized in Table of 11 8//013

4 weir crest.5h w L FLOW V 1 b h 1 h w nappe p Plan View Section - plunge pool depth Figure 5. - Suppressed Rectangular Weir Table 5.1 Rectangular weir classifications (Chin 006) /L /L<0.08 weir classification long-crested 0.08 /L 0.33 broad-crested /L >0.33 narrow or sharp crested flow condition Subcritical flow over the weir crest. Critical flow is near the middle of the weir crest. Critical flow location and length ma not be stable. flow rate measurement suitabilit The weir is of limited use for flow measurements. Variation of Cw with /L is small so reliable flow measurements can be made. Not stable enough for reliable measurements. For the rectangular weir used in this experiment the weir discharge equation is Q C w g * b*( H) 3 3 (Eq. 5.4) Q Flow rate (ft³/sec) g cceleration due to gravit (3. ft/sec ) b Width of channel (ft, assumes weir crest width is the channel width) H Total head over weir (see Eq. 5.5) Discharge coefficient (dimensionless) Cw The discharge coefficient, C w, is used to account for several factors that are difficult to determine analticall, including the viscous and surface tension of the flow, the height of the backwater level vs. the height of the weir as well as the ratio of h 1 /L. The weir discharge coefficient, C w, is primaril dependent on the total head (H, Eq. 5.5) of the water at the upstream face of the weir and includes the height of the water above the weir and the average approach velocit (V 1, Eq. 5.6). The total head is tpicall measured at a distance of about.5*h w upstream from the upstream face of the weir where the water surface profile is relativel level. 4 of 11 8//013

5 H h 1 V1 g (Eq. 5.5) V 1 Q b * (Eq. 5.6) Note that is the full depth of the water at the point where h 1 is measured. 3. Flumes. nother common method used to measure flow in open channels is with flumes. Flumes are structures placed or formed into the stream channel and work b forcing the fluid to accelerate as it passes through the tapered (width) constriction created b the flume structure. The constrictions ma narrow the channel, re-shape the slope of the channel bottom, or use a combination of both. B narrowing the channel or changing the bottom slope the water surface elevation following the constriction (the control point) falls relative to the elevation leading to the constriction which results in the flow changing from subcritical to supercritical flow. Flumes are frequentl used in channels for irrigation suppl and wastewater processing. few examples of flume shapes are shown in Figure 5.3. Some of the main advantages of flumes compared to weirs are that the head loss is less and flumes can be designed to pass sediment, which can help prevent clogging and periodic maintenance required for sediment removal. Certain design parameters of the flume must be carefull considered and designed to prevent the flume outflow from becoming submerged to ensure that the outflow remains supercritical. The practical importance of this is that as long as the water leaving the flume is at a lower elevation than at the entrance and is flowing at supercritical velocit, the tail water conditions (following the flume) will not have much effect on the head water elevation across the range of flow rates for which the flume is intended to operate. The flume used for this experiment is most like the cutthroat flume shown in Figure 5.4. The name denotes that it is similar to the Parshall flume (which is one of the most commonl used tpes) but the vertical profile changes through the throat bottom are cut off. It is sometimes used to save construction costs (compared to the Parshall flume) and where downstream conditions can be relied on to maintain supercritical flow immediatel following the flume. In our lab setup it is placed just before the vertical drop inlet at the end of the channel. Since the water surface elevation changes throughout the flume structure and for some distance before it, the water surface height,, should be measured at a distance of 0 to 30 times the width of the control point. Because of equipment space limitations, the flow rate through the flume will be calibrated using the water surface height at a point upstream of the flume entrance where the water surface is level. 5 of 11 8//013

6 Figure 5.3 Flume shape examples (USBR 1993) Subcritical Flow w Supercritical Flow X = 0W to 30W is recommended, but it ma not be practical for this experiment. Plan View control point h Section - Figure 5.4 Flume dimensions 6 of 11 8//013

