A fluid is any substance that takes the form of its container. This includes both liquids and gases, but we will focus on liquids in this study guide. Since fluids are amorphous (shapeless) and made of molecules that are allowed to move relative to each other, we cannot treat them the same as solids. Unlike solids, forces cannot be exerted on a single point of a fluid. Therefore, we must measure quantities such as force and energy in terms of their density. In the study of fluids, volume and mass density are more important quantities than mass.
Pressure: Measure of force per unit area. SI units: Pa
Pascal’s Law: The pressure on a fluid is distributed equally throughout the whole fluid.
Archimedes’ Principle: Describes the upward buoyant force on an object in a fluid. The buoyant force is proportional to the weight of the displaced volume of the fluid. SI units: N
Bernoulli’s Equation: Equation for the conservation of energy of fluids.
The pressure of a fluid represents the force exerted by the fluid’s molecules colliding with each other. Pressure can be measured in two ways. Absolute pressure is measured with 0 pressure being a vacuum. Gauge pressure is measured where 0 is the ambient air pressure at sea level.
A small force applied over a small surface on one end of a fluid's container will produce a large force on a large surface on the other end of the container - the pressure ratio is equal. This is known as Pascal's law and is the physical principle behind all hydraulic machinery. To the right is a diagram that illustrates this concept.
Image Credit: Lidingo, CC-BY-SA 3.0
If there is an object within the fluid, the fluid exerts a pressure on the object.
Image Credit: Yupi666, GNU-FDL 1.2
\(p = \frac{m}{v}\)
ρ - mass density
m - mass
V - volume
\(p = \frac{F}{A}\)
P - pressure
F - force
A - area
\(u_g = pgh\)
\(u_g\) - gravitational potential energy density
g - acceleration due to gravity
h - height
\(ke = \frac{1}{2}pv^2\)
ke - kinetic energy density
\(p = \frac{m}{v}\)
Continuity of fluid flow: \(\Delta p + \Delta ke + \Delta U_g = 0\)
Bernoulli’s equation: \(A_iV_i = A_fV_f\)