Geology 550 Spring 2005 LAB 3: HYDRAULICS OF PRAIRIE CREEK Objectives: 1. To examine the distribution of velocity in a stream channel 2. To characterize the state of flow using dimensionless variables 3. To examine alternative ways of calculating boundary shear stress and flow resistance EXCEL Programs/Templates available: Discharge calculates Q from current-meter measurements Survey template for reducing cross-section or profile level survey data Velocity Profile template for calculating/plotting velocity profiles These files can be downloaded by pointing your browser to: www.humboldt.edu/~geodept/geology550/550_macros_templates_index.html Data needed: Prairie Creek: current-meter discharge measurements velocity profiles water-surface profile cross-sections These data can be downloaded by pointing your browser to: www.humboldt.edu/~geodept/geology550/550_datasets_index.html Please put all answers on the attached answer sheets. 1. CALCULATION OF DISCHARGE AT XSS 1 4 a. Use the attached data to calculate the water discharge, Q, at XSS 1 through 4. The method is described on the discharge handout. You may do it by hand, or use the data supplied online. The easiest method by far is to use the Excel DISCHARGE program I have supplied you. Run DISCHARGE, open the discharge data sheets, copy the tape distance, depth, revs, time data, and paste into the worksheet created by DISCHARGE. You will need to compute Q (discharge), w (top width), A ( cross-sectional area of flow), d (mean depth), and v (mean velocity). Remember that A Q d = v = w A Convert the resulting values to metric units also. b. Compare the discharges at XSS 1 through 4. Do they differ appreciably? What is the percent difference between the largest and the smallest values? Suggest probable causes for the differences and state which you think are the better estimates of the true discharge and why. Finally, decide on a "best estimate" of the discharge at the time of our visit.
2. COMPUTATION OF BOUNDARY SHEAR STRESS Use metric values in the following computations. You will have to convert the data I've given you. a. Use the water-surface profile data supplied with this lab (data and profile also online) to compute the mean water-surface slope in the vicinity of each cross section. I have plotted the water-surface profile for you using 200X vertical exaggeration. If you wish you can replot the data yourself. You will have to decide over what length to average the slope. You want to be sure that you use a long enough reach that you average out possible surveying errors. b. Use the mean depth at each section (determined from gaging measurements) to calculate the boundary shear stress, τ o. Remember, τ ο = γds o γ = 9810 N/m 3 c. The velocity profile measurements at each cross-section are given in the data tables accompanying this lab. They are also available online. I have plotted the velocity profiles for you on semi-logarithmic graph paper. If the data follow the ideal logarithmic turbulent velocity profile, the observed velocities in each profile should plot along a straight line, especially in the zone near the bed. Do your best to fit the points with a straight line, concentrating especially on the points in the lowest 10-20% of the profile (the topmost point often is slow because of drag at the air-water interface). You can now use the plots to calculate u * and k s in the equation for velocity above a rough boundary: u = 2.5 ln ( 30.0 y ) u k * s To fit this equation to data, it must be solved simultaneously for two different measured values of velocity and depth. When this is done, we get the result: u 1 y 1) u 2 u * = 0.4 ln (y 2 u 1 and u 2 are most easily measured at the top and bottom of a log cycle; y 1 and y 2 are the corresponding depths. k s is given by: u 1) ln k s = ln(30.0 y 1 ) 0.4(u * k s can also be found by multiplying the y-intercept (the value of y where u=0 on the graph) by 30.0, i.e. k s = 30.0 y int For each profile I would like you to compute: u *, τ ο, k s from the velocity profile data. Then compute τ ο at each profile using the total boundary shear (γys) formula. Use the local depth of water at the vertical for Y.
