SECTION 7.7 Fluid Pressure and Fluid ForceFull description
Hydrostatic force on a plane surface. How it is calculated? Which things are reqiuired and what procedure should be adoptedFull description
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The 1st official supplement for Force on Force, the modern skirmish wargame!
Descripción: The 2nd official supplement for Force on Force, the modern skirmish wargame!
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This experiment is designed to help you understand how to locate the center of pressure and compute the hydrostatic force acting on a submerged surfaceFull description
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Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com ME 3350 – Fall 16
handout 2.6
HYDROSTATIC FORCE ON A CURVED SURFACE EXAMPLES EXAMPLE 1: CURVED SURFACE BELOW FLUID Consider a curved gate (radius: R ; width perpendicular to the page: w ) submerged at a depth H in a fluid of density .
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What is the resultant hydrostatic force FR acting on the gate?
CALCULATION OF THE HORIZONTAL COMPONENT OF THE RESULTANT PRESSURE FORCE The horizontal component of the hydrostatic force acting on a curved surface is equal to the hydrostatic force acting on the vertical projection of the curved surface. The vertical projection of the curved surface is a plane surface of height R and width (perpendicular to the page) w .
At a depth z , the water exerts a pressure force dFH on the surface element dA along the vertical projection of the gate:
Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com ME 3350 – Fall 16
handout 2.6
The horizontal component of the resultant pressure force is obtained by integration:
Therefore:
CALCULATION OF THE VERTICAL COMPONENT OF THE RESULTANT PRESSURE FORCE The vertical component of the hydrostatic force acting on a curved surface is equal to the hydrostatic force acting on the horizontal projection of the curved surface plus the weight of the fluid block. (The fluid block is the fluid domain located between the horizontal projection of the curved surface and the curved surface)
Therefore:
The weight of the fluid block is the weight of fluid in a quarter cylinder of radius R and width w :
The hydrostatic force acting on the horizontal projection of the curved surface is the product of the pressure at depth z H and the horizontal projected area A (i.e., area of a rectangular surface of length w and width R :
Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com ME 3350 – Fall 16
handout 2.6
Since those two forces F and W act in the same direction, the vertical component of the resultant hydrostatic force acting on the curved surface is:
EXAMPLE 2: CURVED SURFACE ABOVE FLUID
CALCULATION OF THE HORIZONTAL COMPONENT OF THE RESULTANT PRESSURE FORCE The horizontal component of the hydrostatic force acting on a curved surface is equal to the hydrostatic force acting on the vertical projection of the curved surface.
The calculation of the horizontal component of the resultant pressure force is similar to example 1. At a depth z , the fluid exerts a pressure force dFH on the surface element dA along the vertical projection of the curved surface:
Produced with a Trial Version of PDF Annotator - www.PDFAnnotator.com ME 3350 – Fall 16
handout 2.6
Therefore, the horizontal component of the resultant pressure force acting on the curved surface is:
CALCULATION OF THE VERTICAL COMPONENT OF THE RESULTANT PRESSURE FORCE The vertical component of the hydrostatic force acting on a curved surface is equal to the hydrostatic force acting on the horizontal projection of the curved surface plus the weight of the fluid block.
The weight of the fluid block is:
The hydrostatic force acting on the horizontal projection of the curved surface is:
Since those two forces act in opposite directions, the vertical component of the resultant hydrostatic force on the curved surface is:
