Question

Q1: 1.) Mention all types of energies and distinguish the macro-types of mechanical energy 2.) How is Bernoulli relation related to the main forms of mechanical energy 3.) Write Bernoulli equation in its three forms and name each components in the three forms 4.) Write the energy equation in its complete form. 5.) In the UK, the demand for electric power is usually much higher during the day than it is at night, and utility companies often sell power at night at much lower prices to encourage consumers to use the available power generation capacity and to avoid building new expensive power plants that will be used only a short time during peak periods. Utilities are also willing to purchase power produced during the day from private parties at a high price. Suppose a utility company is selling electric power for $(0.034(n/100))/kWh at night and is willing to pay $(0.08+(n/100))/kWh for power produced during the day. To take advantage of this opportunity, an entrepreneur is considering building a large reservoir (40+(n/10)) m above the lake level, pumping water from the lake to the reservoir at night using cheap power, and letting the water flow from the reservoir back to the lake during the day, producing power as the pump-motor operates as a turbine generator during reverse flow. Preliminary analysis shows that a water flow rate of (2+n/100)) m/s can be used in either direction, and the irreversible head loss of the piping system is (4+n/1000)) m. The combined pump motor and turbine generator efficiencies are expected to be 75 percent each. Assuming the system operates for 10 h each in the pump and turbine modes during a typical day, determine the potential revenue this system can generate per year. The entrepreneur decided to play with the piping diameters in order to increase power generation. He chose a pipe area upstream of the pump-turbine system as (0.03 (n/1000)) mº and a diameter of (0.03+n/1000)) m downstream of the pump-turbine system. How would this affect his revenue. n=the last two digits of your ID number. You may develop and submit an excel sheet to perform the calculation

n = 32

Answer 1

1) Types of energies

1. Thermal (Heat) Energy

Thermal energy is created from the vibration of atoms and molecules within substances. The faster they move, the more energy they possess and the hotter they become. Thermal energy is also called heat energy.

2. Chemical Energy

Chemical energy is stored in the bonds of atoms and molecules – it is the energy that holds these particles together. Stored chemical energy is found in food, biomass, petroleum, and natural gas.
3. Nuclear Energy
Nuclear energy is stored in the nucleus of atoms. This energy is released when the nuclei are combined (fusion) or split apart (fission). Nuclear power plants split the nuclei of uranium atoms to produce electricity.
4. Electrical Energy
Electrical energy is the movement of electrons (the tiny particles that make up atoms, along with protons and neutrons). Electrons that move through a wire are called electricity. Lightning is another example of electrical energy.
5. Radiant Energy
Also known as light energy or electromagnetic energy, radiant energy is a type of kinetic energy that travels in waves. Examples include the energy from the sun, x-rays and radio waves.
6.LightEnergy                                                                                                                                                                                                                                                                                                                Light energy is a form of electromagnetic radiation. Light consists of photons, which are produced when an object's atoms heat up. Light travels in waves and is the only form of energy visible to the human eye.
7. Motion Energy
Motion energy – or mechanical energy – is the energy stored in objects; as objects move faster,more energy is stored. Examples of motion energy include wind, a flowing river, a moving car, or a person running.
8. Sound Energy
Sound energy is the movement of energy through substances. It moves in waves and is produced when a force makes an object or substance vibrate. There is usually much less energy in sound than in other forms of energy.
9. Elastic Energy
Elastic energy is a form of potential energy which is stored in an elastic object - such as a coiled spring or a stretched elastic band. Elastic objects store elastic energy when a force causes them to be stretched or squashed.
10. Gravitational Energy
Gravitational energy is a form of potential energy. It is energy associated with gravity or gravitational force – in other words, the energy held by an object when it is in a high position compared to a lower position.
Types of mechanical energies

• Mechanical energy, also known as motion energy, is how an object moves based on its position and motion. It occurs when a force acts upon an object and the object uses the transferred energy as movement. If an object is moving, it is using mechanical energy. There are two types of mechanical energy: potential energy (stored energy of position) and kinetic energy (energy of motion). The mechanical energy of an object is the sum of its potential energy and its kinetic energy. Objects with higher amounts of mechanical energy will move more than objects with low mechanical energy.
• Macro type Mechanical energy means macro the kinetic and potential energies of macro level phenomena’s.
• Kinetic energy is energy possessed by a body by virtue of its movement. Potential energy is the energy possessed by a body by virtue of its position or state. While kinetic energy of an object is relative to the state of other objects in its environment, potential energy is completely independent of its environment. Hence the acceleration of an object is not evident in the movement of one object, where other objects in the same environment are also in motion. For example, a bullet whizzing past a person who is standing possesses kinetic energy, but the bullet has no kinetic energy with respect to a train moving alongside.

2). The simplest form of Bernoulli’s equation (steady and incompressible flow) states that the sum of mechanical energy, potential energy and kinetic energy, along a streamline is constant. Therefore, any increase in one form results in a decrease in the other.

• Bernoulli’s equation considers only pressure and gravitational forces acting on the fluid particles. Therefore, if there is no change in height along a streamline, Bernoulli’s equation becomes a balance between static pressure and velocity.

3) Following are the three forms of bernoullis equation
1. ENERGY FORM
For steady state in-compressible flow the Euler equation becomes

• E = p1 / ρ + v12 / 2 + g h1 = p2 / ρ + v22 / 2 + g h2 - Eloss = constant

where
E = energy per unit mass in flow (J/kg, Btu/slug)
p = pressure in the fluid (Pa, psi)
ρ = density of fluid (kg/m3, slug/ft3)
v = velocity of fluid (m/s, ft/s)
Eloss = energy loss per unit mass in flow (J/kg, Btu/slug)
2. Head Form
(1) can be modified by dividing with gravity like

• h = p1 / γ + v12 / (2 g) + h1 = p2 / γ + v22 / (2 g) + h2 - Eloss / g = constant (2)

where
h = head (m fluid column, ft fluid column)
γ = ρ g = specific weight of fluid (N/kg, lbf/slug)
3. Pressure form

• P = p1 + ρ v12 / 2 + ρg h1 = p2 + ρ v22 / 2 + ρg h2

where
p = pressure (Pa, psi)
ploss = pressure loss (Pa, psi)
pd = 1/2 ρ v2 = dynamic pressure (Pa, psi)

4) Energy equation in its full form according to fluid dynamics

| |Ple+ :) • Inle+ :)) - ва + . () + (%) ә, әт) дир) дvр) дwp) дитxx) * z(" az) Әх ду дz t əx ситух) Ә(итах) д(vтҳу) дутуу дутуу) " ду дz дхо ду д(wТ) д(wТуі) д(wTu) * дx + + +pf.

The given equation is the conservation form of the energy equation, written in terms of the total energy, (e+V2/2)

where

e = internal energy

v = velocity

u = velocity component in x direction

v = velocity component in y direction

w = velocity component in z direction