U形渠道圆柱体（筒）量水槽试验研究
摘要
本论文在Hager和Zohrab Samani等研究成果的基础上,提出了一种适用于圆弧底上切一直线段的U形渠道的圆柱体(筒)量水槽。该量水槽的测流原理是利用垂直安装在U形渠道轴线上的圆柱(筒)缩窄渠道过流断面产生足够的水面降落,使其测流断面产生临界水流状态,形成稳定的水位～流量关系,通过测量驻点水位计算渠道流量。试验研究中,采用理论分析和模型试验相结合的方法,推导出了U形渠道圆柱体(筒)量水槽的临界水深和理论流量计算公式,确定了量水槽的流量校正系数和自由出流条件下的流量计算经验公式,并进行了量水槽的性能分析。
U形渠道圆柱体(筒)量水槽量测流量时,由于临界流断面的流速分布不均匀和流线弯曲的影响,计算的流量应乘以一个校正系数。对于圆弧底上切一直线段的U形渠道,当θ和r确定后,弦长L与渠道断面存在唯一对应关系,因此,其校正系数可以作为相对能量H/L的函数求得,其中H为上游能量,L为U形渠道的弦长。通过不同柱体直径和不同流量试验资料分析表明,相对能量(H/L)和相对流量(Qm/Qc)具有非常好的相关关系,其中Qm为实测流量,Qc为计算的理论流量。并利用试验数据建立了相对能量(H/L)和相对流量(Qm/Qc)的无因次关系式。
采用9种不同圆柱体(筒)直径进行了试验研究,分析了U形渠道圆柱体(筒)量水槽的水位流量关系、圆柱体的直径(收缩比ε)选择范围、测流误差和临界淹没界限。根据试验数据分析,临界水深、上游水深和驻点水深相互之间均呈现良好的线性关系,驻点水深与实测流量和计算流量也呈现良好的线性关系。圆柱体直径是影响U形渠道圆柱体(筒)量水槽测流误差的一个重要参数,如果选择的柱体直径过大或过小,都会引起测流误差。但是,只要限定柱体直径在某一范围内,即量水槽收缩比ε在某一范围内,那么,由柱体直径的改变导致上游水位的变化所引起的测流误差将小于某一数值。通过试验数据分析得出,收缩比ε在0.57～0.69范围内时,测流误差较小,并且壅水高度较小(Δh≤0.1m)。因此,U形渠道圆柱体(筒)量水槽的柱体直径可在收缩比ε为0.57～0.69区间内进行选择。同时得出,量水槽的最大误差为3.78%,临界淹没度S为0.73～0.84。
本论文的创新点为:①首次针对圆弧底上切一直线段的U形渠道进行了圆柱体(筒)量水槽试验研究,推导出了其理论流量计算公式,并得出了自由出流条件下的流量计算经验公式;②提出了U形渠道圆柱体(筒)量水槽计算流量应乘以一个校正系数,其校正系数可以作为相对能量H/L的函数求得,并利用试验数据建立了相对能量(H/L)和相对流量(Qm/Qc)的无因次关系式;③分析了驻点水深、临界水深和上游水深的关系,三者之间存在很好的线性关系,驻点水深与实测流量和计算流量也呈现良好的线性关系。因此,认为用驻点水深来计算理论流量是正确可靠的;④分析了U形渠道圆柱体(筒)量水槽圆柱体的直径(收缩比ε)选择范围、测流误差和临界淹没界限。
U形渠道圆柱体(筒)量水槽具有结构简单,施工制作容易,成本低;对于小型U形渠道,可以移动使用,不产生淤积,管理使用方便;测量精度较高,根据试验结果,最大误差为3.78%,满足灌区量水要求;量水槽的断面收缩比为0.57～0.69,圆柱体(筒)直径选择范围较大;量水槽最大淹没度为0.84,具有较宽的自由出流范围,不易造成淹没出流等优点。
Based on the achievements of Hager and Zohrab Samani et al., a cylinder measuring water device was put forward for U-shape channel with a circular arc-shape bottom and tangent straight sides in this paper. The principle of this measuring water device was that using a cylinder vertically installed on the axis of U-shape channel to contract and narrow the water flowing section, produces enough water surface falling and forming the critical flow state. It can be obtained the stable correlation between water level and discharge. So the discharge could be measured only by water level at the stagnation point. In the experiment study, using the method integrated the theoretical analysis with the model testing, the calculating formulae of critical water depth with the discharge has been derived out. The adjustment factor for the discharge and the experiential calculating formula for the discharge under the condition of free outflow have been determined. Moreover, the performance of the measuring water device has been analysed.
When using the cylinder to measure the discharge in U-shape channel, due to the water velocity nonuniform distribution and the impact of crooked streamline at critical flow section, so the calculated discharge should be revised by an adjustment factor. For the U-shape channel with a circular arc-shape bottom and tangent straight sides, after the central angle (θ) and radius (r) of arc-shape bottom were given, there was unique correlation between the chord length (L) to the channel section. Therefore, the adjustment factor can be given by the function of relative energy H/L (ratio of upstream water head (H) to the chord length (L)). Through the analysis for the experiment data by the different diameters of the cylinder with the different discharges, have shown very good correlativity between the relative energy H/L and the relative discharge Qm/Qc (ratio of measured discharge (Qm) and the calculated theoretical discharge (Qc) ). Also using the experiment data, without dimension equations of relative energy H/L and relative discharge Qm/Qc have been established.
