# What is the unit MKS heat

## System of units

### From ESOCAETWIKIPLUS

engl: system of units Category: Level 1

When using an FEM program, the units of the physical quantities must be taken into account. Within the numerical processing of the data, there is no definition of a specific physical system of measurements or units. In order for the input and output data to be "correct", consistent units must be adhered to throughout the analysis. This means that the units that are used for entering the numerical values are also consistently applicable in the output. This means that the FEM program can be used in numerous areas of technology and physics. Accordingly, there are numerous possible and useful combinations of units.

For the definition of a consistent system of units, basic specifications for basic units have to be made. The other units, which hereby form a consistent set of units, can be derived from it. The basic definitions are generally made for the physical quantities

- Force,
- Length,
- Time,
- Mass and
- Work, energy

met.

### SI units

The standard in the European area is the SI or mks system. The relationship for the quantities, given in SI units, is represented by the following relationships

With these relationships, the FEM user can derive any set of units suitable for the current application. Unit combinations that are customary or appropriate and more frequently used in everyday technical life are listed in the table shown here on the right.

In addition to the units for the physical quantities listed above, the units for pressure or, correspondingly, for mechanical stresses are specified here as derived quantities. The numerical value that results in the respective system for the density of water at room temperature is also given.

### Other systems of units

The standardized SI units are listed under the designation "SI".

"Cgs" lists the units customary in physical applications.

The units labeled "fps (US)" show the values that are still common in the Anglo-Saxon area. The force is given in "poundal" (pdl), the length in "foot" (ft), the time in s, masses in "pound" (lb) and work in the combined unit of force length, here "pound foot "(lbf ft).

With the designation "Var.1" a variant of a combination of units is shown, which is appropriate for calculations in mechanical engineering. For example, the dimensions of the components in mm, the modulus of elasticity and mechanical stresses in (N / mm2) and natural frequencies in (Hz) or (s-1) can be entered or read off. Special attention is required when entering mass or density values in (10 ** 3kg) (i.e. in tons) or in (10 ** 3kg / mm ** 3) (i.e. in tons per mm * * 3) must be specified. To do this, look at the equation above, which is now supplemented with other entries:

Read each phrase as: "a unit of force is equal to a unit of mass times a unit of length divided by a unit of time-squared". Then the conversion and the use in the numerical simulation becomes understandable.

With this system of units, the numerical value to be entered as the density of steel in a calculation with this combination of units is approximately DENS = 7.8e-9. The unit of mass can no longer be freely selected because there is the above-mentioned relationship between the units. If the decision for the length (mm), force (N) and time (s) has been made, the unit of mass can no longer be freely selected, but (10 ** 3kg) must be used.

### example

Geothermal probes are to be designed for a heat pump in a house. These are probes with pipes that are drilled 20..40m diagonally into the ground of the property. These probes are used to extract the heat from the ground in winter. In summer, heat can be fed back into the system.

The heat exchange takes place over weeks and months. Therefore, a simulation with the SI system of units with seconds [s] as the time unit is unfavorable. It is calculated with a system of units with hours [h] as the time unit. So the units are

- instead of the SI system force in 1136, length in [m], time in [s], mass in [kg], energy in [J], derived from this power in [W] = [J / s],
- the system force in [12.96 * 10
^{6}N], length in [m], time in [h], mass in [kg], energy in [3.6 * 10^{3}J], derived from this performance in [3.6 * 10^{3}J / h].

A comparison shows that

- in the SI system of units a material with the material data thermal conductivity λ = 10 [W / (m K)], density ρ = 1500 [kg / m
^{3}], Heat capacity c = 100 [J / (kg K)] is heated to 0.024 ° C in 3600 [s] by adding heat of hgen = 1 [W / m³], - In the changed system of units, a material with the material data thermal conductivity λ = 10 [3.6 * 10
^{3}J / (h m K)], density ρ = 1500 [kg / m^{3}], Heat capacity c = 0.02778 [3.6 * 10^{3}J / (kg K)] in 1 [h] by applying heat of hgen = 1 [3.6 * 10^{3}J / (h m^{3})] is also heated to 0.024 ° C.

### tips and tricks

A simulation program works at its core - i.e. with the numerical solution - without dimensions of the numerical values (like a pocket calculator). This assumes that the quantities that these numerical values represent are defined in a consistent system of units.

It is up to the user to create the right conditions for this.

The simulation program often takes on this management. Then the unit is named at the interface between the user and the software and numerical values with units are entered and output.

The user should nevertheless check the units and cover possible borderline cases and possible errors.

Errors in the use of the units are usually shown by the fact that the result deviates from the expected result by several orders of magnitude. Especially if there are deviations by a factor of around 10^{3} occur, this indicates the units. In a modal analysis, a factor of around 30 is typical because mass and stiffness are "below the root" and therefore √10^{3} acts.

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