Newton laws of motion:

9 min readFeb 5, 2021

First law: an object at rest stays at rest, and an object in motion stays in motion with the same speed and same direction, unless an unbalanced force: A dirty dish lying on the table will not move or get cleaned unless you apply some force and put it in the dishwasher.
Second law (Inertia law)
Third law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in opposite direction on the first body When you sit in a chair, you are constantly pushing on the chair with a downward force. The chair is also pushing you back with an upward force; otherwise, the chair would collapse and you would fall.

Gearbox: is a set of gears that can be added to a motor to drastically decrease speed and/or increase torque for a constant power from the motor, the rotational equivalent of linear force.

Gear train(Übersetzung): The input torque TA acting on the input gear GA is transformed by the gear train into the output torque TB exerted by the output gear GB. Gears are change due to what is called Gear Ratio / Velocity Ratio.

The rotary machine’s output torque is increased by multiplying the torque by the gear ratio.

Two meshing gears transmit rotational motion.

Wirbelschneckenmischer: zum kontinuierlichen Mischen von HD-PE (High Density PolyEthylen) mit Additiven.

Verschliess (Abrieb): wenn zwei metallische Oberflächen ohne ausreichende Schmierung aufeinander reiben: sie nutzen sich ab: Verschliess. Dann erzeugen sie kleine Partikel: Abrieb

Bearing:

Friction is bound to occur between the rotating shaft and the part that supports the rotation. Bearings are used between these two components. The bearings serve to reduce friction and allow for smoother rotation.

Reducing the static between moving
Using oil to lubricate it
Appropriate axial and radial clearance

In order to choose the type of bearing, the three basic load components on the bearing is to be defined. We have to consider the weight of the component, the force and the drive forces. The loads are generally radial and axial.

Finite Element Calculation for the temperature profile on a metal plate:

To measure temperature stress in an object, we use temperature sensor. But what if the temperature which we are going to measure has many of nodes? Putting all sensors on that nodes is less efficient. Solution for this problem is reducing the quantity of sensors and put it on boundary system and use that for computation purpose. Navier stokes are the equations, which will be solved with Navier stokes.

Bernoulli Equation:

AP(V)+V2/2g+DeltaZ+E=0

The PV change
The kinetic energy change or “velocity head”
The elevation change
The friction loss

Thermodynamic/phenomenology

Classical thermodynamics is the description of the states of thermodynamic systems at near-equilibrium, that uses macroscopic, measurable properties.

Statistical mechanics supplemented classical thermodynamics with an interpretation of the microscopic interactions between individual particles or quantum-mechanical states usually for lower temperatures than 0.

Equation of state: describes the state of matter at a given temp., pressure, volume (see the figure below). Given temp., vol., and press., the liquid fraction can be identified. The simplest equation of state is the ideal gas equation. Van der Waals added two terms to ideal gas equation. These terms contain critical parameters. Peng Robinson fits better than Van der Waals due to more parameters. Peng Robinson has acentric factor in addition to critical parameters.

Partial pressure of gas: In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas if it alone occupied the entire volume of the original mixture at the same temperature.

Double Clutch - Zwei Scheiben Kupplung (GSK): release and reengage the clutch of a vehicle simultaneously when changing gear.

Centrifual force and acceleration:

Thermodynamic laws:

Thermo means heat and dynamic force

Zeroth law: if two thermodynamic systems are each in thermal equilibrium with a third one, then they are in thermal equilibrium with each other.
First law: conservation of energy. The energy will be transformed and not created.

Closed System: The internal energy of a system can be increased by heating the system or working on the system.

exchange only energy with its surronding Delta U=Q-W

Open System: exchange energy and matter with its surronding (such as pump): Delta E= Q-W+mHin-mHout+min(h+V2/2+gZ)-mout(h+V2/2+gZ)

3. Second law: Entropy of a system increases. Heat flows from a hot coffee to the table because the heat energy will be more disordered.

Entropy is measured in J/K and is the measure of how energy is distributed within the system.

Enthalpy is describing the energy of system.

Gibbs relates entropy and enthalpy and tells us whether the process is spontaneous or not. If Gibbs is negeative, the process is spontaneous.

4. Third law: the efficiency can not be 100%

Vapour compression refrigeration system:

The cooling medium will be compressed through the compressor to increase the temperature to more than the ambient temp., then cooled down via the condensor. Next, the flowrate will be controlled by the valve. Finally, it will be sent to the evaporator, which gets the heat from the box of the refrigerator. 300 W will be the cooling duty in the evaporator and 400 W will be the heating duty in the condensor. The rest can be supplied from the electrical motor.

During the process of expansion, the temperature of the liquid refrigerant is also reduced. The compressor compresses the refrigerant to a high-pressure vapor, causing it to become superheated

Vapour absorption refrigeration system:

The compressor is replaced by an absorber, a pump, a generator, and a pressure reducing valve. Ammonia vapour enters the absorber where it gets dissolved in water, this reaction is exothermic and a lot of heat is released. The solubility of Ammonia is inversely proportional to temperature hence cooling water is circulated to maintain the low temperature of the solution.

