Download CE 204 FLUID MECHANICS

Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
CE 204
FLUID MECHANICS
Onur AKAY
Assistant Professor
Okan University
Department of Civil Engineering
Akfırat Campus
34959 Tuzla-Istanbul/TURKEY
Phone: +90-216-677-1630 ext.1974
Fax: +90-216-677-1486
E-mail: [email protected]
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Forces on Plane Surfaces (Review):
A plane surface or panel is a flat surface of arbitrary shape.
A description of the pressure at all points along a surface is called pressure distribution.
For a uniform pressure distribution, the CP is located at the centroid of area of the panel.
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Forces on Plane Surfaces (Review):
For a hydrostatic pressure distribution, the CP is located below the centroid of area.
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Magnitude of Resultant Hydrostatic Force (Review):
Hydrostatic force = (Pressure at the centroid of area) x (Panel area)
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Line of Action of the Resultant Force (Review):
Area
Moment of
Inertia
- Applies only to a single fluid of constant density
- Pressure at liquid surface p=0 gage
- Gives only the vertical location of the CP
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Forces on Curved Surfaces:
AC: Simulate as vertical gate
CB: Simulate as horizontal gate
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Forces on Curved Surfaces:
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Problem 3.76:
Determine the hydrostatic force acting on the radial gate if the gate is 15 m long (normal to
the page). Show the line of action of the hydrostatic force acting on the gate.
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Buoyancy:
The upward force that is produced on a body that is totally or partially submerged in a fluid.
The Buoyant Force Equation:
Displaced
volume
Onur Akay, Ph.D.
Archimedes´ principle
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Stability of Immersed and Floating Bodies:
Stability: Determines whether an object will tip over or remain in an upright position when
placed in a liquid.
Immersed Bodies: Center of buoyancy (C) is at the centroid of the displaced volume.
Stable
(righting couple)
Onur Akay, Ph.D.
Neutral
CE 204 Fluid Mechanics
Unstable
(overturning couple)
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Floating Bodies: Center of Buoyancy (C) may take different positions.
MOVIE
Metacenter, M: Point of intersection of the lines of action of FB.
Metacentric Height, GM: Distance between G and M.
If M is above G, the ship is stable (GM+)
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Floating Bodies:
GM (+): STABLE
GM (-): UNSTABLE
Righting or Overturning Moment:
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Relative Equilibrium:
If a fluid mass is subjected to an external acceleration , an additional force will be
introduced (No relative motion of the liquid particles, no shear stress).
Liquid Subject to Horizontal & Vertical Acceleration:
Fluid Mass Under Constant Linear Acceleration
The acceleration affects depth but does not change the relationship:
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Fluid Mass Rotating at Constant Angular Velocity :
Constant angular velocity: w (rad/s)
Rotating Fluid Mass
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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Chapter 3 Fluid Statics
Forces on Curved Surfaces, Buoyancy, Stability of Immersed and Floating Bodies, Relative Equilib.
Onur Akay, Ph.D.
CE 204 Fluid Mechanics
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