توزيع سرعت متوسط عمقي و تنش برشي در كانال هاي با بهترين مقطع هيدروليكي ذوزنقه اي و مستطيلي به روش نگاشت همديسي

چكيده انگليسي :

Depth averaged Velocity and Boundary Shear Stress in Channels with the Best Trapezoidal and Rectangular Hydraulic Sections Using Conformal Mapping Method Fatemeh Farshi fatemeh farshi@yahoo com Date of Submission March 7 2011 Department of Civil Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language Farsi Supervisor Dr Abdorreza Kabiri Samani akabiri@cc iut ac ir Advisor Dr Mohammad Reza Chamani mchamani@cc iut ac ir Abstract Boundary shear stress and depth averaged velocity are the most common characteristics of flow in open channels Using depth integration for velocity distribution depth averaged velocity can be calculated When water flows in an open channel a force called boundary shear stress arises and starts to erode the boundaries The problem of detaching the bed and the side wall shear stresses is very important in almost all studies of open channel flows For example to study boundary shear stress and velocity profile one must divide the bed shear stress from the total shear stress to estimate the bed load transport in open channel flows Similarly to study channel migration or to prevent bank erosion one must know the side wall shear stress Moreover a side wall correction procedure is often needed in laboratory flume studies of velocity profiles bed form resistance and sediment transport These parameters are useful in various problems such as water conveyance erosion river morphology and Pollutants transitions So knowledge and accurate estimation of these two parameters are basis to safe design of open cannels Previous investigations demonstrate that in the absence of secondary currents the boundary shear stress acting on the bed must be balanced by the downstream component of the weight of water contained within the bounding orthogonals An efficient way to study the boundary shear stress distribution in open channel flows is the idea of using conformal mapping method This idea has not rendered any conclusive results but afterwards researchers used the idea to estimate isovels and orthogonals Orthogonals have an important role in open channel flow whose their stream wise velocity gradient is almost zero Hence one can call them as zero shear stress surfaces In case of uniform flow the weight component between two orthogonals can be balanced by the shear force between them Modeling boundary shear stress is more difficult than depth averaged velocity because of the secondary currents Secondary circulation is a result resolving flow velocity into longitudinal and transverse components respect to the flow direction in the channel The transverse component of the velocity generates the secondary circulation It can occur in both straight and curved channels regarding to different flow aspects Secondary circulation is affected by temperature gradients sediment turbulence non uniformity of boundary shear and the curvature of streamlines In this study average bed and wall shear stress on smooth boundary trapezoidal channels and boundary shear stress and depth averaged velocity are analyzed for the best trapezoidal and rectangular hydraulic sections using conformal mapping method For verification of analytical results experiments were performed and velocity profiles were measured using a static pitot tube Comparing analytical and experimental results shows that the analytical models have good agreement with the experimental results Also results show that using Einstein s theory causes more accurate results for estimating the flow characteristics for the channel bed while there in inconsistency between the results for side walls based on Einstein s theory Presented analytical models tend to simple and safe design for the best hydraulic sections A remarkable result is that due to the special characteristics of the best hydraulic sections average and maximum bed and wall shear stresses are almost equal Key Words Shear stress Depth averaged velocity Secondary currents Conformal mapping

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توزيع سرعت متوسط عمقي و تنش برشي در كانال هاي با بهترين مقطع هيدروليكي ذوزنقه اي و مستطيلي به روش نگاشت همديسي

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