1. On a single graph using the same scale on both axes, plot specific energy, E (horizontal axis) against depth of flow, D 2. Identify critical depth, label the subcritical and supercritical regimes and indicate the energy loss 3. Add the two asymptotic lines of E = V2/2 g and E = D/n EN2314 Laboratory - Fluid Mechanics Experiment 1. PUMP CHARACTERISTICS [H&S: Slips/trips/falls, Legionella pneumophila, Electrocution, Stroboscope frequency] Introduction In the water industry, centrifugal pumps are designed to deliver a certain flowrate at a given elevation, overcoming friction along the way. However, the flowrate a pump is capable of delivering is dependent on the pressure it has to overcome in the piped system. For example, a pump will provide its maximum flow to a horizontal pipe, but if the end elevation increases, the resulting flow will be less; this relationship is non-linear. Also, the efficiency of the pump will vary, again non- linearly, depending on the head / flow combination, but it will peak at what is known as its Best Efficiency Point. Design therefore requires knowledge of pump characteristic curves - the relationship of head, flow and efficiency. Pumps are also used in combination, so an understanding of pump performance in series and parallel is also important. Theory Variables: g acceleration due to gravity [m/s²] H pressure head [m] η pump efficiency [%] N pump speed [rpm] P P₁ input power [W] Ро output power [W] 2202Te P2 delivery pressure [Pa] P3 delivery pressure [Pa] Q discharge [m³/s] density of water [kg/m³] torque [Nm] @ angular velocity [rad/s] P1 suction pressure [Pa] Pressure head, H [m]: H = Ap/pg Rotating body power (input), P, [W]: P₁ = T @ Where: Hydraulic power (output), Po [W]: ω= 2 π Ν / 60 Po=pg HQ Pump efficiency, ŋ [%]: Experimental procedure n = Po/Pi To start the equipment Check that the water level in the water vessel is between the Maximum and Minimum markers on the side of the vessel Check that the apparatus is connected to the electrical supply and that power is switched on 1) 2) 3) Open all valves V₁ to V5 4) Wait 20 seconds whilst the instrumentation auto tares 5) On first use or after a period of storage a. Switch in Pump 1 followed by Pump 2 and run for a minute or two to fill the system with water, flushing out all the air b. Check the water level in the vessel and top up if necessary c. Switch off Pump 2 then Pump 1. d. Close all valves to leave the system primed. Dr JD Millington 1 Cardiff University 3) 4) 5) 6) 1) 2) EN2314 Laboratory - Fluid Mechanics Experiment 1(a): Pump performance characteristics (single pump) P3 Water Vessel Flow Meter H Pump 2 P1 Figure 1. Single pump test set-up Table 1. Pump characteristics results table P2 Pump 1 OBSERVATIONS DATA CALCULATIONS Flow Pressure Pump Pump Flow Power Head Efficiency Rate Inlet Outlet Speed torque rate Input Output Q P1 P2 N T Q H Pin Pout l/m bar bar rpm Nm l/s M W W % 1.24 1.00 Set the valves on the apparatus for flow through Pump 1 only (see figure 1) and start the pump. On table 1, record flow meter reading (1/m), Pump 1 inlet pressure p₁ (bar), Pump 1 outlet pressure p2 (bar) and pump rotational speed (rpm). Typical initial values are Q = 81 l/m, p₁ = -0.18 bar, p2 = 0.35 bar, N = 2892 rpm, with T = 1.24 Nm for full flow. Close the delivery valve V5 to increase the outlet pressure in 0.1 bar steps on p2. Repeat steps 2 to 3 until valve V5 is nearly fully closed. Typical final values are Q = 18 l/m, p₁ = 0.00 bar, p2 = 1.4 bar, N = 2941 rpm, with T = 1.00 Nm for near-zero flow. Switch off Pump 1 and close all valves. Calculate torque at intermediate valve closures by assuming a uniform variation of torque between 1.24 Nm at maximum flow and 1.00 Nm at near-zero flow - refer to 'practicalities' section on page 5. Dr JD Millington 2 Cardiff University