[[Introduction to Fluid Mechanics - Fox, McDonald.pdf#page=88&selection=27,0,27,28|Introduction to Fluid Mechanics, Summary and Useful Equations]] | Application | Equation | | ------------------------------------------------------------------------- | ------------------------------------------------------------ | | Hydrostatic pressure variation | $\frac{dp}{dz}=-\rho g=-\gamma$ | | Hydrostatic pressure variation (incompressible fluid) | $p-p_{0}=\Delta p=\rho gh$ | | Hydrostatic pressure variation (several incompressible fluids) | $\Delta p=g\sum_{i}\rho_{i}h_{i}$ | | Hydrostatic force on a submerged plane (integral form) | $F_{R}=\int_{A}pdA$ | | Hydrostatic force on a submerged plane | $F_{R}=p_{c}A$ | | Hydrostatic force on a submerged plane | $F_{R}=p_{c}A$ | | Location $y'$ of hydrostatic force on submerged plane (integral) | $y'F_{R}=\int_{A}ypdA$ | | Location $y'$ of hydrostatic force on submerged plane (algebraic) | $y'=y_{c}+\frac{\rho g\sin\theta I_{\hat{x}\hat{x}}}{F_{R}}$ | | Location $y'$ of hydrostatic force on submerged plane ($p_{0}$ neglected) | $y'=y_{c}+\frac{I_{\hat{x}\hat{x}}}{Ay_{c}}$ | | Location $x'$ of hydrostatic force on submerged plane (integral) | $x'F_{R}=\int_{A}xpdA$ | | Location $x'$ of hydrostatic force on submerged plane (algebraic) | $x'=x_{c}+\frac{\rho g\sin\theta I_{\hat{x}\hat{y}}}{F_{R}}$ | | Location $x'$ of hydrostatic force on submerged plane ($p_{0}$ neglected) | $x'=x_{c}+\frac{I_{\hat{x}\hat{y}}}{Ay_{c}}$ | | Horizontal and vertical hydrostatic forces on curved submerged surface | $F_{H}=p_{c}A$ and $F_{V}=\rho gV$ | | Bouyancy force on submerged object | $F_{b}=\rho gV$ |