Duct Segment Identification: AC

  • Target Volumetric Flow rate (Design) Q = 440 cfm (Given)
  • Minimum Transport Velocity (Vt) = 3500 fpm (Given)
  • Maximum Duct Diameter = 4.8”

Q = V * A

Hence A = Q / V

= 440 / 3500 = 0.1257 Sq. ft

A = (Pi * D2)/ 4

Hence D = 4.8”

  • Selected Duct Diameter = 4.5”

We don’t have a diameter of 4.8”. Let’s choose a diameter that is less than the obtained one and is available.

  • Duct Area = 0.11 sq. ft.

By taking diameter = 4.5”

  • Actual Duct Velocity = 4000 fpm

V = Q / Duct Area = 440 / 0.11

  • Duct Velocity Pressure, VP = 0.998” wg

We know VP = (V / 4005)2

  • Maximum Slot Area = N / A
  • Slot Area Selected = N / A
  • Slot Velocity Pressure = N / A
  • Slot Loss Coefficient = N / A
  • Acceleration Factor = N / A
  • Slot Loss per VP = N / A
  • Slot Static Pressure = N / A
  • Duct Entry Loss Factor = 0.4

From FIGURE VS-95-13 given he = 0.4VPd for straight takeoff

  • Acceleration Factor = 1

Acceleration Factor is generally taken as 1 for hoods.

  • Duct Entry Loss per VP = 1.4

Duct Entry Loss per VP = Duct Entry Loss Factor + Acceleration Factor

  • Duct Entry Loss = 1.397

Duct Entry Loss = Duct Entry Loss per VP * Duct VP

  • Other Losses = N / A

Hood Static Pressure (SPh) = 1.397

Hood Static Pressure (SPh) = Slot Static Pressure + Duct Entry Loss + Other Losses

  • Straight Duct Length = 5’ (Given)
  • Friction Factor (Hf) = 0.0614

From TABLE 5-5 at V = 3500 fpm and D = 4.5”

  • Friction Loss per VP = 0.307

Friction Loss per VP = Straight Duct Length * Friction Factor

  • No. of 900 degree elbows = 0.5
  • Elbow Loss Coefficient = 0.24

From FIGURE 5-16 for a 4 PIECE ELBOW and R / D = 2

  • Elbow Loss per VP = 0.12
  • No. of Branch Entries = 1
  • Entry Loss Coefficient = 0.28
  • From FIGURE 5-17 for θ = 450
  • Entry Loss per VP = 0.28

Entry Loss per VP = No. of Branch Entries * Entry Loss Coefficient

  • Special Fittings Loss Factors = N / A
  • Duct Loss per VP = 0.707

Duct Loss per VP = Friction Loss per VP + Elbow Loss per VP + Entry Loss per VP + Special Fittings Loss Factors

  • Duct Loss = 0.706

Duct Loss = Duct Loss per VP * Duct VP

  • Duct SP Loss = 2.103

SP Loss = Hood Static Pressure + Duct Loss

  • Other Losses = N / A
  • Cumulative Static Pressure = 2.103
  • Governing Static Pressure = -2.103’ wg

It is a negative pressure.

  • Corrected Volumetric Flow rate = 446
  • Corrected Velocity = 4055
  • Corrected Velocity Pressure = 1.025
  • Resultant Velocity Pressure = N / A
  • Before calculating corrected volumetric flow rate, velocity and velocity pressure first calculate SP of BC section. Take the SP, which is higher between AC and BC sections.
  • Now corrected volumetric flow rate is given by the formula in spreadsheet that is Qdesign . Plugging the values we will get the above answers.

Duct Segment Identification: BC

  • Target Volumetric Flow rate (Design) Q = 350 cfm (Given)
  • Minimum Transport Velocity (Vt) = 3500 fpm (Given)
  • Maximum Duct Diameter = 4.28”

Q = V * A

Hence A = Q / V

A = 350 / 3500 = 0.1 Sq. ft

A = (Pi * D2)/ 4

Hence D = 4.28”

  • Selected Duct Diameter = 4”

We don’t have a diameter of 4.23”. Let’s choose a diameter that is less than the obtained one and is available.

  • Duct Area = 0.087 sq. ft.

By taking diameter = 4”

  • Actual Duct Velocity = 4009 fpm

V = Q / Duct Area = 350 / 0.087

  • Duct Velocity Pressure, VP = 1.002” wg

We know VP = (V / 4005)2

  • Maximum Slot Area = N / A
  • Slot Area Selected = N / A
  • Slot Velocity Pressure = N / A
  • Slot Loss Coefficient = N / A
  • Acceleration Factor = N / A
  • Slot Loss per VP = N / A
  • Slot Static Pressure = N / A
  • Duct Entry Loss Factor = 0.4

From FIGURE VS-95-13 given he = 0.4VPd for straight takeoff

  • Acceleration Factor = 1
  • Duct Entry Loss per VP = 1.4
  • Duct Entry Loss = 1.403
  • Other Losses = N / A

