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The formula of the hydraulic diam­eter

Centrifugal fans move large volumes of air reli­ably and effi­ciently. However, their actual effi­ciency doesn’t depend solely on the fan itself. The size and shape of the air duct are just as impor­tant – and this is where the hydraulic diam­eter comes into play.


Michael Strehle, Flow Solu­tion — Aero­dy­namic Devel­op­ment (Image | ebm-papst)

The hydraulic diam­eter (dh) is a calcu­lated para­meter. It allows non-circular flow cross-sections – such as rectan­gular or square chan­nels – to be compared to an ideally circular pipe. The formula is surpris­ingly simple: It relates the cross-sectional area A through which the air flows as a ratio of the wetted perimeter U – that is, the perimeter of the duct in contact with the air. This is based on a funda­mental prin­ciple of physics: The larger the flow area rela­tive to the wall area, the more easily air can flow. This is because as soon as air flows through a duct, fric­tion occurs at the wall surfaces – resulting in pres­sure losses and, conse­quently, energy losses. The geom­etry thus deter­mines the effi­ciency or loss of the entire system 

A large hydraulic diam­eter means favor­able flow condi­tions: The air encoun­ters little resis­tance, and little energy is required to achieve the desired effect. A small hydraulic diam­eter means more contact with the walls, greater fric­tion, deflec­tion, and loss. A simple illus­tra­tion makes this clear: In a wide, even stream, water flows calmly and effi­ciently. In a shallow, winding stream, on the other hand, the water is slowed down, swirls, and loses energy. The same is true for airflows. Why is this impor­tant for centrifugal fans like the RadiPac 3? 

These fans are designed to accel­erate air evenly and very effi­ciently. However, in prac­tice, when the air exits the fan, it often encoun­ters rectan­gular hous­ings, tight instal­la­tion spaces, or other­wise unfa­vor­able duct config­u­ra­tions. We’ve addressed this by signif­i­cantly reducing the fric­tion losses of air flowing from the centrifugal to the axial direc­tion in the new Radi­Flow impeller. The result: The effi­ciency of the entire system remains optimal for a very long time, even with a small hydraulic diam­eter – that is, with unfa­vor­able duct shapes (see diagram). As a general rule, it is always worth­while to ensure flow-friendly geome­tries, smooth tran­si­tions, and balanced cross-sections in the airflow path to fully exploit the perfor­mance capa­bil­i­ties of modern fans. The hydraulic diam­eter makes these rela­tion­ships visible and calcu­lable.

If the ratio of the hydraulic diam­eter dh to the fan diam­eter D (x-axis) decreases, a corre­sponding correc­tion factor must be applied to the effi­ciency (y-axis). (Graph | ebm-papst)

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