Vapour absorption refrigeration system versus compression:

The absorption chiller consumes less electronic energy because it uses thermal energy and fossil fuels. The solution pump is the system’s only moving part; therefore, these systems are much smaller than compression refrigeration systems, and quieter, having no noisy compressor.

Magnetic Refrigeration:

Magnetic refrigeration is a cooling technology based on the magnetocaloric effect. This technique can be used to attain extremely low temperatures, as well as the ranges used in common refrigerators.

A magnetocaloric material warms up when a magnetic field is applied. The warming is due to changes in the internal state of the material releasing heat. When the magnetic field is removed, the material returns to its original state, reabsorbing the heat, and returning to original temperature.

Vapor Liquid Equilibrium:

Equilibrium is a static condition in which no changes occur in the macroscopic properties of a system with time. The temperature, pressure, and phase compositions reach final values.

Raoult’s Law:

If you have a pure component, the vapor pressure is higher than if there is a nonvolatile component in the solution. By having a nonvolatile component, the space of the surface layer will be occupied with that component. To calculate the vapor pressure:

Mole fraction of the component * vapor pressure

Major assumptions:

The vapor phase is an ideal gas, which may happen only for low to moderate pressures.
The liquid phase is an ideal solution, whose molecular species are not too different in size and are of the same chemical nature such as ortho-, meta-, para-xylene.

yiP=xiPsat

Raoult’s law can be applied only to species of know vapor pressure, and this requires the species to be subcritical.

Henry’s Law:

The amount of dissolved gas in a liquid is proportional to its partial pressure above the gas.

If a system of air in contact with liquid water is presumed at equilibrium, then the air is saturated with water. The mole fraction of water vapor in the air is found from Raoult’s law applied to the water with the assumption that no air dissolves in the liquid phase. The lower the temperature and the higher the pressure, the more gas will be dissolved.

yiP=Psat

If one wishes to calculate the mole fraction of air dissolved in the water, Henry’s law can be applied:

yiP=xiHi

Henry’s constant come from experiment.

Modified Raoult’s Law:

A more realistic equation for liquid solutions with a deviation from ideality:

yiP=xi(activity coefficient)Psat

Non-ideal gas:

Fugacity coefficient including compressibility factor can be used and calculated from cubic state of equations.

Pitzer’s correlation:

It is highly recommended to use the NRTL for two liquids in a distillation column, while UNIQUAC would be used for other processes. UNIQUAC is based on the interactions of surface area in the molecules. Soave Redlich Kwong is used for vapor applications.

Today the UNIQUAC model is frequently applied in the description of phase equilibria (i.e. liquid–solid, liquid–liquid or liquid–vapor equilibrium). The UNIQUAC model also serves as the basis of the development of the group contribution method UNIFAC,[3] where molecules are subdivided into functional groups. In fact, UNIQUAC is equal to UNIFAC for mixtures of molecules, which are not subdivided; e.g. the binary systems water-methanol, methanol-acryonitrile and formaldehyde-DMF.

Critical pressure:

for every temperature, there is a critical pressure, in which the condensation occurs. This temperature is calculated by Van-Der-Waals Equation.

Bubble Point Calculation:

If Ptot given, guess T to satisfy: Ptot=x1P1Sat+x2P2Sat
If T given, get Ptot=x1P1Sat+x2P2Sat
Then y1=x1P1sat/Ptot

Dew Point Calculation:

If Ptot given, guess T to satisfy: y1Ptot/P1sat+…=1
If T given, get Ptot=1/(y1/P1sat+…)
Then y1=x1P1sat/Ptot

Example of dew point calculation for a mixture of water and nitrogen:

calculate the partial pressure of each component
calculate the temperature with a partial pressure of water (partial pressure of water: vapor pressure)using Antoine equation

Flash Calculation

For mixtures:

Known: Pressure, Temperature, Flow rate and composition coming in

Unknown: Top vapor rate, yi, bottom liquid rate, xi

Raoult’s law for each component
Mole balance: F=L+V/FZi=Vyi+Lxi

For single components:

The expansion is isenthalpic.

Calculation of Mole Fraction through the expansion:

Known: First and last pressure, the liquid and vapor fraction at the first pressure, vapor composition at the first pressure

Unknown: liquid fraction at the second pressure, mole fraction of the components in the vapor and liquid phase

Raoult’s law for each component using equation of states for acitiviy coefficient and fugacity

Temperature difference calculation by evaporation of a liquid in a vessel:

Assumptions:

Cp vapor is lower than Cp liquid
Temperature difference with the time would be ignored.

mass of liquid*Cp of liquid*Temperature difference of liquid=mass of vapor*enthalpy difference of vapor

Calculation of condensat load on piping for the steam trap:

Calculation of heat loss through the pipeline (the minimum temperature of winter, -26C, the saturation temperature of steam, the heat capacity of iron and the mass of iron)
Assume the minimum enthalpy of steam
The mass of condensate can be calculated.