ALTITUDE EFFECTS

FAN SIZING AND OPERATION
DAVID R. OLSON, PE
Things are different when you are over a mile above sea level. There’s less air at this altitude. The density of the atmosphere at sea level is 0.075 pounds per cubic foot. That means that every cubic foot of 70°F air weighs 0.075 pounds with a barometric pressure of 29.92” Hg (14.7 lbs/in^{2}). In Denver, Colorado with an elevation of 5,280 feet above sea level, the barometric pressure equals about 27.8” Hg (12.04 lbs/in^{2}). Denver air at 70°F has a density of 0.0617 pounds per cubic foot. That means that there is only 82.3% of the air in Denver as there is at sea level locations. The air density in the Colorado mountains is even less. The altitude of Aspen, Colorado is 7,928 feet above sea level. Consequently, the air density there is just less than 0.0554 pounds per cubic foot, or about 73.9% of that found at sea level. The reduced air density experienced at high elevations does not just make it more difficult for individuals to breathe; it impacts the operation and performance of all sorts of mechanical equipment. This article will focus on the impacts of altitude on the sizing of fans.
The atmosphere at altitude is less dense than that found at sea level and lower elevations. Consequently, it takes less energy to move air at high altitudes than at lower elevation locations. The lower density means that there are less air molecules per cubic foot. A cubic foot of air is a cubic foot of air – regardless of your location on the planet. Each cubic foot of air in Denver weighs less than a cubic foot in Los Angeles, Seattle or other sea level locations. It stands to reason that it takes less energy to move this lighter weight airflow down a duct or through a grille.
Airflow is measured in cfm – cubic feet per minute. A fan of a particular diameter and operating rpm, delivering 10,000 cfm at sea level will utilize more energy than a similar fan at high altitude. Engineers use the fan affinity laws to predict just what the difference in energy consumption – and ultimately the fan motor size will be.
The fan affinity laws define the following relationships between flow, fan speed, fan size, air density and power requirements.
CFM_{2} = CFM_{1} x (RPM _{2}/RPM_{1}) x (D_{2}/D_{1})^{3}
SP_{2} = SP_{1} x (RPM_{2}/RPM_{1})^{2} x (D_{2}/D_{1})^{2} x (d_{2}/d_{1})
BHP_{2} = BHP_{1} x (RPM_{2}/RPM_{1})^{3} x (D_{2}/D_{1})^{5} x (d_{2}/d_{1})
When certain values are held constant, such as flow rate – [CFM_{2} = CFM_{1}], constant speed – [RPM_{2} = RPM_{1}] and fixed fan size – [D_{2} = D_{1}]_{, }the following relationships hold true:
CFM_{2}/CFM_{1} = RPM_{2}/RPM_{1 }= SP_{2}/SP_{1} = d_{1}/d_{2}
BHP_{2}/BHP_{1} = (d_{1}/d_{2})^{2}
Where:
CFM = flow rate RPM = fan rotational speed d = air density (lbs/ft^{3}) BHP = impeller power
SP = static pressure (“ w.c.) D = fan diameter (ft)
CFM, RPM and static pressure vary inversely with density. Brake horsepower varies inversely with the square of density.
When selecting fans for use at high elevation, it is essential for engineers to correct the manufacturer’s catalog data for actual density conditions occurring at the elevation of the project. A fan that develops 2” w.c. static pressure at sea level, will develop 1.64” w.c. static pressure at Denver’s 5,280 feet elevation. If this fan selection requires 5 bhp at sea level, in Denver, the fan motor will require 4.1 bhp due to the less dense air. The CFM and RPM will remain the same indicated for the sea level selection.
Therefore, to effectively select a fan for a project in Denver, calculate the required static pressure to move a certain air quantity down a certain duct system. Divide the calculated static pressure by the relative density (0.823) and use this resultant static pressure to select the fan with a manufacturer’s sea level tables. Determine the resultant brake horsepower predicted by the sea level fan curves, and then multiply this brake horsepower by the same relative density factor (0.823) to obtain the required brake horsepower at altitude.
When communicating to sales representatives and bidding contractors, fan schedules must be clearly identified as to the intended cfm, rpm, static pressure and horsepower. I have seen some engineers who will show these values strictly at the altitude of the project, and others who show it based upon equivalent sea level values. In my experience, I like to show altitude rated cfm values, rpm’s and horsepower’s, and sea level static pressures – ie: 5,000 cfm (alt) @ 2.5” esp (sl).
Most manufacturers simplify these calculations today with proprietary software to select fans. Accordingly, a designer or engineer must simply determine the required cfm and static pressure at altitude, and enter the selection program with these values. As part of the software, the project altitude will be entered by the user. Then the program will be automatically correct the horsepower and static pressure to the correct values to correspond with the manufacturer’s sea level selection tables.
I believe it is important to know and understand the basic’s in fan selection prior to utilizing these simplified selection programs for fan sizing. It is important to be able to estimate a fan size and horsepower requirement, and understand the impacts that altitude has upon the performance of mechanical equipment when designing HVAC systems at high altitude.
Note: This article is intended for the convenience, clarification and use by qualified individuals and HVAC designers only. All fan sizing and installation must comply entirely with the governing edition of the International Mechanical Code adopted by the Authority Having Jurisdiction (AHJ) or other similar mechanical codes adopted by the AHJ. David R. Olson, PE and Integrated Mechanical Systems, Inc. does not accept liability for fan sizing or installation deficiencies which result from use of this article by less than fully qualified individuals and/or failure to follow the adopted building and mechanical codes within any jurisdiction where a construction project including fans or air moving equipment may occur. All fans and air handlers shall be designed under the strict guidance and responsible charge of a licensed professional engineer and fully licensed HVAC contractors in the jurisdiction of the project.