Main variables:

When we write \(a\) instead of \(\vec{a}\), we refer to the magnitude of that vector. For instance, \(\vec{a}\) is the acceleration vector, and \(a\) is the magnitude of the acceleration.

Subindex ‘i’ means initial. Subindex ‘f’ means final. For example, \(\vec{v}_i\) represents the initial velocity.

Main Equations:

The density of an object is:

\begin{equation*}
\rho = \frac{m}{V}.
\end{equation*}

Pressure:

\begin{equation*}
P = \frac{F}{A}.
\end{equation*}

Pressure in a fluid of uniform density:

\begin{equation*}
P = P_0 + \rho g h.
\end{equation*}

Buoyant force (Archimedes’ principle):

\begin{equation*}
F_B = \rho_F V_{fd} g.
\end{equation*}

Volume flow rate:

\begin{equation*}
Q = \frac{ \Delta V}{ \Delta t} = A v.
\end{equation*}

Volume flow rate in differential form:

\begin{equation*}
Q = \frac{dV}{dt} = A v.
\end{equation*}

Continuity equation:

\begin{equation*}
A_i v_i = A_f v_f.
\end{equation*}

Bernoulli equation:

\begin{equation*}
P_i + \rho g z_i + \frac{1}{2} \rho v_i^2 = P_f + \rho g z_f + \frac{1}{2} \rho v_f^2.
\end{equation*}