FLUIDS AND FLUID DYNAMICS
We can classify matter into three basic categories based on their properties: solid, liquid, and gas. A gas takes on the shape and volume of a container it is in. A liquid takes the shape of the container that it fills but retains a fixed volume. A solid has a specified shape and volume. Liquids and gases are called fluids. Fluid dynamics is the branch of science that involves the study of movement of liquids and gases.
Definitions and Properties
Viscosity
This refers to the thickness of the fluid. Viscosity is a measure of opposition to flow. The opposite of viscosity is fluidity which is the measure of easiness to flow. A fluid with a low viscosity is a thin fluid, and a high viscosity fluid is known as a thick fluid. It is easier to move through a thin fluid than a thick fluid.
Two types of viscosity are:
- Dynamic viscosity
- Kinematic viscosity
Dynamic viscosity is defined as the measure of the internal resistance of a fluid to flow. Kinematic viscosity is defined as the ratio of dynamic viscosity to density. If dynamic viscosity is denoted as μ and density as ρ, then Kinematic viscosity:
ν = μ / ρ.
Density
The density of a material is defined as its mass per unit volume. In other words, density is the ratio of mass and volume of a material.
To calculate the density (ρ) of an object with mass (m) and volume (v), we can use the formula ρ = m / v
The SI unit of density is kilogram per cubic meter (kilogram per meter cubed).
Pressure
Pressure is a measurement of the force applied per unit area. We know the unit of force is Newton and the unit of area is square meter. Therefore, the unit of pressure will be Newton per square meter. But the generally adopted SI unit of pressure is Pascal (P).
Flow
The movement of liquids and gases is called the flow of the fluid.
As fluids flow, the density and pressure of the fluids are significant properties. The viscosity defines how resistant the liquid is to change. Therefore, knowing these variables is necessary for examining the flow.
Based on the various properties of the flow, it can be classified into different categories.
Steady and Unsteady Flow
If the flow of fluid is not changing over time, it is considered a steady flow. A current flowing at a constant rate through a straight pipe would be an example of a steady flow.
If the flow has properties that change over time, then it is called an unsteady flow. Rainwater flowing into a drain during a storm is an example of unsteady flow.
Laminar Flow and Turbulent Flow
A smooth flow of liquid is called a laminar flow. A flow that involves apparent disorder or non-linear motion is called a turbulent flow.
The difference between laminar or turbulent flow is usually associated with the Reynolds number (Re). The Reynolds number depends on the properties of the fluid and the conditions of its flow.
Re = Inertial force / Viscous forces
Or
Re = (ρ V L) / μ
where ρ is the density, μ is the viscosity, V is the velocity of the flow and L is the scale of length.
Pipe Flow
Pipe flow describes a flow that touches or comes in contact with the rigid boundaries on all sides, such as water moving through a pipe or air moving through an air duct.
Open-Channel Flow
Open-channel flow denotes the flow in other situations where there is at least one free surface that is not touching or in contact with a rigid boundary. Examples of open-channel flow include water flowing in a river, floods, and irrigation canals.
Compressible and Incompressible flow
Gases are usually compressible fluids as the volume that contains it can be decreased. The size of an air duct can be decreased to half the original size and it can still carry the same amount of gas at the same rate.
Liquids can also be compressed, but there is a limitation on the amount of compression that can be made. Therefore, liquids are generally referred to as incompressible.
FORCES ON FLUIDS
Fluids are substances that continually deforms when a force is applied to them unlike solids and continues to deform even after the force is removed.
Pressure
Pressure is the force applied per unit area, and its SI unit is Pascal. The pressure will be higher if a force is exerted over a small area compared to the pressure when the same force is applied over a larger area.
Atmospheric pressure
The pressure exerted by the gases in Earth’s atmosphere is called atmospheric pressure. Earth’s atmosphere is retained against the surface of the Earth by gravity.
Gravity gives weight to the gases and lets the gases apply pressure on us in all directions. There is a weight of about 10N on every square centimetre of your body surface. Fluids in our body apply pressure back, so we do not notice this pressure. As you go up, air pressure is reduced, and the concentration of air molecules reduces.
This is the reason for less oxygen with every breath at higher altitudes. You will notice atmospheric pressure most when you go up to higher altitudes or climb down from higher altitudes. The atmospheric pressure varies non-uniformly with altitude. It changes more swiftly at lower altitudes. Atmospheric pressure can be measured by an instrument called ‘the barometer’.
Water pressure
Like atmospheric pressure, water pressure depends on depth. Because water is denser than air, a certain volume of water has more mass and weighs more than the same volume of air.
Pressure difference
Fluids move from areas of higher pressure to areas of lower pressure. For instance, when you inhale, your diaphragm muscle expands the volume of your chest cavity and thus lower the pressure. Air outside will be at a higher pressure, and it will rush into the lower pressure area in your lungs.
When you exhale, your diaphragm pushes up, reducing the volume of your chest, squeezing the air in your lungs, and raising its pressure. The air moves out into the lower pressure atmosphere.
Buoyant forces
A lifting force experienced by an object fully merged or submerged in a fluid is called buoyant force. This phenomenon is called buoyancy.
Then how do objects sink in a fluid if there is an upward force acting on it?
For sinking objects, their weight is greater than the buoyant force.
Pascal’s law
Pascal’s law states that when pressure is applied to a fluid in an enclosed container, it will get transmitted without loss to every portion of the fluid and to the walls of the container.
The principle was first introduced by a scientist called Blaise Pascal. According to Pascal’s law, in a hydraulic system, a pressure exerted on a piston generates an equal increase in pressure on another piston in the same system.
It can be represented mathematically as:
F=PA
Where:
F = force applied
P = pressure transmitted
A = cross-sectional area
A hydraulic press is an important application of Pascal’s law.
