Resistance Coefficients in Uniform Flow - Lab Report Example

Experiment 2: Resistance Coefficients in Uniform Flow Table of Contents Introduction 2 Objective 2 Theory and background 2 Experimental Procedure 3 Experimental Data and Results 4 Conclusion 6 Introduction This experiment was meant to analyse the characteristics of uniform flow and to examine the behaviour of flexible structure. Uniform flow is used as a condition to establish the artificial channel dimensions. Determining the normal depth helps in determining the free surface position and the channel depth required to complete the design dimensions of the channel. Therefore, resistance coefficient determination is in a unique value of the normal depth. The focus of this lab experiment is to analyse the relationship between structure and liquid. The experiment is based on the idea that a liquid causes structure deformation, which induces changes in fluid flow boundary conditions. Objective The aim of the experiment was to find out the conditions under which a uniform flow can occur as well as to find out resistance coefficients Manning’s coefficient, Chezy Coefficient, and the Darcy friction factor. Through this experiment, Manning coefficient, Chezy’s coefficient and Darcy friction factor were established. This was done by calculating manning’s roughness coefficient, chezy’s coefficient (c), and the darcy-weisbach friction factor (f) using the results obtained from the experiment. Theory and background Under uniform flow condition accelerative forces are equal to the decelarative forces. Based on this fact, the normal depth in an open channel flow can be calculated using Chezy formula, Manning formula or Darcy-Weisbach formula. These formulas are expressed as shown below: a. Chezy formula V =C Where V is the velocity in L/s, R is the hydraulic radius in m, S is the slope of the channel, and C is Chezy’s flow resistance factor. b. Darcy-Weisbach’s formula V = Where V is the velocity in L/s, R is the hydraulic radius in m, S is the slope of the channel, g is gravitational forceand f is Darcy-Weisbach’s friction factor. c. Manning formula V = Where V is the velocity in L/s, R is the hydraulic radius in m, S is the slope of the channel, and n is the roughness coefficient called Manning’s n. Experimental Procedure The experiment began with adjusting of the channel to a mild slope (subcritical flow condition) using the jack controller and ensuring that the valve at the downstream end of the flume is fully open before you turn on the pump. The pump was then turned on ensuring that the speed of the pump is set to 800 rpm (this is the highest speed you should start with). The reading on the flow meter was recorded after making sure that the flow inside the flume had stabilized. The flow depth where the uniform flow is established was then measured. To measure these depths, a straight edged ruler was placed on the outside walls of the flume to read the depth. The speed of the pump was then reduced gradually (by 50 rpm) and by adjusting the slope of the flume established a uniform flow and the flow rate and the depths were recorded. The measurements were repeated for up to ten different flowrates. Five of these measurements were under subcritical flow condition and the rest under supercritical flow condition. Where necessary the end valve closed slowly to establish a subcritical flow in the flume. After finishing the experiment, all the tools used for your experiment were cleaned and stored safely. Experimental Data and Results The appendix section contains the experimental results For Manning’s n V = For Chezy’s C C =V/ The table in the appendix section shows variations from the universally accepted values after transferring the estimated friction factor, f, calculated to moody chart. The variation is caused by the errors when reading the results. For Darcy- friction factor, f, using a Colebrook –White equation results was somewhat different from the calculated values 1. The errors are apparently the cause of this variation. Other causes of this variation could have been the calculation errors as well as irregularities in flow rate as well as poor recording and change of speed of pump. The graph below shows velocity V, versus R2/3S1/2 Based on the graph above, it is the average value of the flume is 5.995. It can be deduced from the graph that the calculated values for the Manning’s roughness coefficient in the smooth channel have little variations from the published values. This is due to calculation errors, observation errors and other irregularities in the experiment. From the graph the average value for C for the flume is 5.65. Data for the critical slope using average n and c are displayed in the appendix. Based on these data and the graph above, it is clear that the manning’s coefficient, Chezy’s C, and Darcy-Weisbach friction factor have different values but they do not vary greatly from the published values. The cause of this variation is apparently the experimental errors such as observation mistakes and calculation errors. Velocity Vs. graph has a positive gradient because the flow rate is zero before the pump is starts operating, but as the pump starts to operate, the flow rate starts increasing gradually until it reaches maximum value. Conclusion Generally, the experiment was successful because the objective was achieved. From the experiment, it was possible to find out the conditions under which a uniform flow can occur as well as to find out resistance coefficients Manning’s coefficient, Chezy Coefficient, and the Darcy friction factor. It was depicted that determination of the normal depth helps in determining the free surface position and the channel depth required to complete the design dimensions of the channel. As noted in the experiment, the values depend on the depth of the channel specifically Chezy’s C and manning’s coefficient was noted to have interrelation with the materials property. It was also established that the friction factors of the pipe causes a marginal energy loss and thus a reduced pressure difference. Another important aspect that was noted from the experiment is that the results obtained were slightly different from the calculated values. The errors are apparently the cause of this variation. Other errors that caused this variation could have been the calculation errors as well as irregularities in flow rate as well as poor recording and change of speed of pump. References Nayak, P., Khatua, K. &Patra, K. (2009).Variation of Resistance Coefficients in a Meandering Channel.Department of Civil Engineering, N.I.T.Rourkela Sukanta, J. (2007) “Stage-Discharge Relationship in Simple Meandering Channels”,M.Tech thesis submitted at IIT, Kharagpur, India. Exp. No. SPEED RPM Q (l/s) y (mm) V (m/s) R(m) So Sc √rs R 2/3 S1/2 Re Fr nexp ntable nave Cexp Cave fexp fColebrook State of flow [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] 1 550 50.65 135.71 0.42 0.18 -2 0.0614 0 161643.281 0.47182 0.01337 0.024 0.0084 0.000000 0.00000 0.00000 0.000002 Sub critical 2 450 36.98 113.68 0.40 0.20 -2 0.0602 0.4234 157432.413 0.48421 0.01958 0.024 0.08612 3.786518 1.89887 0.00169 0.006753 Sub critical 3 400 29.22 99.2 0.42 0.20 -2 0.0612 0.5273 158763.218 0.47152 0.01821 0.024 0.086574 3.684414 3.94180 0.00106 0.005879 Sub critical 4 350 20.58 82.7 0.38 0.20 -2 0.0603 0.5012 159987.662 0.42672 0.01997 0.024 0.326527 3.761935 3.977471 0.00163 0.005491 Sub critical 5 550 51.04 106.41 0.34 0.30 -6 0.0764 0.9876 173573.651 0.37429 0.0571 0.036 0.31249 2.422924 3.11863 0.00250 0.00714 Sub critical 6 500 44.76 62.05 0.49 0.23 -10 0.821 0.0041 173489.166 0.41864 0.0849 0.031 0.016631 0.000211 1.34261 0.00179 0.005184 Sub critical 7 450 37.77 49.81 0.42 0.25 -14 0.802 0.4987 196932.347 0.42952 0.0926 0.031 0.091115 3.265181 1.56317 0.00240 0.006419 supercritical 8 400 30.41 46 0.42 0.25 -16 0.802 0.6781 198451.391 0.4177 0.0989 0.031 0.175612 3.071827 3.35961 0.00242 0.00644  supercritical Read More