Mechanical energy term is a very wide term and it is used in many engineering and physical systems. Mechanical energy balance is generally used in lots of engineering and practical applications. Mechanical energy has a very basic principle. In this article,

Table of Contents ;

- The general definition of mechanical energy,
- Mechanical energy balance in physical systems,
- Applications where mechanical energy balance is used,
- Mechanical energy balance calculator for mechanical systems,

topics are mentioned about mechanical energy.

## What is the Mechanical Energy?

There are various types of **energy** and mechanical energy is the total useful energy of the combination of these energies. Cakculation of the mechanical energy changes according to the different mechanical systems. But in the most general viewpoint, mechanical energy is the combination of the potential energies and kinetic energies of each part of the system.

Mechanical Energy = Potential Energy + Kinetic Energy

In a mechanical or physical system, there can be different parts that may have potential energies such as springs.** **Potential energies of springs are calculated with the formulation of;

According to this formula, ‘x’ is the total length that spring is stressed and ‘k’ is the spring constant.

Also, another energy originates from the height of objects on the surface of the earth. There is a potential energy difference between the different heights. The potential energy is calculated as;

In this formula, ‘m’ is the mass of the object, ‘g’ is the gravitational acceleration of the earth which is 9,81 m/s², and ‘h’ is the total height of the object.

Kinetic energy is directly related to the speed of the object.

The kinetic energy of an object is calculated with the formula above. In this formula, ‘v’ is the velocity of the object.

To calculate the mechanical energy of a mechanical system, you need to calculate all the potential and kinetic energies of the elements of the system.

## Mechanical Energy Balance in Mechanical Systems

Mechanical energy is used to produce or create useful mechanical works. Or mechanical work is used to obtain mechanical energy in most of the systems. According to the second law of thermodynamics, energy is neither created nor destroyed. In most mechanical systems, the elements of mechanical energy, potential, and kinetic energies, are transferred by each other to produce mechanical work. Think about hydroelectric energy plants in that the water flux from high altitudes to low altitudes is used to produce electricity. In this water flux, the turbines are rotated with the power of water flux and this rotation produces mechanical work. In the generators, this mechanical work is converted to electrical energy production. The produced electricity can be calculated easily with the mechanical energy balance.

The mechanical energy balance must be built between the first situation of the water and the second situation of the water. Water comes from high altitudes to lower altitudes. The potential energy difference between the altitudes is used for the production of mechanical work.

### Mechanical Energy Balance Formula

This is the most general mechanical energy balance for most engineering systems. Here, the total energy change for a fluid flux is calculated. The important terms here;

- P1 is the pressure of the fluid in the first point.
- P2 is the pressure of the fluid in the second point.
- V1 is the velocity of the fluid in the first point.
- V2 is the velocity of the fluid in the second point.
- Z1 is the altitude of the fluid in the first point.
- Z2 is the altitude of the fluid in the first point.
- m is the total flow rate of the fluid.

The total mechanical power that is sent to the generator can be calculated with this formula. For example for the hydroelectric plant power generation calculation, the pressures of the fluid are equal because the water comes from atmospheric pressure and goes to the atmospheric pressure. Velocities are zero at both points where high and low altitudes. The only parameter is the difference in the altitudes. If you eliminate the pressure and velocity variables from the general mechanical energy balance formula, you will have the mechanical work formula for the hydroelectrical energy plant.

## Applications That Mechanical Energy Balance is Used

There are different kinds of applications that which mechanical energy balance is mainly used. Just like hydroelectric plants, the energy equation is written between the first and the second points.

**Wind turbines:**To rotate the propeller of the wind turbines, the velocity or the kinetic energy of the flowing air is used. We need to examine the flow velocity of air right before the wind turbine blades and right after the wind turbine blades to find the total electricity that is produced. There is no difference in the pressure and altitudes for wind turbine applications.**Fluid Pumping Systems:**In lots of the systems, fluids are pumped to higher altitudes or pumped away. So, the total mechanical energy that is transferred to flowing fluid is very important here. The total power of the pump is added to the total mechanical energy of the fluid, and the maximum altitude that flow can flow is calculated with the mechanical energy balance equation.

## Mechanical Energy Balance Equation Calculator

We prepared a calculator to calculate the total mechanical energy difference of a system. For all the engineering systems that produce mechanical energy or consume mechanical energy, this calculator can be used.

The use of the calculator is very simple. You just need to enter the pressure, velocity, and altitude values with the flow rate of the fluid, and the calculator automatically calculates the total energy difference between the two points of the system. After entering the required values inside the brackets, just click on the ‘Calculate!’ button to see the difference in mechanical energy. Click on the ‘Reset’ button to make another calculation.

## Conclusion

Mechanical energy can be explained like this in terms of engineering and physics.

Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

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