Problem 4.72[Difficulty: 4]Given:Gate held in place by water jetFind:Required jet speed for various water depthsSolution:Basic equation: Momentum flux in x direction for the wallNote: We use this equation ONLY for the jet impacting the wall. For the hydrostatic force and location we use computing equationsFRpcA⋅=y'ycIxxAyc⋅+=Assumptions: 1) Steady flow 2) Incompressible flow 3) Uniform flowHenceRxVρ⋅V−Ajet⋅()⋅=ρ−V2⋅πD2⋅4⋅=This force is the force generated by the wall on the jet; the force of the jet hitting the wall is thenFjetRx−=ρV2⋅πD2⋅4⋅=where D is the jet diameterFor the hydrostatic forceFRpcA⋅=ρg⋅h2⋅h⋅w⋅=12ρ⋅g⋅w⋅h2⋅=y'ycIxxc⋅+=h2wh3⋅12⋅h2⋅+=23h⋅=where h is the water depth and w is the gate widthFor the gate, we can take moments about the hinge to obtainFjet−hjet⋅FRhy'−⋅+
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 10/19/2011 for the course EGN 3353C taught by Professor Lear during the Fall '07 term at University of Florida.