Pressure

A fluid is a body that does not keep a shape of its own but adapts to that of its container: a liquid such as water, a gas such as air, or a liquid metal such as mercury. For a fluid the concept of “force applied at a point” is of little use, because the same push is distributed over the whole contact surface. What matters is the pressure: how much force acts per unit area.

Principle — Pressure

The pressure $P$ exerted by a force $\vv{F}$ perpendicular to a surface of area $A$ is $\ev{P = \frac{F_\perp}{A}}$

The SI unit of pressure is the pascal (Pa), equal to $1\;\text{N/m}^2$. Since the pascal is a tiny quantity compared with everyday pressures, practical units are often used instead: $1\;\text{bar} = 10^5\;\text{Pa}$ and $1\;\text{atm} \approx 1{,}013\cdot 10^5\;\text{Pa}$, the latter roughly equal to atmospheric pressure at sea level.

Pressure is a scalar

Pressure is a scalar quantity — a number, not a vector. At a point in a fluid it has no direction: the force on an immersed surface element is always perpendicular to the surface itself, whatever orientation we give it. Rotating the element changes the direction of the force but not the value of the pressure.

For solids pressure reduces to “force per unit contact area”: a knife cuts because, by concentrating the force of the arm on a thin blade, it generates an enormous pressure over a tiny surface. For fluids the story is richer. In a fluid at equilibrium every portion, however small, must have zero net force: from this simple requirement follow the three fundamental laws of fluid statics that we shall study on the following pages.

Collegamenti

Argomenti: Fluidostatica e fluidodinamica Concetti: Pressione

Esercizi collegati: Esercizio svolto — Pressa per la frutta · Esercizio svolto — Pressione del cuore · Esercizio svolto — La colonna d’aria che schiaccia i nostri piedi