Hydrostatic Force (= Force due to the pressure （静水压力(=力由于压力）.pdf

Hydrostatic Force (= Force due to the pressure of a fluid at rest) e.g Force exerted on the wall of storage tanks, dams, and ships) Q. How is Hydrostatic Force on the vertical or inclined planes determined? Basic conditions for a Plane surface submerged in a fluid - Force on the surface: Perpendicular to the surface (No τ) - Pressure: Linearly dependent only to the vertical depth 1. On a Horizontal surface (e.g. the bottom of a tank) Pressure at the bottom, p γh : Uniform on the entire plane ∴ Resultant force FR pA γhA (A : the bottom area of container) 2. On an Inclined surface Consider a plane shown y - At surface: p = p atm - Angle θ between free surface x the inclined plane - y axis: Along the surface x axis: Out of the plane Along the vertical depth h Pressure linearly changes Hydrostatic force changes Differential Force acting on the differential area dA of plane, dF (Pressure) ⋅(Area) (γh) ⋅(dA) (Perpendicular to plane) Then, Magnitude of total resultant force FR FR ∫AγhdA ∫Aγ(y sinθ)dA where h y sinθ γ sinθ ydA 1st moment of the area ∫A - Related with the center of area ydA y A where y : y coordinate of the center of area (Centroid) ∫A c c c.f. Center or 1st moment xdm MX ydm MY (X Y : Center of Mass) ∫ C ∫ C C C M M xdA = x ydA = y (x y : Center of Area) ∫A c ∫A c c c Moment of inertia or 2nd moment