Introduction

PRESSURE OF A FLUID. A fluid is a substance that begins to flow when even a very small external force is applied to it -- it offers very little resistance to deformation. If an object is submerged at rest in a fluid, the fluid exerts a force on every part of the object's surface, and this force always acts normal (perpendicular) to that surface. If F is the magnitude of the normal force acting on a surface area A, the PRESSURE is defined as the force acting per unit area, $P=\dfrac{F}{A}$. Pressure is a SCALAR quantity (it has a magnitude at a point but is not itself associated with any particular direction, even though the force it produces on any given surface does act along that surface's normal); its SI unit and dimensions are N m$^{-2}$ (pascal, Pa) and $[ML^{-1}T^{-2}]$ respectively. A commonly used non-SI unit is the ATMOSPHERE (atm), defined as the pressure exerted by the Earth's atmosphere at sea level: $1\ \text{atm}=1.013\times10^{5}\ \text{Pa}$. DENSITY AND RELATIVE DENSITY. Two further quantities describe the nature of a fluid. The DENSITY of a fluid is its mass per unit volume, $\rho=m/V$, with dimensions $[ML^{-3}]$ and SI unit kg m$^{-3}$; it is a positive scalar quantity. A liquid is largely incompressible, so its density stays nearly constant at ordinary (about 1 atm) pressure, while a gas's density does vary noticeably with pressure. The RELATIVE DENSITY (or specific gravity) of a substance is th …