d. Compare the values of τ ο derived from each method. How well do they agree? Discuss possible reasons for differences. Now look at the values of k s. Do they appear to have any physical meaning with regard to the roughness elements you saw in the river? If they do not, suggest some reasons for the discrepancy. 3. COMPUTATION OF FLOW CHARACTERISTICS a. Computation of thickness of laminar sublayer and buffer layer. Use the following relations to calculate the position of the top of the laminar sublayer and the buffer layer. top of laminar sublayer: top of buffer layer: 4ν y l = u* 50ν y l = u* ν = kinematic viscosity = 1.31 x 10-6 m 2 /s (at 10 degrees C) Based on these calculations, what percent of the flow depth is viscous-dominated? b. Computation of mean Reynolds number Calculate the mean Reynolds number at each cross-section using the mean depth, d and mean velocity V. R= VR ν Vd ν Which of the cross-sections are the more turbulent? What factors cause them to be so? (Field observations are wanted here.) c. Computation of mean Froude number. Calculate the mean Froude number for each cross-section using mean depth and velocity. Then calculate the Froude number at each profile. F = u gd note that for a cross-section u and y are mean values; for a single profile u is mean velocity while y is total depth of flow there. Based on these numbers, were any of the flows supercritical? If so, which? How does this compare with your field observations?
4. RESISTANCE TO FLOW a. Calculation of Chézy C and Manning n. You have values of mean depth (d) and mean velocity (v) from gaging measurements; the long profile gives slope (S e ). Use these to calculate the value of the Chézy C and the Manning n for each cross-section. You will have to decide over what distance to average the slope. Remember that: v = C RS C ds v = n k m R 0.67 S 0.5 n k m d 0.67 S 0.5 b. Computation of Darcy-Weisbach friction factor At each cross-section compute the mean Darcy-Weisbach friction factor f f = 8τ o ρv 2 5. VELOCITY DISTRIBUTION IN CROSS SECTIONS a. Velocity distribution in cross sections On the blowups of your XS supplied with this lab (also online) plot all of your velocity measurements (both those from gaging and those from the velocity profiles) at their appropriate depth and distance on the the cross-sections and contour them at 0.1 ft/sec intervals. Explain the distribution of velocity in your cross-section (why does it have the pattern it does?) and compare your cross-section with those downstream. How do the velocity distributions differ? Is there any systematic pattern? How do you explain any differences in pattern?
LAB 3 ANSWER SHEET 1 1a. Discharge and flow characteristics at Prairie Creek XSS 1 through 4 Q A w d V ft 3 /sec ft 2 ft ft ft/sec XSEC 1 XSEC 2 XSEC 3 XSEC 4 Q A w d V m 3 /sec m 2 m m m/sec XSEC 1 XSEC 2 XSEC 3 XSEC 4 Attach computations
1b. Comparison of discharges at XSS 1 through 4 and discussion. 2 2. a,b mean slope and boundary shear stress at cross-sections S mean τ ο m/m N/m 2 XSEC 1 XSEC 2 XSEC 3 XSEC 4
c. boundary shear stress and computed roughness diameter at each velocity profile 3 Y m τ ο γ YS N/m 2 τ ο vel profile N/m 2 u * m/s k s m XS 1 @ 28.0 XS 1@ 36.0 XS 2 @ 65.6 XS 2@ 67.1 XS 2@ 68.6 XS 3@ 43.0 XS 3@ 50.5 XS4 @ 16.2 XS4 @ 19.2 Include graphs showing fit of lines and show computations.
4 Compare the τ ο values computed from velocity profiles with those computed from water depth and slope, and analysis of differences. Analysis of k s values and their meaning, if any, with reasons.
3. a. Computation of viscous-layer and buffer-layer thicknesses at profiles 5 XS 1 @ 36.0 y l mm y t mm % of flow depth that is viscousdominated XS 2 @ 67.1 XS 3 @ 50.5 XS 4 @ 16.2
b,c Computation of Reynolds and Froude numbers 6 Y m u mean m/s R F XS 1 mean XS 2 mean XS 3 mean XS 4 mean XS 1 @ 36.0 XS 2 @ 67.1 XS 3 @ 43.0 XS 3 @ 50.5 XS 4 @ 16.2 Attach computations Which of the cross-sections is more turbulent? Give reasons for why this should be. Were any flows supercritical? Which ones, if any? What caused the transition to supercritical flow (if any)? Compare with field observations?
4. a,b Computation of Chézy C, Manning n, and Darcy Weisbach f at the four XSS 7 S o C n f XS 1 XS 2 XS 3 XS 4 5. a. Discussion/explanation of pattern of velocity in your cross-section and those downstream. Include contoured cross-section for your site.