Using the nine different diameters of cylinder to carry out the experiment in U-shape channel, the correlation between water level and discharge for the cylinder measuring water device, the cylinder diameter selecting range (which determines the shrinkage ratio), the measuring error and the boundary of critical submergence flow have been analyzed. According to the analysis for the experiment data, between the critical water depth, the upstream water depth and the stagnation-point water depth total have been shown the favorable linear correlation one another, also among the stagnation-point water depth, measured discharge and calculated discharge have shown the good linear relationship too. The diameter of cylinder was the important factor for affecting the measuring precision. If the diameter of the cylinder selected too big or too small, total will be caused the measuring error. However, only limited the diameter of the cylinder in a certain of range, i.e. the shrinkage ratio(ε) in a certain of range, well then the discharge measuring error could be acceptable. Through the analysis for the experiment data, have obtained when the shrinkage ratio(ε)was within 0.57 to 0.69, the measuring error will be rather small and the backwater level will be less than 0.1m. So the diameter of the cylinder should be selected within the shrinkage ratio from 0.57 to 0.69, the maximum absolute error was less than 3.78%, and the critical submergence degree was 0.73 to 0.84.
The innovation points in this paper were:①Pointed to the U-shape channel with a circular arc-shape bottom and tangent straight sides to carry out the experiment and research on the cylinder water measuring device for the first time, has derived the calculation formula for the theoretical discharge and obtained the experienced calculation equation of discharge under the condition of free outflow;②Put forward the calculated discharge should be revised by an adjustment factor that could be determined by the function of relative energy H/L, Also using the experiment data, the without dimension equations of relative energy H/L and relative discharge Qm/Qc have been established;③The relationship between stagnation-point water depth and the critical water depth with the upstream water head have been analysed, between the three depths have shown rather good linear relations. Also the stagnation-point water depth with the measured discharge and calculated discharge have been shown good correlation too. Therefore, it was reliable that using the stagnation-point water depth to calculate theoretical discharge;④The selecting range of appropriate diameters of cylinder, the error of measuring discharge and the critical submergence degree have been analysed.
The cylinder water measuring device has the advantages such as simple structure, easy construct and install with a low cost and high measuring precision, with a maximal absolute error of 3.78% to satisfy the water measuring requirement in irrigation district. It could be used from one place to other, and no sediment problem in the U-shape channel. The section shrink ratio of this device was from 0.57 to 0.69, therefore, the diameter range of cylinder could be chosen widely. The maximum submergence degree was 0.84, so with wide range of free outflow, and hardly to cause the submergence outflow and so on.
U形渠道圆柱体(筒)量水槽量测流量时,由于临界流断面的流速分布不均匀和流线弯曲的影响,计算的流量应乘以一个校正系数。对于圆弧底上切一直线段的U形渠道,当θ和r确定后,弦长L与渠道断面存在唯一对应关系,因此,其校正系数可以作为相对能量H/L的函数求得,其中H为上游能量,L为U形渠道的弦长。通过不同柱体直径和不同流量试验资料分析表明,相对能量(H/L)和相对流量(Qm/Qc)具有非常好的相关关系,其中Qm为实测流量,Qc为计算的理论流量。并利用试验数据建立了相对能量(H/L)和相对流量(Qm/Qc)的无因次关系式。
采用9种不同圆柱体(筒)直径进行了试验研究,分析了U形渠道圆柱体(筒)量水槽的水位流量关系、圆柱体的直径(收缩比ε)选择范围、测流误差和临界淹没界限。根据试验数据分析,临界水深、上游水深和驻点水深相互之间均呈现良好的线性关系,驻点水深与实测流量和计算流量也呈现良好的线性关系。圆柱体直径是影响U形渠道圆柱体(筒)量水槽测流误差的一个重要参数,如果选择的柱体直径过大或过小,都会引起测流误差。但是,只要限定柱体直径在某一范围内,即量水槽收缩比ε在某一范围内,那么,由柱体直径的改变导致上游水位的变化所引起的测流误差将小于某一数值。通过试验数据分析得出,收缩比ε在0.57～0.69范围内时,测流误差较小,并且壅水高度较小(Δh≤0.1m)。因此,U形渠道圆柱体(筒)量水槽的柱体直径可在收缩比ε为0.57～0.69区间内进行选择。同时得出,量水槽的最大误差为3.78%,临界淹没度S为0.73～0.84。
本论文的创新点为:①首次针对圆弧底上切一直线段的U形渠道进行了圆柱体(筒)量水槽试验研究,推导出了其理论流量计算公式,并得出了自由出流条件下的流量计算经验公式;②提出了U形渠道圆柱体(筒)量水槽计算流量应乘以一个校正系数,其校正系数可以作为相对能量H/L的函数求得,并利用试验数据建立了相对能量(H/L)和相对流量(Qm/Qc)的无因次关系式;③分析了驻点水深、临界水深和上游水深的关系,三者之间存在很好的线性关系,驻点水深与实测流量和计算流量也呈现良好的线性关系。因此,认为用驻点水深来计算理论流量是正确可靠的;④分析了U形渠道圆柱体(筒)量水槽圆柱体的直径(收缩比ε)选择范围、测流误差和临界淹没界限。
U形渠道圆柱体(筒)量水槽具有结构简单,施工制作容易,成本低;对于小型U形渠道,可以移动使用,不产生淤积,管理使用方便;测量精度较高,根据试验结果,最大误差为3.78%,满足灌区量水要求;量水槽的断面收缩比为0.57～0.69,圆柱体(筒)直径选择范围较大;量水槽最大淹没度为0.84,具有较宽的自由出流范围,不易造成淹没出流等优点。
