\begin{equation} \rho = \frac{m}{V} \qquad (\textnormal{Density}) \tag{1} \end{equation} \begin{equation} p = \frac{F}{A} \qquad (\textnormal{Pressure}) \tag{2} \end{equation} \begin{equation} p = \frac{dF_{\perp}}{dA} \end{equation} \begin{equation} \Delta p = - \rho g \, (y_2 - y_1) \qquad (\textnormal{Pressure in uniform density fluid}) \tag{3} \end{equation} \begin{equation} p = p_0 + \rho \, g \, h \end{equation}
Pascal's law: Pressure applied to an enclosed fluid in a container is transmitted
to every part of the fluid and to the walls of the container.
Archimede's principle: When a body is partially or completely submerged in a fluid,
the fluid exerts a force on the body equal to the weight of the displaced fluid.
\begin{equation} A_1 \, v_1 = A_2 \, v_2 \qquad (\textnormal{Continuity equation, incompressible fluid}) \tag{4} \end{equation} \begin{equation} \frac{dV}{dt} = A \, v \qquad (\textnormal{Volume flow rate}) \tag{5} \end{equation} \begin{equation} p_1 + \rho g y_1 + \frac{1}{2} \rho v_1^2 = p_2 + \rho g y_2 + \frac{1}{2} \rho v_2^2 \qquad (\textnormal{Bernoulli's equation}) \tag{6} \end{equation}
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