7 Calculating the flow rate as a function of the water surface elevation, h 1, is relativel simple provided that the outflow is not submerged. The basic equation for a cutthroat flume with a control width of less than 1 foot is b Q a (Eq. 5.7) Q Flow rate (ft³/sec) a a constant, tpicall between 0.5 and.0 b a constant, tpicall between 1.0 and.0 depth of water entering the flume Outflow is considered submerged for flumes with a throat width of less than 1 foot if the ratio of the water surface elevation at the discharge is equal to or greater than 0.6 times the height of the water surface entering the flume. This should be checked during the experiment to ensure that the outflow is not submerged at an flow rate. 4. Hdraulic and Energ Grade Lines The water surface profile itself can be of interest in man engineering scenarios. For example, storm water (SW) and wastewater (WW) sewers are tpicall designed for gravit flows. Onl in special cases are the designed to properl function if the water becomes pressurized. The elevation of the water surface profile can be estimated at an point in the sstem b computing and plotting the hdraulic grade ine (HGL). The HGL includes the head (energ) due to the depth of the water in the pipe or conduit and the bottom of the pipe or conduit above the sstem datum elevation. To avoid allowing the water to become pressurized and thus creating problems in the gravit flow sstem, SW and WW sstem designers work to ensure that pipes are sized and aligned so the HGL does not reach the intrados or top of the inside of the pipe or above some distance below a manhole cover. If the velocit head component is added to the hdraulic grade line, the result is the energ grade line (EGL). The EGL can be used to keep track of total energ and energ losses in the sstem to avoid undesirable effects on the sstem. One such undesirable condition that can be caused b an excessivel low EGL would be where the velocit of the water carring solids slows to the point that the solids drop out and accumulate further reducing the capacit of the pipe. You should refer to the text book or other references for more discussion about HGL and EGL. Procedure Refer to the equipment manual for laout of the open channel demonstrator. The basic procedure is to perform the setup and make initial gate, weir, flume and channel measurements. Start the pump and wait until the flow rate and water surface elevations become stable. For each flow rate indicated b the inline flow meter, record the flowrate and the water surface elevations at each ke point for all three flow measurement structures. fter all data are recorded, complete the calculations to fill the tables, write the report and answer the questions. 7 of 11 8//013

8 1. djust the underflow gate opening to 5/8 ± 1/16 inch.. Be sure the rectangular weir and flume structures are firml anchored to the channel. 3. Measure channel, gate, weir and flume dimensions. 4. Full close (CW) the 1-1/ -inch globe and 3-inch globe valves. 5. Turn the main C and slope motor breakers ON. 6. djust the slope of the channel to be as near level as practical. 7. Turn the pump motor ON. Open the 1-1/ -inch globe valve full for the maximum flow rate. llow the channel flow to stabilize, this should take about one minute. Call this the 100% flow rate. 8. While waiting for the water surface elevations to stabilize, position the two ultrasonic fluid level meters to measure the water surface elevation upstream of the weir and upstream of the flume. Be sure to follow the suggested water surface measurement locations for the respective flow structures. 9. Once the water surface profile appears to be stable, measure and record the observed flow rate and water surface profile dimensions needed for each flow structure. 10. Photograph the profile of the water surface in the channel. Position the camera so that the photograph shows the surface of the headwater in the tank behind the gate near the left-hand edge of the picture and the flow exiting the flume is visible near the right-hand edge of the picture. It ma be helpful to include brightl colored objects to help identif those points in the photograph. 11. djust the flow rate b closing the 1-1/-inch valve incrementall. Make the adjustments so the indicated flow rate is at approximatel the 90%, 80%, 70%, 60%, 50%, 40%, 30% and 0% relative to the initial maximum flow rate (but do not use a flow rate less than 5 gpm due to measurement errors that ma occur in the flow meter). llow the channel flow to stabilize at each step before taking the water surface measurements. Since the flow meter updates at 5-second intervals, ou should wait 10 to 15 seconds after changing the flow rate before making measurements. 1. Repeat steps 9 and 11 until measurements at all the flow rates have been completed. The water profile photograph is onl needed for the highest flow rate case. 13. Drain water from the channel and dr the channel bottom below the ultrasonic level meters. Use the ultrasonic level meters to measure the distance (d1 and d in Table 5.) to the empt channel bottom. Record these measurements in the appropriate place in the data tables. Overall ou will have: Nine different flow rates and seven water surface elevation/height readings [Gate (1, g, 3), rectangular weir (, ), flume (, h)] for each flowrate, plus phsical dimensions of the structures and channel as required. 8 of 11 8//013