Hood Static Pressure (SPh) = 1.403

  • Straight Duct Length = 5’ (Given)
  • Friction Factor (Hf) = 0.0709
  • No. of 900 degree elbows = 0.5
  • Elbow Loss Coefficient = 0.24
  • Elbow Loss per VP = 0.12
  • No. of Branch Entries = 1
  • Entry Loss Coefficient = 0.28
  • Entry Loss per VP = 0.28

Entry Loss per VP = No. of Branch Entries * Entry Loss Coefficient

  • Special Fittings Loss Factors = N / A
  • Duct Loss per VP = 0.755
  • Duct Loss = 0.757

Duct Loss = Duct Loss per VP * Duct VP

  • Duct SP Loss = 2.16

Duct SP Loss = Hood Static Pressure + Duct Loss

  • Other Losses = N / A
  • Cumulative Static Pressure = 2.16
  • Governing Static Pressure = -2.16” wg

It is a negative pressure

  • Corrected Volumetric Flow rate = N / A
  • Corrected Velocity = N / A
  • Corrected Velocity Pressure = N / A
  • Resultant Velocity Pressure = N / A

Duct Segment Identification: CD

  • Target Volumetric Flow rate (Design) Q = 796 cfm

Add corrected volumetric flow rate of AC section to the volumetric flow rate of BC section.

  • Minimum Transport Velocity (Vt) = 3500 fpm (Given)
  • Maximum Duct Diameter = 6.45”

Q = V * A

A = 796 / 3500 = 0.227 Sq. ft

A = (Pi * D2)/ 4

Hence D = 6.45”

  • Selected Duct Diameter = 6”

We don’t have a diameter of 6.45”. Let’s choose a diameter that is less than the obtained one and is available.

  • Duct Area = 0.1963 sq. ft.

By taking diameter = 6”

  • Actual Duct Velocity = 4055 fpm

V = Q / Duct Area = 796 / 0.1963

  • Duct Velocity Pressure, VP = 1.025” wg

We know VP = (V / 4005)2

  • Maximum Slot Area = N / A
  • Slot Area Selected = N / A
  • Slot Velocity Pressure = N / A
  • Slot Loss Coefficient = N / A
  • Acceleration Factor = N / A
  • Slot Loss per VP = N / A
  • Slot Static Pressure = N / A
  • Duct Entry Loss Factor = N / A
  • Acceleration Factor = N / A
  • Duct Entry Loss per VP = N / A
  • Duct Entry Loss = N / A
  • Other Losses = N / A

Hood Static Pressure (SPh) = N / A

  • Straight Duct Length = 35’ (Given)
  • Friction Factor (Hf) = 0.0432

From TABLE 5-5 at V = 3500 fpm and D = 6”

  • No. of 900 degree elbows = 1
  • Elbow Loss Coefficient = 0.24

From FIGURE 5-16 for a 4 PIECE ELBOW and R / D = 2

  • Elbow Loss per VP = 0.24

Elbow Loss per VP = No. of 900 degree elbows * Elbow Loss Coefficient

  • No. of Branch Entries = N / A
  • Entry Loss Coefficient = N / A

Entry Loss per VP = No. of Branch Entries * Entry Loss Coefficient

  • Special Fittings Loss Factors = N / A
  • Duct Loss per VP = 1.752

Duct Loss per VP = Friction Loss per VP + Elbow Loss per VP + Entry Loss per VP + Special Fittings Loss Factors

  • Duct Loss = 1.8

Duct Loss = Duct Loss per VP * Duct VP

  • Duct SP Loss = 1.8

Duct SP Loss = Hood Static Pressure + Duct Loss

  • Other Losses = N / A
  • Cumulative Static Pressure = -1.8
  • Governing Static Pressure = -3.97” wg

To get the governing static pressure first calculate VPr and then calculate SP3. Add this value to cumulative static pressure. This gives you governing static pressure.

  • Corrected Volumetric Flow rate = N / A
  • Corrected Velocity = N / A
  • Corrected Velocity Pressure = N / A
  • Resultant Velocity Pressure = N / A

Duct Segment Identification: DE

  • Target Volumetric Flow rate (Design) Q = 350cfm
  • Minimum Transport Velocity (Vt) = 4000 fpm

From FIGURE VS-95-04

  • Maximum Duct Diameter = 4.01”
  • Selected Duct Diameter = 4”
  • Duct Area = 0.0873 sq. ft.
  • Actual Duct Velocity = 4009 fpm
  • Duct Velocity Pressure, VP = 1.002” wg
  • Maximum Slot Area = 0.125

Given slot dimensions are 1” * 18”

  • Slot Area Selected = 0.125
  • Slot Velocity = 2800
  • Slot Velocity Pressure = 0.489
  • Slot Loss Coefficient = 1.78

From FIGURE VS-95-04

  • Acceleration Factor = 0
  • Acceleration Factor is taken as 0 for slots
  • Slot Loss per VP = 1.78
  • Slot Loss per VP = Slot Loss Coefficient + Acceleration Factor
  • Slot Static Pressure = 0.87
  • Slot Static Pressure = Slot Velocity Pressure * Slot Loss per VP
  • Duct Entry Loss Factor = 0.25
  • From FIGURE 5-15 for a 900 rectangular hood
  • Acceleration Factor = 1
  • Duct Entry Loss per VP = 1.25
  • Duct Entry Loss = 1.25
  • Other Losses = N / A

