HYDROSTATIC FORCES MAGNITUDE FORCE PRESSURE x AREA LINE

HYDROSTATIC FORCES MAGNITUDE, FORCE = PRESSURE x AREA LINE OF ACTION CENTRE OF PRESSURE

HYDROSTATIC FORCE ON A HORIZONTAL SURFACE • CONSTANT PRESSURE • PASCAL’S PARADOX T W DAVIES 2

HYDROSTATIC FORCE ON VERTICAL SURFACES • INCLINED/VERTICAL SURFACES • PRESSURE CHANGES WITH DEPTH • NEED TO INTEGRATE OVER SURFACE T W DAVIES 3

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 T W DAVIES 4

CENTRE OF PRESSURE • Turning moment on a representative element • Sum all such elements • Equate to moment of resultant force acting through centre of pressure T W DAVIES 5

CENTER OF PRESSURE • FULLY SUBMERGED SURFACE – top is y 1 from free surface – bottom is y 2 from free surface – I. e. h = y 2 - y 1 • ycp = 2/3. (y 23 - y 13) / (y 22 - y 12) T W DAVIES 6

CENTRE OF PRESSURE • LIMITS – when y 1 = 0, then y 2 = h and ycp = 2/3. h – as submergence increases, ycp approaches ycg T W DAVIES 7

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 T W DAVIES 8