This chapter explores the mechanical properties of fluids, including pressure, viscosity, and surface tension, and explains key principles such as Bernoulli's principle and the concept of streamline flow.
In this chapter, we explore the behavior and properties of fluids, both liquids and gases, which can flow. This characteristic of fluids differentiates them from solids. Understanding how fluids behave is essential as they play significant roles in various processes in our daily lives and natural phenomena.
Fluids are defined as substances that flow and do not have a fixed shape. Unlike solids, they are influenced by external forces and pressure.
Pressure (A0) is defined as the force per unit area exerted uniformly on a surface:
[ P = \frac{F}{A} ]
where F is the force acting perpendicular to the surface area A. The SI unit of pressure is the Pascal (Pa), defined as N/m². Other units include:
Pascal’s Law states that a change in pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and the walls of its container. This principle allows hydraulic systems to work effectively, enabling heavy loads to be lifted using small forces.
The pressure in a fluid increases with depth due to the weight of the fluid above:
[ P = P_{a} + \rho gh ]
Where:
Gauge pressure is defined as the difference between the measured pressure and the atmospheric pressure:
[ P_{g} = P - P_{a} ]
In fluid dynamics, streamline flow refers to the smooth, laminar flow of a fluid in which all the particles move in parallel layers and do not mix.
Steady flow occurs when the velocity of a fluid at any point does not change over time, although velocities can vary at different points in the fluid. The path traced by a fluid particle under steady flow is called a streamline.
Bernoulli’s Principle relates the pressure, velocity, and height in flowing fluids. In a streamline flow, the sum of the kinetic energy, potential energy, and pressure energy remains constant:
[ P + \frac{1}{2} \rho v^{2} + \rho gh = constant ]
This principle explains various phenomena such as lift in an airplane, where the pressure difference above and below the wing creates lift due to differences in flow speed and pressure.
Viscosity is a measure of a fluid's resistance to deformation or flow. It describes how thick or thin a liquid is. Viscosity increases with temperature for gases and decreases for liquids. The equation for shear stress in fluids is:
[ \tau = \eta \left( \frac{du}{dy} \right) ]
where ( \tau ) is shear stress, ( \eta ) (eta) is the coefficient of viscosity, and ( \frac{du}{dy} ) is the shear rate.
Surface tension is the energy (or force) required to increase the surface area of a liquid due to cohesive forces among molecules at the interface
[ Surface,Tension (S) = \frac{F}{L} ]
(where F is the force and L is the length). Molecules at the liquid's surface experience a net inward force due to attraction from molecules within the liquid. This results in a minimized surface area in drops and bubbles, giving them a spherical shape.
The angle of contact is formed at the intersection of a liquid's surface with a solid surface, indicating how well the liquid wets the surface. An obtuse angle indicates poor wetting (e.g., mercury on glass), while an acute angle indicates good wetting (e.g., water on glass).