linear head loss
The head loss is calculated by Darcy's formula.
In which is the hydraulic diameter[6] and is the friction factor.
Now, both the pressure loss and the friction factor depend on the properties of the fluid, which change with the length of the duct traveled, so taking into account the variations in the properties of the air with temperature, specific humidity, altitude and pressure, we arrive at:
In which is the head loss in section AB, it is a coefficient that depends on the material and is indicated in the following table, it is the length of the section and it is the speed.
pressure loss in accessories
The head loss obtained is known as linear head loss or head loss per meter of straight conduit. But when singularities occur in the duct, such as curves, reductions, branches, etc., an additional pressure loss is produced known as pressure loss in accessories.
Every accessory involves a change in speed or trajectory and therefore a variation in kinetic energy, which translates into a loss of pressure.
In which is the dynamic loss coefficient, different for each type of accessory[7] and is the speed at its entrance.
In many cases, what is known as Equivalent length of the accessory is usually used, which is nothing more than estimating the length of rectilinear conduit that produces the same head loss as the accessory and in the linear head loss formula, considering as the length of each section, its actual length plus the equivalent length of its accessories.
calculation methods
Low speed systems can be calculated by three main methods:.
It is a very simple method, but only applicable to very basic installations without major distribution requirements. It consists of selecting an output speed, taken from the attached table, at the fan discharge and reducing it in each section along the duct.
The diameter of the circular duct necessary for each section is calculated by:.
If the duct is going to be rectangular, the measurements are taken from the circular section of equivalent diameter.[8].
The head loss of each section is then calculated from the corresponding nomogram or using the formula:.
In which is the section flow, it is the perimeter of the rectangular duct and its section.
Finally, the pressure losses of the most unfavorable path are added.[9] The total corresponds to the static pressure required in the fan.
This is a better method than the previous one in that it is applicable to most of the most frequent installations and gives good results, especially if the distribution is symmetrical. If it is not, the system may be difficult to balance.[10] The method consists of calculating the ducts so that they have the same pressure loss per unit length throughout the entire system.
For the calculation, we begin by establishing the head loss, using the nomogram or Darcy's formula, corresponding to the total flow required and the recommended speed, taken from the previous table, or, a head loss can be set, known from experience as good.[11]
Crossing the flow of each section with the fixed head loss and rounding to the speed closest to the recommended one, the diameter of the necessary conduit is obtained (see figure). It can later be converted to a rectangular duct.
It can also be calculated using the formula:.
Finally, the total head loss is calculated by multiplying the set head loss by the length of the most unfavorable path.
This method is based on Bernoulli's Principle, according to which, in a conduit through which a fluid circulates, the sum of the dynamic pressure due to its speed, the static pressure due to its pressure and the pressure due to its height is a constant value. Considering the horizontal duct, that is, without variation in height along its route, the static and dynamic pressure remain, in such a way that if the speed and therefore the dynamic pressure decrease in a section, the static pressure will increase by the same value.
This is the basis of the method, which consists of sizing the duct so that the increase in static pressure due to the decrease in speed in one section compensates for the friction losses in the next. In this way the static pressure remains constant and is the same at each outlet.
You begin by selecting an initial speed from the table of recommended speeds, but taking care that it is as high as possible, to prevent the final speed from being too low or the duct being too large. With this speed, the section of the first section is calculated and its head loss is determined, the same as in the previous method.
The following sections must comply with the foundation of the method. Therefore, for any section:
The first member is the sum of the linear head loss in the section plus the sum of the head losses in the accessories of said section and plus the head loss in the bypass or reduction at the entrance to the section whose entrance speed is . The second member is the dynamic pressure loss or static pressure gain when going from speed to speed.
This is an expression in which the only unknown variable is , but it will require an iterative calculation, which is why two graphs are usually used; In the first, the relationship for the section is obtained and in the second, by crossing this value with the inlet velocity, the exit velocity or the recovered pressure can be found, which allows us to calculate the section of the section.
Currently there are software programs with which a simple, fast calculation is achieved and, if the data is entered correctly, very satisfactory results.[12].