Hydraulics Hydrology Jump Resistance Coefficient - Research Paper Example

EXPERIMENT 1: HYDRAULIC JUMP Name Professor Institution Course Date Experiment 1: Hydraulic jump Introduction Hydraulic jump refers to a situation where the level of water raises suddenly that result in loss of energy through water turbulence. Hydraulic jump is a very significant occurrence in most cases, which includes energy dissipation down the spillways to prevent erosion from taking place and to facilitate the mixing of air and other agents within water for various processes in water treatment. The phenomenon of hydraulic jump is incredibly common. This is frequently demonstrated in the use of kitchen sinks. The study of the principle of hydraulic jump is usually carried out due to its presence and occurrence in nature. This phenomenon is sometimes experienced in streams and rivers as well as in oceans. Hydraulic jump takes place when fluid flowing in a vertical direction is imposed on a vertical surface (Larock, 2004, p. 223). This experiment involved the consideration of the depth and impact of a horizontal water surface. The broad aspect of hydraulic jump is split into three separate regions. These ones include the subcritical region, the critical region as well as the supercritical region. Each one of these region is significant in the experimental investigation of hydraulic jump due to the definition of the area of the jump and its operational principles. The development and conduction of this experiment took place based on the theory of these regions. Objective The objective of this experiment involved the identification of the conditions necessary for the occurrence of a hydraulic jump. There was also the determination of relative water depths at both downstream and upstream of the jump as well the energy loss experienced within the jump. Theory The momentum and mass conservations are used in the description of the hydraulic jump. Considering uniform and horizontal rectangular sections of a channel, the mass and momentum conservations can be written in the form of (Kasenow, 2001, p. 291): Conservation of mass between 1 and 2 Linear momentum conservation According to Newton’s second law, the total force experienced by a body in a fixed direction is the same as the increasing momentum rate of the boy in that direction. For the occurrence of superficial flow at section 1, the Froude number is greater than 1. For the occurrence of subcritical flow at section 2, the Froude number is less than 1 and the value of Y2 Is greater than the value of Y2 leads to the formation of a hydraulic jump. The estimation of energy dissipated through a hydraulic jump can be done from: The flow in the laboratory is normally subjected to regulation from the upstream end using a sluice gate, which brings about the development of supercritical flow, which is rapid and shallow. The placement of an adjustable weir can be done at the downstream end to cause the flow occurring in front of the channel were to become subcritical. The formation of a hydraulic jump then takes place within the transition to the downstream subcritical flow starting from the upstream supercritical flow. The hydraulic jump phenomenon is analogous to that of shockwave, which is normally experienced in aerodynamics. In this case, the subsonic, the supersonic flows meet, and this leads to the development of shock front at the transition of these two regimes of flow. Control volumes used in the analysis of a hydraulic jump When open channels such as spillways are opened through lifting of gates, the fluid that passes through the gate does so at a high associated kinetic energy and a high velocity. It is usually desirable to achieve the conversion of the high kinetic energy, which is in the form of high velocity to a high potential energy. This is due to the erosive features associated with high velocity fluids. However, there are problems that are associated with the varying depth of the fluid over a short length of channel are common. Fluid flow that is rapidly varied in this nature results in a hydraulic jump, which occurs during a sudden increase in depth of a flowing fluid. This is observed when the open channel experiences a change from fast to slow with regard to fluid velocity. The essence of a hydraulic jump is mainly the dissipation of energy as well as the reduction of flow velocity. The energy loses that are experienced in hydraulic jumps and the similarity between the downstream and upstream energy are not significant in the analysis of fluid flow. Classification of hydraulic jump Classification of hydraulic jumps can be done with regard to the characteristics of the flow patterns. This involves classification in accordance with photographic and visual observations where the classification of undular jumps is made. Weak Jump (1 < Fr1 < 2.5) For the Froude numbers that are slightly more than unity, there is the development of free surface undulations with relatively long wavelengths and small amplitudes. In this case, a two-dimensional flow is experienced and shockwaves as well as rollers are not visible. Oscillating Jump (2.5 < Fr1 < 4.5) When the Froude number increases, the development of lateral shock waves is experienced in the upstream section. There is also the intersection of the shock waves that occurs to slight extent in the downstream section. After the intersection, there is the continuation of propagation for the shock waves, which reaches the wall in the opposite side at a location below the wave. There is another intersection and reflection of the waves of the waves above and around the second wave (Larock, 2004, p. 142). Steady Jump (4.5 < Fr1 < 9) A lateral intersection of shock waves above the first wave takes place for larger Froude numbers. During the initial intersection, the is the development of a wave breaking mechanism in which case there is the appearance of a small roller above the wave. The location of the roller is