Formulas of Fluid Mechanics

Some of the important concepts and their formulas is mentioned below:

Bernoulli’s equation

Bernoulli’s equation is one of the basic principles in fluid mechanics. Bernoulli’s Principle yields a relation of pressure, velocity, and potential energy of the fluid in motion. It is given that the sum of the fluid energy at all points across a streamline is constant, and the pressure, kinetic energy, and potential energy summed at all points are equal to a constant. This is derived from the equation of motion and is applied in the analysis of fluid flow in various areas. The formula is as follows:

P + (1/2)ρv² + ρgh = constant

Pascal’s law

Another important principle of fluid mechanics is Pascal’s law, which states that the pressure exerted by a fluid on a surface is directly proportional to the surface area. The law is applied very widely when the fluid is at rest and pressure at some depth in a fluid of constant density is to be ascertained. The law is also used when pressure distribution in any system of fluids is to be analyzed. The mathematical expression is:

P1 = P2

Conservation of Mass

According to the principle of mass conservation in fluid mechanics, mass is conserved within a fluid for a fluid of constant density inside a control volume. This essentially means that the sum of the total mass entering a control volume will be equal to the sum of the total mass leaving the control volume plus the mass stored within the control volume.

This principle is used in the study of fluid flow in those systems in which mass is conserved, such as in open channels and pipes. It has been given as :

ρvA = m

Conservation of Momentum

The conservation of momentum states that, in fluid mechanics, the sum of partial derivatives of the velocity components with respect to space and time is equal to the multiplication of the fluid density and the acceleration due to gravity. The equation is in the form:

 ρvA(v + v’) = m(v’ – v)

Conservation of Energy

The principle of conservation of energy for fluid mechanics is the principle that the total energy of a fluid is conserved down a streamline, suggesting that the summation of internal, kinetic, and potential energy per unit volume is the same. Such a conservation law can be applied to the analysis of the flow of fluids under some conditions in which energy is conserved, such as hydrodynamics and fluid dynamics. The equation is written as:

ΔE = ΔU + ΔK + ΔP

Fluid mechanics is a branch of physics that deals with the study of fluids and their behavior under different conditions. All the fluids are substances that can flow and take the shape of their container. This article is an introduction to basic ideas of fluid mechanics, including the properties, classifications, principles, and applications of fluid mechanics.