Pressure Drop Calculations

Thermal Analysis
Pressure Drop Calculations in a Chassis
Before performing thermal analysis on a chassis, it is necessary to calculate total pressure drop within the system.
This 1 Formula
consists of the pressure
drops of1all- system subcomponents.
Formula
Formula 1 The total pressure drop (system curve), which also depends
on the volumetric
flow
rate
in
the
system,
can
be
shown
as:
Formula 1 -
Formula 2 -
mula 1 -
mula 2 -
mula 3 -
Formula 2, -where
Formula
3 - and
are the system component
resistances,
volumetric flow rate.
mula 6 -
mula 7 -
The following shows the calculation of several of the above
Formula 2 The units are square meter for the area, cubic
Formula 1resistances.
meter per second for volumetric flow rate and Pascal for
Formula
2 - 1pressure.
Formula
Formula 3 Formula 2A.- Perforated plate:
Formula
3- 2Formula
is the
- can be used to deliver air
Generally, oneFormula
or two fan 3trays
Formula 4 through a chassis. TheFormula
operating4point
- of a fan tray is whereFormula 3 the system curve intersects the fan tray curve.
Formula
1 -4 Formula
Formula 5 Operating
Points
Formula 6 Formula 6 Formula 7 Formula 7 Formula 8 Formula 8 -
Where A is the area of open
holes exposed to air flow
Formula 3 -
B. Filter:
Figure 1 shows the operating point. It is recommended
to
Formula
5operate the fans belowFormula
the stall range.
Formula 4 5-
Formula 4 -
mula 4 -
mula 5 -
,
4. Flow bending from inlet to plenum
5. Contraction to the inlet plenum
6. Expansion from inlet to plenum
7. Circuit cards component blockade
8. Circuit card friction (generally small)
9. Flow bending to exit plenum
10. Contraction to exit of plenum
11. Expansion from exit of the plenum
Formula
2 -5 - 4 Formula
Formula
Where A is the filter exposed area and L
is the filter loss coefficient provided by
manufacturer.
Formula 6 Formula 5 Formula
3 -6 - 5C.- Boards:
Formula
Formula
Formula 7 Formula 6 Formula
4 -7 - 6 Formula
Formula
Formula 8 Formula 7 Formula
5 -8 - 7 Formula
Formula
Where L is the board length and A is
the effective free area of the channel.
If there are N similar boards mounted
in a chassis in parallel, their equivilent
resistence is calculated as:
Formula 9 Formula 8D.- Fan trays contraction and expansion:
Formula
9
Figure 1. Graph showing the intersection of system and fan curve.
Formula
6 -9 - 8 Formula
Formula
mula 8 The flow going into and out of the fan trays exhibits contraction
Formula 9 Formula
This intersection equals the system pressure, and thus
pro- 10 and expansion with their associated losses.
9vides the flow rate through
the system.
is
Formula
10 - Total pressure drop Formula
7 -10 - 9 Formula
generally affected by the following subcomponents Formula
if they
areFormula
mula 9 - part of that specific chassis:
Formula 10 Sudden Expansion:
Formula 11 1. Air filter
Formula 10 Formula 11 2. Honeycomb
Formula
8 -11 - 10 Formula
Where A1 is the small area
Formula
mula 10 - 3. Fan tray due to sudden expansion and contraction
and A2 is the larger.
Formula 11 of flow through blades
Formula 12 Formula 11 Formula 12 PAGE 7
Formula
9
Formula
12
Formula 11 mula 11 Formula 12 - 02062 P. 781.769.2800 WWW. QATS .
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DVANCED TThermal
HERMAL SSolutions,
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., NFormula
ORWOOD
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Rd.,RDNorwood,
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02062
Formula
12Ph.
- 781-769-2800 WWW.QATS.COM
Formula 13 -
Formula
7 -5 Formula
Formula 1 Formula
5ormula
4-
Formula 11 -
Formula
8 -6 Formula
Contraction:
Formula
2Formula
6ormula 5 -
Formula
9 -7 Formula
Where A is the small area.
Formula 3 Formula
7 - tray
ormula
6 - E. Fan
Formula
10 - Formula
When8 fans
are mounted in a fan tray, the combined fan curve
is calculated
Formula
4 - based on the fan laws. For M fans in parallel
Formula
8ormula
7 - assembled
in one fan tray, the fan volumetric flow rate increases11
by -a factor of M for the same pressure drop. For two fan
Formula
Formula
trays9in-series such as a push-pull system, pressure doubles
for the same
Formula
5 - volumetric flow rate. So if the characteristic curve
Formula
9 - fan is:
ormula
8 - of one
Formula
1210
- Formula
Formula 6 Formula
10 ormula
9The
curve of the combined fans can be
Formula
13characteristic
- Formula
11
represented as:
Formula 7 Formula
ormula
10 - 11 Formula
1412
- Formula
The factor 2 is for two fan trays and M is the number of
Formula
8 - tray.
fans in one
Formula
ormula
11 - 12 -
The
Formula
15total
- -head generated by a push-pull system is:
Formula
13
Formula 9 Formula
ormula
12 - 13 -
Where
is the
fan duct size.
Formula 14 -
The above relations can be used for a quick analysis of a
system12
to -find the volumetric flow rate, which can then yield
Formula
the system temperature rise if the total heat dissipation is
known. As a simple example, consider a system that has two
fan trays. Each fan tray has two fans. This system has five
perforated
Formula
13 - plates with a 56% opening. Let’s assume the area
open to air flow is about 0.03 m2 and that the system also has
a filter at the inlet with a loss coefficient of 0.008. The fan
curve indicates that maximum pressure is 225 Pa at zero flow
and 0.13
Formula
14 m- 3/sec at zero pressure. Assuming a linear relationship between the pressure and the volumetric flow rate would
give the single fan curve as:
Formula 15 Assuming negligible resistance from boards and fan hubs,
Table 1 shows the resistances due to all the parameters and
their calculated values.
Solve the following equation:
Which yields a value for G equal to 0.12 m3/sec for the system
volumetric flow rate.
References:
1. Ellison G., Thermal Computations for Electronic Equipment,
Krieger Publishing Company, 1984.
Formula 10 Formula
ormula
13 - 14
Inlet Cross section (m ) ...............................................................................................................................................0.03
2
Single perforated plate resistance ................................................................................................................................ 2933
FormulaCombined
15 - perforated plate resistance ......................................................................................................................... 14668
Filter resistance ......................................................................................................................................................4540
Formula
11 Formula
15
ormula 14 - Total- system resistance ..........................................................................................................................................1 9208
Fan curve ..................................................................................................................................................... 225-1665XG
Push pull Fan tray curve ............................................................................................................................... 2(225-1665/2*G)
Formula 12 ormula 15 -Table 1. Flow resistances for different system components.
The second term is the velocity pressure head associated with
Formula
13 - fan that contributes to the total pressure. Solving
the entrance
the following equation, it would yield the system pressure drop
and volumetric flow rate:
Formula 14 PAGE 8
Formula 15 A
DVANCED TThermal
HERMAL SSolutions,
OLUTIONS, Inc.,
I NC.89-27
89-27Access
A CCESS
., N ORWOOD
, MA
02062
P. 781.769.2800
WWW. QATS .
Advanced
Rd.,RDNorwood,
MA
02062
Ph. 781-769-2800
WWW.QATS.COM