Experiment 1(b): Pumps in series Water Vessel P1 EN2314 Laboratory - Fluid Mechanics Flow Meter Figure 2. Pumps in series set-up P3 Pump 2 P2 Pump 1 Table 2. Pumps in series results table OBSERVATIONS CALCULATIONS Pressure Power Flow rate Flow rate Head Inlet Outlet Outlet output Q I/m P1 P2 P3 Q H Pout Bar bar bar l/s M W 1) 2) 3) 4) 5) Set the valves on the apparatus for flow through Pumps 1 and 2 in series (see figure 2) and switch on Pump 1 followed by Pump 2. On table 2, record flow meter reading (1/m), Pump 1 inlet pressure p₁ (bar), Pump 1 outlet pressure p2 (bar), and Pump 2 outlet pressure pз (bar). Typical initial values are Q = 81 l/m, p1 = -0.22 bar, p2 = 0.18 bar, p3 = 0.40 bar. Close the delivery valve V5 to increase the outlet pressure in 0.4 bar steps on p3. Repeat steps 2 to 3 until valve V5 is nearly fully closed. Typical final values are Q = 10 l/m, p₁ = 0.00 bar, p2 = 1.5 bar, p3 = 2.8 bar. Switch off Pump 2 then Pump 1 and close all valves. Dr JD Millington 3 Cardiff University 1) 2) 3) 4) 5) EN2314 Laboratory - Fluid Mechanics Experiment 1(c): Pumps in parallel Water Vessel P1 Flow Meter P3 Pump 2 Figure 3. Pumps in parallel set-up - P2 Pump 1 Table 3. Pumps in parallel results table OBSERVATIONS CALCULATIONS Pressure Power Flow rate Flow rate Head Inlet Outlet Outlet output Q I/m P1 P2 P3 Q H Pout Bar bar bar l/s m W Set the valves on the apparatus for flow through Pumps 1 and 2 in parallel (see figure 3) and switch on Pump 1 followed by Pump 2. On table 3, record flow meter reading (1/m), Pump 1 inlet pressure p₁ (bar), Pump 1 outlet pressure p2 (bar), and Pump 2 outlet pressure pз (bar). Typical initial values are Q = 118 l/m, p₁ = -0.08 bar, p2 = 0.82 bar, p3 = 0.63 bar. Close the delivery valve V5 to increase the outlet pressure in 0.2 bar steps on p3. Repeat steps 2 to 3 until valve V5 is nearly fully closed. Typical final values are Q = 21 l/m, p1 = 0.00 bar, p2 = 1.39 bar, p3 = 1.40 bar. Switch off Pump 2 then Pump 1. Dr JD Millington 4 Cardiff University EN2314 Laboratory - Fluid Mechanics Practicalities SI unit of flowrate = m³/s = 1000 l/s; divide flow in l/m by 60 to convert to l/s SI unit of pressure = Pa (= N/m²); 1 bar = 100,000 Pa To use the Stroboscope, set the flash rate to 2850 flashes per second and increase or decrease the flash rate until the pump impeller appears to be stationary. The pump's torque cannot be recorded, but it can be determined from data on the pump's information nameplate, which gives a power of 0.37 kW and a pump speed of 2850 rpm: T=P₁/w=30 P₁ / π N = 30 x 370 / (2850 x 3.141) = 1.24 Nm This value applies for the pump operating at full capacity for unrestricted flow; assume this will reduce to around 1.0 Nm at as flow tends to zero. Clockwise to close valves, anticlockwise to open (you should know this already!) Closed: Open: Submission (1 page limit) 1. Experiment 1(a): Calculate Q (l/s), H (m), Pin (W), Pout (W) and n (%). 2. Experiments 1(b) and (c): Calculate Q (I/s), H (m) and Pout (W). 3. 4. For experiment 1 (a), plot a graph of Q (horizontal axis) against H and η, and identify the Best Efficiency Point. On the same graph, plot a graph of Q against H for experiment 1 (b). 5. On the same graph, plot a graph of Q against H for experiment 1 (c). 6. Comment on the graphs (e.g. is the efficiency what you expect?), explain the relationship between multiple pump operation, estimate the values of Q when H = 0, explore any erroneous results. Recommended reading: + ○ Hydraulics OneNote Notebook Wk 9.1 ○ Section 11.7 of Understanding Hydraulics by Hamill (2011) Dr JD Millington 5 Cardiff University/n CIVL 321 LABORATORY Spring 2024 Laboratory Group Report Format Organization of Report: I. Title page (see sample) II. Laboratory description handout III. Results table IV. Graphs* V. Answers to questions* VI. Appendix a. Raw data sheet b. Complete set of sample calculations * as requested in handout General Instructions: 1) Report must be complete, neat, and legible. 