HYDROSTATIC FORCES
MAGNITUDE,
FORCE = PRESSURE x AREA
LINE OF ACTION
CENTRE OF PRESSURE
HYDROSTATIC FORCE ON A
HORIZONTAL SURFACE
• CONSTANT PRESSURE
• PASCAL’S PARADOX
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HYDROSTATIC FORCE ON
VERTICAL SURFACES
• INCLINED/VERTICAL SURFACES
• PRESSURE CHANGES WITH DEPTH
• NEED TO INTEGRATE OVER SURFACE
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MAGNITUDE OF
HYDROSTATIC FORCE ON A
PLAIN SURFACE
• Force on a representative element
• Integrate to give total force
• Show that total force = wetted area x
average pressure
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CENTRE OF PRESSURE
• Turning moment on a representative
element
• Sum all such elements
• Equate to moment of resultant force acting
through centre of pressure
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CENTER OF PRESSURE
• FULLY SUBMERGED SURFACE
– top is y1 from free surface
– bottom is y2 from free surface
– I.e. h = y2 - y1
• ycp = 2/3 . (y23 - y13) / (y22 - y12)
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CENTRE OF PRESSURE
• LIMITS
– when y1 = 0, then y2 = h and ycp = 2/3. h
– as submergence increases, ycp approaches ycg
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FORCES ON CURVED
SURFACES
• HORIZONTAL FORCE ON VERTICAL
PROJECTION OF THE SURFACE, AVP
– resultant force = pav . avp
– c.o.p. as for plain surface
• VERTICAL FORCE ON HORIZONTAL
PROJECTION OF THE SURFACE, AHP
– equal to weight of fluid contained or displaced
– acts through centre of gravity of fluid mass
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