CK12 Calculus - Single Variable

As you can see, it is easyto calculatethe fluid forceon a horizontalsurfacebecauseeachpointon the
surfaceis at the samedepth.The problembecomesa little complicatedwhenwe wantto calculatethe fluid
forceor pressureif the surfaceis vertical.In this situation,the pressureis not constantat everypointbecause
the depthis not constantat eachpoint.To find the fluid forceor pressureon a verticalsurfacewe mustuse
calculus.

The FluidForceon a VerticalSurface

Supposea flat surfaceis submergedverticallyin a fluid of weightdensityw and the submergedportionof

the surfaceextendsfrom to alongthe vertical -axis,whosepositivedirectionis takenas

downward.If is the widthof the surfaceand is the depthof point then the fluidforce

is definedas

Example6:
A perfectexampleof a verticalsurfaceis the face of a dam.We can pictureit as a rectangleof a certain
heightand certainwidth.Let the heightof the dam be metersand of widthof meters.Find the total
fluid forceexertedon the face if the top of the dam is level with the watersurface(Figure24).