2) All pages must be 81/2" x 11", and bound/stapled together in the correct order. The name of the person who prepared each page (except the Title page) must appear in the lower right corner. 3) All report content must be typed, with the exceptions of: 1) The sample calculations. These can be handwritten. 2) The raw data information may also be handwritten on the data sheet. 4) Results tables must be prepared in a spreadsheet program or equivalent with appropriate headings. The dimensional units for all displayed results must be clearly indicated. 5) The sample calculations must take one set of data and show each calculation required to generate the Results table, produce the graphs, and answer the questions (if applicable). All unit conversions must be shown and all calculations must carry at least three (3) significant digits. Sample calculations may be handwritten in pen or pencil – but they must be extremely neat. 6) Graphs must be prepared in a graphing program such as Excel or Matlab and follow accepted engineering practice as indicated below and shown in the example on the following page: a. b. C. d. e. f. g. Each graph must contain a meaningful title that describes its content. Coordinate axes must be appropriately scaled and have major gridlines. Coordinate axes must be labeled with words, symbols (if applicable), and proper units. Experimental data should appear as marker symbols without lines. If requested, x- and y- error bars should be indicated on each data point. Theoretical curves should appear as smooth lines without marker symbols. They should be clearly labeled to indicate they are theoretical results. Least-square curve fits (Trendlines) must be accompanied by the curve fit equation and R² value with at least three (3) significant digits shown. Multiple data sets on the same graph should be clearly identified through the use of labeling or a legend. Grading: The laboratory experiments reports are expected to be neat, succinct, and well written. Unless otherwise stated, all reports must be submitted at the beginning of the laboratory period following the performance of the experiment. Late reports will not be accepted. All students who contribute to the experiment and report will receive the same grade. Sample Title page Specify lab by group number, day, and time. Names listed in alphabetical order by last name Drag Coefficient Measurement of an Ogive-shaped Projectile in Subsonic Flow CIVL 321 Laboratory Spring 2024 California State University, Chico Lab Group #1, Thursday 2 pm Daniel Bernoulli Leonhard Euler William Froude Osborne Reynolds January 25, 2024 Drawdown (m) Sample Graphs & Tables Graphs have meaningful title, axis labels with proper units. Note that the titles tell me more than just "Drawdown vs. time", which I should know already just by looking at the axis labels. Clear legend, data as markers, theoretical as line, and at least 3 significant digits in regression equations. Tables have clear headings for each column with the dimensional units clearly specified. Values are listed with appropriate number of significant digits. 2 Line fit to drawdown at 80 m from well using log transformed time (first 4 data points removed) 1.8 1.6 drawdown (m) 1.4 1.2 1 0.8 0.6 drawdown (obs) Linear (drawdown (obs)) y=0.5912x+ 0.0865 R² = 0.9988 0.4 0.2 0 0 1 2 3 log time (min) Drawdown at 80 m from pumping well Time (min) Drawdown (meters) 2 1.8 0.5 0.16 1.6 1 0.18 2 1.4 0.24 3 0.27 1.2 4 0.47 1 Drawdown (obs) 5 0.50 0.8 Theis solution 7 0.57 0.6 10 0.68 20 0.84 0.4 30 0.96 0.2 50 1.06 0 100 1.29 0 200 400 600 800 1000 1200 Time (min) 200 1.46 500 1.68 1000 1.86

Fig: 1