\youtubethumb{4MVn1PoxGqY}{pre-lecture briefing for this chapter (back when it had a different chapter number)}{\oc (\ccby)}

In fluid mechanics, only three types of forces apply to fluid particles: forces due to gravity, pressure, and shear. This chapter focuses on pressure (we will address shear in \chapterfive), and should allow us to answer two questions:

In fluid mechanics, only three types of forces apply to fluid particles: forces due to gravity, pressure, and shear. This chapter focuses on pressure (we will address shear in \chapterfiveshort), and should allow us to answer two questions:

\begin{itemize}

\item How is the effect of pressure described and quantified?

\item What are the pressure forces generated on walls by static fluids?

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@@ -151,7 +151,7 @@

\item where $\diff\vol\equiv\diff x \diff y \diff z$ is the volume of the infinitesimal cube.

\end{equationterms}

Now generalizing eq.\ref{eq_force_pressure_x} for the other two directions, we can write:

Now generalizing eq.~\ref{eq_force_pressure_x} for the other two directions, we can write:

What are the forces applying on an arbitrary particle in a static fluid?

\begin{itemize}

\item The force due to pressure is related to the pressure gradient: we just quantified this with eq~\ref{eq_pressure_force_in_fluid}.

\item The force due to pressure is related to the pressure gradient: we just quantified this with eq.~\ref{eq_pressure_force_in_fluid}.

\item The force due to shear is zero. We will indeed see in \chapterfive that shear efforts can be expressed as a function of viscosity and velocity. All ordinary fluids are unable to exert shear when static.

\item The force due to gravity is easy to quantify: it is the mass $m$ of the fluid multiplied by the gravity vector $\vec g$.

\end{itemize}

In a moving fluid, the sum of these forces would add up to the mass of the particle times its acceleration. But in a static fluid, the velocity is zero and never changes. We can thus write: