CE361 - Lecture 06

CE361 - Lecture 06 - 2/2/2009 Water Resources Engineering E...

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2/2/2009 1 Water Resources Engineering -Lecture±6 Prepared by T Wagener & P Reed 1 Prepared by T. Wagener & P. Reed Penn State University A tourist boat passes by a section of the Three Gorges dam on the Yangtze river at Sandouping in Hubei province. The dam, which will be the largest in the world when it is completed in 2009, will result in water levels up to 110m higher than current levels, flooding many towns and villages. Flow Processes and Hydrostatic Forces 2

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2/2/2009 2 Content 1. Pressure and Pressure Forces in Static Fluids 2. Velocity Distribution 3 Pressure and Pressure Forces in Static Fluids: Hydrostatic Forces 4 We often need to answer the question: What is the force being exerted on a submerged surface?
2/2/2009 3 Hydrostatic Force When a surface is submerged in a fluid, forces develop on the surface due R F pA = to the fluid. The determination of these forces is important in the design of storage tanks, ships, dams, and other hydraulic structures. For fluids at rest we know that the force must be perpendicular to the surface since there are no shearing stresses present. We also know that the 5 pressure will vary linearly with depth if the fluid is incompressible. The atmospheric pressures cancel out for the example on the left. p h γ = F R – resulting force, p – uniform pressure on bottom, A – area of bottom, γ – specific weight of fluid, h – depth of fluid We’ve got a lot of Dams in this Country! 1800 2000 6 1900 1950

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2/2/2009 4 Hydrostatic Force The hydrostatic force on any submerged plane surface is equal to the product of the plane’s surface area and the pressure acting at the centroid of the plane centroid of the plane surface. 7 Hoover Dam Hydrostatic Force – General Inclined Case 0 Surface is open to atmosphere θ is angle between surface and axis 0 is origin of x-y coordinate y is in line with inclined plane surface The area can have an arbitrary shape --- 8 What are direction, location, and magnitude of the resultant force due to the liquid in contact with the area?
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CE361 - Lecture 06 - 2/2/2009 Water Resources Engineering E...

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