### Re: Moving air in a box

Area: Engineering
Posted By: Adrian Popa, Staff Optical/Microwave Physics
Date: Wed Jan 15 13:36:26 1997
Message ID: 852581748.Eg

```Greetings:

design an efficient air flow system, however let's use a back of the
envelope calculation to get an order of magnitude estimate. Your question
is similar to heating and air-conditioning problems except that the air is
usually modified external to the box rather than in the box although some
gymnasium heaters are suspended in the room volume.

The volume of your box is very large and the air flow velocity is
reasonably slow so air compressibility is not a large factor. The design
of the room shape could help to make air flow uniform through out the box
(room?).

I will use a standard fan ventilation engineering type estimate.

Air horsepower is based on the fundamental fluid-horsepower equation,
neglecting compressibility:

hp (air) = p times Q divided by 33,000

where hp is the power required, p is the total pressure drop
(pounds/square foot) required through the fan and Q is the air flow
(cubic feet per minute).

Mechanical efficiency (ME) is the ratio of air horse power to horsepower
input (electrical, mechanical etc.).

In your question you do not mention the box length or width so I will
assume it is a square box  660 ft on a side (10 acres) with a 30 ft high
ceiling

(43560 square feet/acre times 10 acres times 30 feet high
= 13,068,000 cubic feet).

We can place a 330 foot long by 30 ft high structure across one half of
the floor of the box to mount a bank of fans (F).

<-----660 ft ------>
--------------------
I    <--- F <---    I
I    <--- F <---    I
I    <--- F <---    I
I    <--- F <---    I
I    <--- F <---    I
I                   I
I                   I
I      Air Flow     I
I    ---------->    I
I                   I
---------------------
The  12 ft /sec maximum air  velocity that you require determines the
maximum Q through the fans

Q = 30 (ft) times 330 (ft) times 12 (ft/sec) times 60 (sec/min)

Q = 7,128,000 cubic feet per minute.

Standard ventilation engineering practice for a fan blowing into an large
open volume uses 1/4 pound per square foot as the pressure drop through
the fans. This gives an air horse power

hp (air) = 1/4 times 7,128,000 divided by 33,000
= 54 horse power

It would help to curve the corners of the box and to place large air flow
vanes through out the box to keep laminar air flow through out the volume.
This is typical practice in low speed wind tunnels. Also the distribution
of the fans can be adjusted for laminar air flow

Now comes the hard part of the problem.
What mechanical hp is required to generate our required air flow and
54 hp (air)?

I looked up the largest fan that I have in our labs engineering  catalogs
and I found a 60 inch diameter fan from Peerless Electric (Model VA60C-42).
There probably are larger fans available but I am not aware of them.
Information and design software can be obtained from Peerless at the
following URL:

http://www.industry.net/peerless-winsmith

The VA60C-42 fan duct is 60 inches in diameter, and the fan rotates at
1160 RPM , providing 148,100 CFM of air flow and requires 126.1 BHP.
Thus the hp (air) of the fan is:

hp = 1/4 times 148,100 divided by 33,000 = 1.12 hp (air)

The mechanical efficiency ME = 1.12 hp divided by 126.1 BHP = about 1%

Thus you would require

7,128,000 CFM /148,100 CFM per fan  = 48 fans

48 fans times 126.1 BHP/fan = 6,053 BHP.

As a check if we multiply the hp air of the Peerless fans  we get

48 fans times 1.12 hp per fan = 53.76 hp compared to 54 hp in our first
calculation. Thus the real fans are well characterized by our engineerring
model equation!

The air once moving in the box might reduce the pressure drop through the
fans, however this increased efficiency would be offset by the poor flow
and change in momentum of the air mass as the direction of the air flow
changes at the corners. However, the Peerless fan tables indicate that fan
BHP is quite insensitive to pressure changes of several octives providing us
with a generous margin for error..

```

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