Fans

Total pressure/static/velocity pressure

See this page for an explanation of the difference between static, total, and velocity pressure.

Fan Calculations

The work generated by a fan can be calculated using the equation:

where:
W_fan = the work generated by the fan
Q = the volume flowrate of fluid exiting the fan
ΔP_fan = total pressure difference induced by the fan

Fan efficiency can be calculated using the equation:

where:
W_shaft = shaft work supplied to the fan (presumably from a motor)

Shaft power is function of motor power and motor efficiency, as per this equation:

where:
W_motor = work (presumably electric) done on the motor
n_motor = motor efficiency

EneryPlus requires "total efficiency" as one of the inputs when specifiying fans. This can be calculated simply my multiplying fan efficiency and motor efficiency, or by using this equation:

(all variables are described above)

External Static Pressure

External static pressure (ESP) is typically only used when referring to devices that add total pressure to a fluid stream (ie fans, AHUs). The external pressure of a device is the difference in total pressure between the device's inlet and the device's outlet. For simple objects such as fans, losses induced from things like ducting or filters are often negligible or nonexistant, making the object's ESP equal simply to the pressure produced by the fan. In more complex objects such as an AHU, however, determining ESP is slightly more complex.

This diagram shows, on its upper half, a simplified AHU with air entering from the left. Below is a simplified plot of the average fluid pressure as it moves through the AHU:

As fluid moves through the AHU, its total pressure (P_t) is reduced because of duct losses. P_t is reduced at an even greater rate when the fluid moves through the air filter, and then jumps when it moves through the fan. The difference in the fluid's total pressure between the device's inlet and outlet is the device's ESP, as noted on the diagram. What is important to note is that this can be significantly less than the total pressure increase induced by the fan (ΔP_fan).

Fan/system behavior

This is a fairly complex topic which can't be adequately explained in a paragraph, but the following should give the reader at least some idea of how fans and the systems in which they operate interact.

When a fan runs, it delivers a certain amount of total pressure to the fluid moving through it. The flow delivered as result of this pressure depends on the system through which the fluid is moving. For example, a fan operating within a system that has a lot of complex and narrow ductwork will produce less flow than the same fan operating in a system with simple, large ductwork, because less of this pressure is lost to friction.

The below diagram illustrates this concept to some extent:This diagram illustrates fluid moving through a closed system in which 100% of air is recirculated through the AHU and no outside air is introduced. The two points marked "A" on the system diagram on the top half of the diagram represent the same point within the physical system. The lower half of the diagram shows the variation of total pressure as one moves through the system.

In this simple system, total pressure decreases linearly as fluid moves through the duct due to frictional losses. The pressure then rises when it moves through the AHU, by an amount equal to the AHU's external static pressure. It is important to note that the sum of the system's total pressure losses are exactly equal to the total pressure increase induced by the AHU -- the system is operating at its "equilibrium point."

Were one to increase the amount of total pressure the fan supplies to the fluid (say, for instance, by increasing the speed at which the fan rotates), there would be a corresponding influence in the fluid velocity (and therefore flowrate) of the system, because this is a function of the system's pressure gradient. Frictional losses would also increase because of the higher fluid velocity, and the system would settle into a second equilibrium.