9 nalsis nalze our results as described below for each flow measurement structure. NOTE: You should NOT assume that variables or coefficients for two different structures having similar nomenclature are the same. s a rule, ou should stud the flow conditions at hand and compare them with trusted references for selecting appropriate nomenclature, equations, coefficients, etc. 1. Underflow gate. a) Based on the outflow conditions observed, determine which calculation method (Eq. 5.1 or Eq 5. and 5.3) that ou should use to compute the flowrate. Explain this decision process that adequatel justifies our choice of equations for the analsis. b) Based on our conclusion above, use the appropriate equation(s) to calculate the flowrate, Qcalc for each of the flowrates tested. (Hint: If ou chose to use Eq. 5.1 then ou will first need to compute a single value for Cd that will produce the least amount of error between our observed and calculated values. If ou chose Eq. 5. and 5.3 ou could develop an Excel worksheet that uses the Solver function.) c) Determine the range of flowrates over which our chosen calculation method would produce a calculated flowrate that are within 10 percent of the observed flowrate value.. Rectangular weir a) Compute the rectangular weir coefficient, Cw, b plotting Qobs vs. g * b * ( H) 3 3. Be sure that quantities for both plotted variables have the same unit of measurement. The slope of the linear trendline will be the Cw value. b) Compare our computed Cw value with a suitable reference (list the published value and the reference). How does our computed Cw compare to the published value? c) Compute the ratio h 1 /L and show the weir classification (Table 5.1) at each flow rate. d) ssuming the allowable error of the computed flowrate, computed as [(Qcalc_weir Qobs)/Qobsx100%] is less than 10%, is the computed Cw usable for the entire range of flow rates tested? State the usable flowrate range. 3. Cutthroat flume. a) Set up a spreadsheet to compute a calculated flow rate, Q calc, using Eq. 5.7 with assumed values for a single pair of coefficients a and b. t each flow rate set up a formula to calculate the difference (error) between the observed flow rate, Q obs, and the calculated flowrate Q calc. 9 of 11 8//013

10 b) Use the Solver feature in Excel to find a single pair of coefficients a and b that reduces the error to be as small as possible over the full range of flow rates. c) Determine if submerged flow conditions existed at an of the flow rates tested. If submerged conditions do exist in a particular flow rate range note this in our summar of results and in the analsis section. 4. Hdraulic and energ grade lines a) Set up a spreadsheet to compute the hdraulic and energ grade line heads at each of the water profile points recorded for the underflow, weir and flume structures. Report Please refer to the report requirements included in the sllabus and posted on the course website. References Chin, David. (006). Flow in open channels Hdraulic Structures Water resources engineering, nd Ed. Pearson Prentice Hall, Upper Saddle River, New Jerse, United States. (1993). Water Measurement Manual Third edition. Bureau of Reclamation, Department of the Interior. Washington, DC Table 5. - Raw Data Channel Width, b = ft Depth to channel bottom, d1 = in, d = in Observed Flow Rate Underflow Gate g = = ft Rectangular Weir hw= ft L= ft = ft Cutthroat Flume W = ft X = ft Qobs (gpm) Qobs (cfs) Sta = Sta = Sta = Sta = Sta = h h 10 of 11 8//013

11 Head (ft H O) 1.0 Hdraulic and Energ Grade Lines for Exp 5 Vaughn, Brent 8/11/ Station Energ Grade Line Hdraulic Grade Line Figure 5.5 Example plot and photograph of hdraulic and energ grade lines. 11 of 11 8//013