Merging Emergency Ventilation System Sound Power and Pressure Drop Calculations

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Sound and pressure are simultaneously analyzed in tunnel ventilation system design to explore how both are influenced by each system component.

This article describes a methodology that simultaneously calculates sound and pressure levels for very large tunnel emergency ventilation systems and explains how this methodology benefits the ventilation design process. This method was used on the Sound Transit Northgate Link Light Rail Extension Project (NLLREP) in Seattle, Washington for the ventilation design strategy for two underground stations (Roosevelt and U-District stations) and the connecting bored tunnels. 

ventilation scheme tunnelsFigure 1 – Ventilation scheme

Traditionally on many tunnel projects, sound and pressure loss calculations have been done separately. The primary solution to sound mitigation is to add silencers, which use sound absorbing materials, and geometrical features to attenuate sound waves in the airstream. This adds length to the duct system and often creates more pressure loss, which leads to larger fans and additional sound generation. Therefore, the relationship of sound and pressure is best understood when simultaneously calculating their values. The combined calculation (of the sound and pressure) of the longer silencers determines if the sound meets the environmental regulatory requirements while determining the additional impact on fan horsepower. 

The traditional approach of adding longer silencers to solve sound problems often does not take advantage of the contribution that the system duct work can provide in sound mitigation. A significant proportion of unwanted sound could be mitigated by ductwork system effects in a beneficial way. 

This methodology provides insight that enables the engineer to quickly identify problematic areas within the system, and adjust key parameters such as fan room layout, attenuator size, and duct geometry that would otherwise negatively impact the final design. Knowing how sound and pressure considered together can be made to optimize the cost, mechanical advantage, station footprint, or noise mitigation can be a beneficial tool. 

The NLLREP stations and connecting tunnels required a ventilation system in the event of a train fire emergency. The ventilation strategy chosen was to be a “push/pull” extraction system as shown in Figure 1. 

For this system to work effectively, the fans must be located on either side of the potential fire hazard. The fans can then work in unison to create airflow in one direction with one station fan in exhaust and the adjacent station fan in supply, thereby meeting the required velocity and flow rate to control the smoke in the tunnel. The total pressure loss must be considered in combination with the air flow to determine the required fan motor power needed to move air through the system. 

south roosevelt station elevation tunnels ventilation layoutFigure 2– South Roosevelt Station elevation layout

NLLREP ventilation system fans were sized based on the resistance losses from the tunnel portal to the exit vent shaft in the forward and reverse fan direction. The total pressure loss also provides input to the calculation of the fan sound power generated. The sound generated by the ventilation fan is required to meet the environmental impact statement (EIS) and specific project sound criteria at each designated “receptor” location (where a person might typically be standing). NLLREP ventilation system receptors are located at the tunnel platform, station atrium, and outside ambient, each of which needs to meet the regulatory compliance of the EIS and project criteria. The sound attenuation by each component in the duct system reduces the total sound emitted to the receptor. 

Method of Integrating Pressure and Sound Calculations 

The ventilation system is a series of duct components that provide pressure resistance losses and sound generation and mitigation. These components contribute to the overall pressure loss and sound at the receptor. 

The methodology integrates the calculation of pressure loss and sound generation and attenuation of each component in the system using the computer software Mathcad for documentation and validation of engineering calculations. This software is particularly helpful because it provides a fully documented calculation that can be easily reviewed and altered for different projects. The program is structured by common variables, common geometry, component pressure, component sound, total pressure, and total sound. 

silencer pressure loss Mathcad ventilation tunnelsFigure 3 – Silencer pressure loss from Mathcad®

Common variables and geometry are defined at the front end of the software program to allow for simplifying input and reducing errors. The same reasoning applies to defining common geometric parameters for plenums, dampers, and silencers at the front end of the program. 


Each air pathway in the fan forward and reverse direction is considered when calculating pressure loss as shown in Figure 2. Often only one pathway needs to be determined if it can be shown to be the highest resistance path. If there is no clear distinction of the highest resistance pathway, all air pathways should be evaluated. 

I.E. Idlechik’s Handbook of Hydraulic Resistance provides resistance coefficients for various components within an airstream such as elbows, tees, structural interferences, and dampers, as well as sudden expansions, sudden contractions, and diverging and converging transition losses. Figure 3 is a sample calculation from a Mathcad file describing the pressure loss for a seven foot silencer. In this example, the face velocity (Vs) is calculated to obtain the pressure loss in the forward direction. 

