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.