Dynamic Force on Spillways

DYNAMIC FORCE ON SPILLWAYS There is a continuous change in the velocity of water when water flows over the curved surface of the ogee spillway. The continuous change in velocity phenomenon induces a change in momentum from section to section and thus causes a force on the spillway structure. This force is a know as dynamic force. Consider two sections A and B of water on the curved surface. The resultant of the forces on the element of water is as follows. \[\Sigma F= pQ\bigtriangleup V\] Or \[\Sigma F= pQ(V_{2}-V_{1})\] Where \[r=\frac{w}{g}=Mass -density- of- water\] Q=discharge V2-V1=change in velocity from section B to A \[Resolving -equation .\Sigma F=pQ(V_{2}-_{1})horizontally.and .vertically- we -get\] \[\Sigma F_{h}= pQ(V_{2}h-V_{1_{h}})\] The forces Fh and Fv are the forces acting on free body of water. These forces include gravity force, hydrostatic pressures and reactions of any object in contact with water.  

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