Sheet Metal and Air Conditioning Contractors' National Association (SMACNA) has published that pressure loss is a function of velocity. Similarly, a pressure loss is to be calculated for every ductwork component along the highest resistance pathway. 


In conjunction with the pressure term, a sound power component is considered for all segments in which sound is either regenerated or attenuated. The sound reduction or absorption is defined as the insertion loss (IL). When sound travels through a duct component such as a silencer an insertion loss occurs. 

Equation 1 describes the sound power after a component loss where Lw1 is the sound power level before the component loss and Lw2 is sound power level after the component loss (Reference 2). The insertion loss reduction is calculated over each of eight frequency bands which range from 63Hz to 8000Hz. The human ear is only sensitive to this range of frequencies. 

Equation 1 

emergency ventilation system sound power equation 01 tunnels

The regeneration gain by the silencer is used to calculate the total sound power (Lw3) as shown in Equation 2. The total sound power after the silencer insertion loss (Lw2) is then added logarithmically to the regeneration (LwR) values (Reference 2). The decibel (dB) scale is logarithmic and as such a doubling or halving of energy changes the sound level by 3dB; it does not double or half the sound level as might be expected. 

Equation 2

emergency ventilation system sound power equation 02 tunnels

A silencer insertion loss and regeneration values for a silencer are available from manufacturers' data for each of the eight frequency band levels in both the forward and reverse fan direction. Insertion loss can be determined for any component in the system. Sheet Metal and Air Conditioning Contractors' National Association (SMACNA) provides methods to calculate insertion and regeneration values for various types of ductwork components. 

Total Pressure/Sound 

The total pressure loss of the ventilation system is determined by a summation of losses for components along the flow path. After each component has been evaluated for pressure loss, the total summation is used to evaluate the fan brake horsepower. The fan sound power is evaluated from the total pressure loss as shown by Equation 3 (Reference 2). 

Equation 3

emergency ventilation system sound power equation 03 tunnels

When calculating the total sound power at the receptor, each component is evaluated from the fan to each receptor location. In other words, the fan sound power calculated from Equation 3 is taken to be reduced from the insertion component by Equation 1. For components with regeneration, the total sound is combined using Equation 2. Sound power, which is a measure of the sound intensity, must then be converted to sound pressure or the power component that directly affects the ear drum. The sound pressure levels are evaluated for the receptors, typically in a tunnel, station, or ambient locations. 


During the design of the ventilation system at U-District Station, the use of tunnel fans to exhaust the atrium presented a challenging sound control problem. The fans were in close proximity to the atrium receptor. This allowed very little attenuation to occur. Early in the design, it was determined that the sound levels did not meet project criteria with the configuration of the atrium damper in-line with the fan. 

Three options were investigated to attenuate the sound. The first option was to add a matrix of silencers at the atrium wall opening. This was a viable solution but not considered to be the best choice due to the cost and aesthetics. The second and third options were to offset the damper to provide additional elbow attenuation. The second option utilized an unlined elbow, whereas the third option used an acoustically lined elbow. 

Figure 4 shows the final configuration of the ventilation system. The acoustically lined elbow option provided the necessary attenuation to meet project criteria with minimal impacts to the fan horsepower. The program allowed exploration of different options to reach a feasible, cost effective, and architecturally appealing solution by understanding the parameters that controlled the sound. 

sound attenuation material u district station ventilation system tunnelsFigure 4 – Sound attenuation material at U-District Station


Traditionally, pressure loss analysis has received more attention in the design of tunnel ventilation systems than sound analysis. In recent years, environmental policy, regulatory requirements, and space constraints are making it more important to understand sound mitigation. This methodology of combining sound and pressure simultaneously in the design of ventilation systems provides an efficient tool for understanding how both sound and pressure are influenced by each system component. In addition to demonstrating compliance with the regulatory requirements, the method provides a means to explore other options more efficiently than before. It allows for an optimum design that minimizes motor power requirements, meets sound requirements, and minimizes space requirements. 


  1. Idelchick, I.E., Handbook of Hydraulic Resistance. 4th Edition. 
  2. HVAC Sound and Vibration Manual. s.l. : Sheet Metal and Air Conditioning Contractors' National Association, First Edition Dec. 2004. 
  3. HVAC Systems Duct Design. s.l. : Sheet Metal and Air Conditioning Contractors' National Association, Third Edition 1990. 

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