Based on the achievements of Hager and Zohrab Samani et al., a cylinder measuring water device was put forward for U-shape channel with a circular arc-shape bottom and tangent straight sides in this paper. The principle of this measuring water device was that using a cylinder vertically installed on the axis of U-shape channel to contract and narrow the water flowing section, produces enough water surface falling and forming the critical flow state. It can be obtained the stable correlation between water level and discharge. So the discharge could be measured only by water level at the stagnation point. In the experiment study, using the method integrated the theoretical analysis with the model testing, the calculating formulae of critical water depth with the discharge has been derived out. The adjustment factor for the discharge and the experiential calculating formula for the discharge under the condition of free outflow have been determined. Moreover, the performance of the measuring water device has been analysed.
When using the cylinder to measure the discharge in U-shape channel, due to the water velocity nonuniform distribution and the impact of crooked streamline at critical flow section, so the calculated discharge should be revised by an adjustment factor. For the U-shape channel with a circular arc-shape bottom and tangent straight sides, after the central angle (θ) and radius (r) of arc-shape bottom were given, there was unique correlation between the chord length (L) to the channel section. Therefore, the adjustment factor can be given by the function of relative energy H/L (ratio of upstream water head (H) to the chord length (L)). Through the analysis for the experiment data by the different diameters of the cylinder with the different discharges, have shown very good correlativity between the relative energy H/L and the relative discharge Qm/Qc (ratio of measured discharge (Qm) and the calculated theoretical discharge (Qc) ). Also using the experiment data, without dimension equations of relative energy H/L and relative discharge Qm/Qc have been established.
Using the nine different diameters of cylinder to carry out the experiment in U-shape channel, the correlation between water level and discharge for the cylinder measuring water device, the cylinder diameter selecting range (which determines the shrinkage ratio), the measuring error and the boundary of critical submergence flow have been analyzed. According to the analysis for the experiment data, between the critical water depth, the upstream water depth and the stagnation-point water depth total have been shown the favorable linear correlation one another, also among the stagnation-point water depth, measured discharge and calculated discharge have shown the good linear relationship too. The diameter of cylinder was the important factor for affecting the measuring precision. If the diameter of the cylinder selected too big or too small, total will be caused the measuring error. However, only limited the diameter of the cylinder in a certain of range, i.e. the shrinkage ratio(ε) in a certain of range, well then the discharge measuring error could be acceptable. Through the analysis for the experiment data, have obtained when the shrinkage ratio(ε)was within 0.57 to 0.69, the measuring error will be rather small and the backwater level will be less than 0.1m. So the diameter of the cylinder should be selected within the shrinkage ratio from 0.57 to 0.69, the maximum absolute error was less than 3.78%, and the critical submergence degree was 0.73 to 0.84.
The innovation points in this paper were:①Pointed to the U-shape channel with a circular arc-shape bottom and tangent straight sides to carry out the experiment and research on the cylinder water measuring device for the first time, has derived the calculation formula for the theoretical discharge and obtained the experienced calculation equation of discharge under the condition of free outflow;②Put forward the calculated discharge should be revised by an adjustment factor that could be determined by the function of relative energy H/L, Also using the experiment data, the without dimension equations of relative energy H/L and relative discharge Qm/Qc have been established;③The relationship between stagnation-point water depth and the critical water depth with the upstream water head have been analysed, between the three depths have shown rather good linear relations. Also the stagnation-point water depth with the measured discharge and calculated discharge have been shown good correlation too. Therefore, it was reliable that using the stagnation-point water depth to calculate theoretical discharge;④The selecting range of appropriate diameters of cylinder, the error of measuring discharge and the critical submergence degree have been analysed.
The cylinder water measuring device has the advantages such as simple structure, easy construct and install with a low cost and high measuring precision, with a maximal absolute error of 3.78% to satisfy the water measuring requirement in irrigation district. It could be used from one place to other, and no sediment problem in the U-shape channel. The section shrink ratio of this device was from 0.57 to 0.69, therefore, the diameter range of cylinder could be chosen widely. The maximum submergence degree was 0.84, so with wide range of free outflow, and hardly to cause the submergence outflow and so on.
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