CIVL 321 LABORATORY Fluid Mechanics Lab #7 Momentum Force of a Vertical Jet Spring 2023 Objective: To use the momentum equation to estimate the force exerted by a jet on a stationary target. You will investigate a range of jet velocities and compare the experimental results to predictions from the theoretical force equation. Procedure: 1. Become familiar with the operation of the "Impulse of a Jet" apparatus. Make sure that the force balance arm is balanced (level). 2. Prepare a blank data table using Excel or Word to record all the raw data. 3. The force Fm exerted on the plate by the jet is measured by use of a balance arm, which is scaled in inches from the pivot. The force is found from the following equation: where Fm measured force on the plate in lbs. Fm=0.2X X= distance of weight from the zero point in inches 4. The force on the plate is pre-set by sliding the weight to prescribed distances of 2 to 8 inches, one inch at a time (therefore you will measurements at 7 different forces). The water flow rate is adjusted with the gate valve until the force of the jet balances the weight for each setting. 5. The volumetric flow rate (discharge) of water is measured for each setting by timing an accumulated discharge weight of 100 lbs. with a stopwatch. Two, 100 lb. weight measurements will be taken for each force setting and the times compared. If the times do not compare favorably (within 1% of each other), another discharge measurement should be made. If the time falls below 1 minute, 200 lbs. should be used. Measure the water temperature at each force setting. 6. Estimate the uncertainty in X (ox) at each flow rate by sliding the balance arm weight to zero and then returning it to the balanced position. Do this several times to develop an estimate. Note that OFm = 0.20x. Material to be Included in Report in Addition to Normal Requirements: 1) The momentum equation in the Z direction can be written as: = EF, PQVout-pQvin Apply the momentum equation to a control volume on a flat target and a hemispherical target to derive equations: =3 = F. -pQvin -pQ²/A F. -2pQv=-2pQ²/A (la: flat) (1b: hemi) Where p is density of water, Q is the flow rate of water, and A is the cross-sectional area of the jet (note: Dye 0.375 inches). This equation assumes elevation differences in the control volume are negligible and that the velocity entering the control volume is the same as that leaving. 2) Plot the theoretical force and measured force versus flow rate for both the flat and hemispherical target on the same graph (for one of these targets you will only have theoretical force). Plot measured values as markers and theoretical results as lines. Include the (0,0) point to help identify trends. 3) Using estimated uncertainties in Fm and Q, add error bars to the measured values on the plot. 4) Plot the measured force versus the theoretical force, including the (0,0) point, and fit an equation to the measured values. 5) Based on the plots from parts 2 and 4 above discuss how efficiently this apparatus transfers fluid momentum into vertical force? 1 Scanned with CamScanner Djet 0.375 inches Hemi (inches) Flow rate and force measurements Slider Slider H₂O Weight Atı position uncertainty Temp (lb) (inches) Atz (s) (s) At3 if needed (s) Ataverage (s) 2 +0.1. 18.2°C 100 159 155 157 3 ±0.1 18.2°C 100 13F 131 131 ± 0.1 18.2°C 100 114 114 114 5 ±0.1 13.2°C 100 102 104 103 6 ±0.1 13.2% 100 10095 94 94.5 7 ±0.1 13.2% 100 89 87 વ 88 8 ± 0.1 13.2% 100 31 BD 80.5 Scanned with CamScanner LAB 7 Q 3 = VA Q 0 H 4 W.I W. T 8 0 EF₂ =pQV out-pQ Vin Flat: EF₂ = -pPQV P Q² =P A HEMI: EFz=-PQV-SQV =2PQV=-2PQ H HEY Hat EFZ Scanned with CamScanner/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 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