The flow through a breast wall spillway is greatly affected by the centripetal force due to a downstream curved profile. Therefore, the mean vertical pressure distribution at the outlet section is not consistent with ...The flow through a breast wall spillway is greatly affected by the centripetal force due to a downstream curved profile. Therefore, the mean vertical pressure distribution at the outlet section is not consistent with the hydrostatic pressure law. This distribution in turn affects the discharge capacity of the breast wall spillway. This paper experimentally studies the effect of a convex downstream profile on the mean pressure variation and the discharge of a breast wall spillway without gates. It is indicated that the effect of the curvilinear streamline on the mean vertical pressure variation is significant. The regression analysis method is used to determine the water head effect Z o of the orifice opening through the mean pressure variation. A discharge prediction formula of the breast wall spillway is obtained under the limited conditions of a laboratory flume. The predicted discharge is compared to the measured discharge. A good agreement is evidenced for the free orifice flow with errors within ？5%, while a big error（20% or even more） is obtained if the hydrostatic pressure law is used for the determination of Zo.展开更多
While considering a mirror and light rays coming either from a point source or from infinity,the reflected light rays may have an envelope,called a caustic curve.In this paper,we study developable surfaces as mirrors....While considering a mirror and light rays coming either from a point source or from infinity,the reflected light rays may have an envelope,called a caustic curve.In this paper,we study developable surfaces as mirrors.These caustic surfaces,described in a closed form,are also developable surfaces of the same type as the original mirror surface.We provide efficient,algorithmic computation to find the caustic surface of each of the three types of developable surfaces(cone,cylinder,and tangent surface of a spatial curve).We also provide a potential application of the results in contemporary free-form architecture design.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51179058,51479058)the State key program of National Science Fund of China(Grant No.51239003)+1 种基金the Special Fund for Public Welfare of Water Resources Ministry(Grant No.201201017)the 111 Project(Grant No.B12032)
文摘The flow through a breast wall spillway is greatly affected by the centripetal force due to a downstream curved profile. Therefore, the mean vertical pressure distribution at the outlet section is not consistent with the hydrostatic pressure law. This distribution in turn affects the discharge capacity of the breast wall spillway. This paper experimentally studies the effect of a convex downstream profile on the mean pressure variation and the discharge of a breast wall spillway without gates. It is indicated that the effect of the curvilinear streamline on the mean vertical pressure variation is significant. The regression analysis method is used to determine the water head effect Z o of the orifice opening through the mean pressure variation. A discharge prediction formula of the breast wall spillway is obtained under the limited conditions of a laboratory flume. The predicted discharge is compared to the measured discharge. A good agreement is evidenced for the free orifice flow with errors within ？5%, while a big error（20% or even more） is obtained if the hydrostatic pressure law is used for the determination of Zo.
基金Project supported by the European Union and the European Social Fund(No.EFOP-3.6.3-VEKOP-16-2017-00002).Open Access funding provided by European Union and the European Social Fund。
文摘While considering a mirror and light rays coming either from a point source or from infinity,the reflected light rays may have an envelope,called a caustic curve.In this paper,we study developable surfaces as mirrors.These caustic surfaces,described in a closed form,are also developable surfaces of the same type as the original mirror surface.We provide efficient,algorithmic computation to find the caustic surface of each of the three types of developable surfaces(cone,cylinder,and tangent surface of a spatial curve).We also provide a potential application of the results in contemporary free-form architecture design.