at the jump centreline. Strong Jump (Fr1 > 9) This is characterized by a big difference with regard to conjugate depths. They display rough action, which brings about the dissipation of energy at a high rate. Experimental Procedure The jack controller was used to adjust the channel to a horizontal position The downstream valve at the end of the fume was then fully opened The pump was then started up considering that its speed was set at 900 rpm as a starting speed A period of about three minutes was allowed for the flow inside the flume to stabilize The downstream valve was slowly closed and the hydraulic jump closely monitored before time was then allowed for stabilization The flow meter was read and vales recorded in a tabulated format as indicated in the results section. The depth of flow at the downstream and upstream sections of the hydraulic jump was measured. This was done through the placement of a straight edged ruler on the outer parts of the wall for the flume. Because of these measurements, the values of y1 and y2 were obtained. The pump speed was slowly reduced by 50 revolutions per minute and then the downstream valve was adjusted and this led to the formation of a hydraulic jump. The depths at both downstream and upstream as well as the rate of flow were recorded. The conduction of measurements was carried out repeatedly for eight different rates of flow. At the end of the experiments, the tool sand instruments used were properly cleaned and appropriately stored. Result and calculation The results obtained from measurements in this experiment were recorded in a tabulated format as indicated below: Exp. No. Q (l/s) Yc (mm) Y1 (mm) Y2 (mm) Y2 exp/ Y1 exp Y2 theo/ Y1 theo Fr1 Type of jump hydraulic Speed (rpm) 1 37.39 92.83 32.46 125.30 3.86 3.64 2.072 Weak jump 480 2 41.25 153.31 33.44 186.75 5.58 3.73 2.430 Weak jump 510 3 54.16 142.46 51.06 193.62 3.79 3.18 2.765 Oscillating Jump 600 4 48.24 159.48 35.07 194.55 5.55 3.69 1.987 Weak jump 550 5 33.90 89.86 33.27 123.13 3.70 3.08 2.876 Oscillating Jump 450 6 26.40 58.67 23.08 81.65 3.54 2.57 2.996 Oscillating Jump 400 7 16.54 53.21 19.77 72.98 3.69 2.98 2.564 Oscillating Jump 350 The value of b was measured and found to be 490 mm and the Froude number, Fr column in the experimental results table was filled using the formula Energy loss through the hydraulic jump: Energy loss through the hydraulic jump is given by: Energy loss through the hydraulic jump= 135.51 KJ Specific energy curve (y-E) for the flow rate: Calculating momentum, the following formula is used: Where q is the rate of flow in (l/s) And g is the gravitational acceleration (9.8m/s2) M1 is the momentum ` Exp. No. Yc (mm) Q (l/s) q^2 (q^2)/2.3 M1 1 92.83 37.39 1398.012 594.8988 594.9276 2 153.31 41.25 1701.563 724.0691 724.0979 3 142.46 54.16 2933.306 1248.215 1248.244 4 159.48 48.24 2327.098 990.2543 990.2831 5 89.86 33.9 1149.21 489.0255 489.0543 6 58.67 26.4 696.96 296.5787 296.6075 7 53.21 16.54 273.5716 116.4134 116.4422 Momentum function verses depth curve (y-M) for the flow rates: Discussion Due to turbulence that is brought about by hydraulic jump, loss of energy is experienced and this is attributed to the flow that takes place during the jump. In which case the flow is slower before the jump than it is behind the jump. The other attribute to this is the high water level that is due to continuity. The theoretical explanation for the occurrence of hydraulic jump is dependent on parameters such as the jump structure, the radius of jump on parameters as well as flow velocity on radius (Larock, 2004, p. 313). Both the theoretical and experimental explanation as observed in this experiment were governed the energy conservation and continuity equations as well as the Navier-Stokes equation. The force experienced on the upstream section of the hydraulic jump exceeded the one on the downstream section and this is contrary to the theoretical presumption. The differenced existing between the theoretical and experimentally determined forces comes about due to the effect of shear forces, which are neglected despite their actual existence. Conclusion In conclusion, the conduction of the hydraulic jump experiment was able to determine among other things that the occurrence of the jump is experienced due to the separation boundary layer as well as the formation of vortex. It also became clear that there is loss of energy that is experienced in during the jump. This is what causes the height of flow for the fluid to be larger after the jump. The experiment also led to establishing and understanding that the occurrence of jump in viscous fluids is wavelike or laminar without turbulence. It was also concluded from the experiment that the theoretical value of the critical depth is approximately equal to the experimental value. There is a decrease in energy losses in the jump with a corresponding decrease in the length of occurrence of hydraulic jump. The value of critical depth as experimentally obtained is a very significant factor in the determination of the conditions that are necessary for the formation of a hydraulic jump. References Akan, A. O., & Houghtalen, R. J. (2003). Urban hydrology, hydraulics, and stormwater quality: Engineering applications and computer modeling. Hoboken, N.J: J. Wiley & Sons. Gribbin, J. E. (2013). Introduction to hydraulics and hydrology with applications for stormwater management. Albany, N.Y: Delmar. HydroGIS'96, Kovar, K., Nachtnebel, H.-P., & Universität für Bodenkultur. (1996). Application of geographic information systems in hydrology and water resources management: Proceedings of the HydroGIS'96 conference held in Vienna, Austria, Hydrological Sciences. Kasenow, M., Rohrich, T., & Waterloo Hydrogeologic Inc. (2001). Applied ground-water hydrology and well hydraulics. Highlands Ranch, Colo: Water Resources Publications Larock, B. E. (2004). Civil engineering hydraulics & hydrology review. Chicago, IL: Kapan Education. Read More