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# SPTP GRNDWATER HYDRO ENG CVEN 489

Texas A&M

GPA 3.53

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This 14 page Study Guide was uploaded by Carolyn Kuhn on Wednesday October 21, 2015. The Study Guide belongs to CVEN 489 at Texas A&M University taught by Staff in Fall. Since its upload, it has received 82 views. For similar materials see /class/226121/cven-489-texas-a-m-university in Civil Engineering at Texas A&M University.

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Date Created: 10/21/15

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Left Right m 8535 N Dimsvmg 33 Am 0 LL 525 MM It measwfd Concentration ugl SO Measurement at station 2 2800 m downstream 394 525 min e Center x Left i Right r Time hrs Ll C oncentration ugl U1 0 4 o W O N O I 0 Measurement at station 3 5232 m downstream e Center x Left Right Time hrs Date distributed Date due CVEN 489501 Special Topics on Mixing and Transport in the Environment Problem Set 7 Longitudinal dispersion and mixing in rivers 3302005 462005 Return your solution in class at the beginning of the lecture period on the date shown above Please show all your work and follow the rules outlined in the course syllabus Problems denoted by G are assigned to the graduate students only Undergraduates may do these problems for extra credit 1 Longitudinal dispersion The Rhine river in the vicinity of Karlsruhe has width B 300 m and Manning7s friction factor 002 The slope is 1 10 4 Assume the river is always at normal depth and that the width is constant for all ow rates 1 E0 CIVIL For each ow rate in Table 17 compute the dispersion coef cient from the equation from Fischer et al 1977 UZBZ hm 1 DL 0011 where U is the mean velocity and u1 is the shear velocity For each ow rate in Table 17 compute the dispersion coef cient from the equation from Deng et al 2001 DL 7 015 ltBgt53ltUgt2 2 hu1 7 860 h u1 with 0145lt1gtltUgtltBgt138 6 07 39 3520 u h 39 where h is the water depth and B is the channel width 3136 TAMU 39 College Station Texas 7784373136 39 979 84574517 39 FAX 979 86278162 3 Plot the dispersion coef cient for each method as a function of ow rate and comment on the trends Do you think it is adequate to do one dye study to evaluate DL Why or why not Table 1 Flow rates in the Rhine river near Karlsruhe Flow rate 1113 Sl 120 240 500 800 1200 2 G Numerical integration The data for this problem are from Nepf 1995 Using the velocity pro le data in Table 27 estimate the longitudinal dispersion coef cient by performing a numerical integration of D 1W hy 1 y hddd 4 7 u u L A0 oDyho 9 where h is the water depth7 u is the shear deviation velocity7 Dy is the lateral turbulent diffusion coef cient7 and z is the vertical coordinate Hint refer to a similar example in Fischer et al 1979 You should obtain a value of DL 15 mZs How does this value compare with estimates using Equation 1 or Equation 2 Table 2 Stream velocity data for calculating a longitudinal dispersion coef cient Station Distance from Total depth Measurement Velocity number bank 1 depth7 zd u CH1 cm H cmSl 1 00 0 0 00 2 300 14 06 30 3 584 42 02 60 08 64 4 813 41 02 168 08 176 5 1041 43 02 134 08 136 6 1372 41 02 136 08 142 7 1702 34 02 90 08 96 8 2032 30 02 50 08 54 9 2362 15 02 10 08 14 10 2692 15 02 08 08 12 11 3150 14 06 00 12 3607 0 0 00 3 Accidental spill in a river A tanker truck has an accident and spills 100 kg of kerosene into a river The spill occurs over a span of 3 minutes and can be approximated as uniformly distributed across the lateral cross section of the river A sh farm has its water intake 25 km downstream of the spill location Refer to Figure 1 Fish farm Spill location inlet 39 E3 7 40 cms b 0 X25km H2m S00001 B25m X Figure 1 Schematic of the accidental spill with the important measurement values B and H are the width and depth of the river U is the average river ow velocity at the accident location and S is the channel slope 1 Use the following relationship to compute the longitudinal dispersion coef cient DL DL 7015 ltBgt53ltUgt2 5 Hu 7 860 H u E and H are the river width and depth U is the average ow velocity u is the shear velocity and 60 is a non dimensional number given by 60 0145 lt gtMS 6 0229 E0 What is the length in the downstream direction that the spill occupies due to its 3 minute duration At what point downstream of the spill do you think it would be reasonable to approximate the spill using an instantaneous point source release 00 Plot the concentration in the river as a function of downstream distance at t 2 hr after the accident From the gure determine the location of the center of mass of the kerosene cloud the maximum concentration in the river and the characteristic width of the cloud in the x direction approximate the cloud using one standard deviation of the concentration distribution 4 Write the equation for the concentration as a function of time at the inlet to the sh farm Plot your equation and determine at what time the maximum concentration passes the sh farm 9 A dye study was conducted in the river at an earlier time and concluded that there is a ow of groundwater into the river along the stretch between the accident and the sh farm How would this information in uence the results reported in the previous steps of this problem References Deng Z Q Singh V P amp Bengtsson L 2001 Longitudinal dispersion coef cient in straight rivers7 J Hydr Engrg 12711 9197927 Fischer H B List E G Koh R C Y lmberger J amp Brooks N H 1979 Mlm39ng in Inland and Coastal Waters Academic Press New York NY Nepf H M 1995 Course notes and problem sets7 MIT Course 177 Water Quality Control

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