Hood Static Pressure (SPh) = 2.12

  • Straight Duct Length = 12’ (Given)
  • Friction Factor (Hf) = 0.0709
  • Friction Loss per VP = 0.85
  • No. of 900 degree elbows = 1
  • Elbow Loss Coefficient = 0.24
  • Elbow Loss per VP = 0.24
  • No. of Branch Entries = 1
  • Entry Loss Coefficient = 0.28
  • Special Fittings Loss Factors = N / A
  • Duct Loss per VP = 1.37
  • Duct Loss = 1.373
  • Duct SP Loss = 3.493
  • Other Losses = N / A
  • Cumulative Static Pressure = 3.493
  • Governing Static Pressure = -3.97’ wg
  • Here again the higher value of SP from CE and DE is taken.
  • Corrected Volumetric Flow rate = 373
  • Corrected Velocity = 4273
  • Corrected Velocity Pressure = 1.138
  • Resultant Velocity Pressure = N / A
  • For finding corrected volumetric flow rate again follow the same procedure.

Duct Segment Identification: EF

  • Target Volumetric Flow rate (Design) Q = 350 cfm (Given)

By adding the volumetric flow rate of DE and corrected volumetric flow rate of section EF

  • Minimum Transport Velocity (Vt) = 3500 fpm
  • Maximum Duct Diameter = 7.8”
  • Selected Duct Diameter = 7”
  • Duct Area = 0.267 sq. ft.
  • Actual Duct Velocity = 4378 fpm
  • Duct Velocity Pressure, VP = 1.2” wg
  • Maximum Slot Area = N / A
  • Slot Area Selected = N / A
  • Slot Velocity Pressure = N / A
  • Slot Loss Coefficient = N / A
  • Acceleration Factor = N / A
  • Slot Loss per VP = N / A
  • Slot Static Pressure = N / A
  • Duct Entry Loss Factor = N / A
  • Acceleration Factor = N / A
  • Duct Entry Loss per VP = N / A
  • Duct Entry Loss = N / A
  • Other Losses = N / A

Hood Static Pressure (SPh) = N / A

  • Straight Duct Length = 24’ (Given)
  • Friction Factor (Hf) = 0.0358
  • Friction Loss per VP = 0.8592
  • No. of 900 degree elbows = 1
  • Elbow Loss Coefficient = 0.24
  • Elbow Loss per VP = 0.24
  • No. of Branch Entries = N / A
  • Entry Loss Coefficient = N / A
  • Special Fittings Loss Factors = N / A
  • Duct Loss per VP = 1.099
  • Duct Loss = 1.318
  • Duct SP Loss = 1.318
  • Other Losses = N / A
  • Cumulative Static Pressure = -1.318
  • Governing Static Pressure = -5.247” wg
  • For calculating governing static pressure again calculate VPr, SP3 and then add the value to cumulative static pressure.
  • Corrected Volumetric Flow rate = N / A
  • Corrected Velocity = N / A
  • Corrected Velocity Pressure = N / A
  • Resultant Velocity Pressure = N / A

Duct Segment Identification: COLLECTOR

Here only losses are taken into account

Given there is a 4” pressure drop across the bag

  • Special Fittings Loss Factors = 4
  • Cumulative Static Pressure = -4.0
  • Governing Static Pressure = -9.247” wg
  • Add governing static pressure of EF to cumulative static pressure.

Duct Segment Identification: FG

  • Target Volumetric Flow rate (Design) Q = 1169 cfm
  • Minimum Transport Velocity (Vt) = 2500 fpm
  • Maximum Duct Diameter = 9.26”
  • Selected Duct Diameter = 9”
  • Duct Area = 0.442 sq. ft.
  • Actual Duct Velocity = 2644.8 fpm
  • Duct Velocity Pressure, VP = 1.2” wg
  • Maximum Slot Area = N / A
  • Slot Area Selected = N / A
  • Slot Velocity Pressure = N / A
  • Slot Loss Coefficient = N / A
  • Acceleration Factor = N / A
  • Slot Loss per VP = N / A
  • Slot Static Pressure = N / A
  • Duct Entry Loss Factor = 0.5
  • Acceleration Factor = 1
  • Duct Entry Loss per VP = 1.5
  • Duct Entry Loss = 0.66
  • Other Losses = N / A

Hood Static Pressure (SPh) = 0.66

  • Straight Duct Length = 8’ (Given)
  • Friction Factor (Hf) = 0.0278
  • No. of 900 degree elbows = 1
  • Elbow Loss Coefficient = 0.24
  • Elbow Loss per VP = 0.24
  • No. of Branch Entries = N / A
  • Entry Loss Coefficient = N / A
  • Special Fittings Loss Factors = N / A
  • Duct Loss per VP = 0.462
  • Duct Loss = 0.203
  • Duct SP Loss = 0.863
  • Other Losses = N / A
  • Cumulative Static Pressure = -0.863
  • Governing Static Pressure = -10.11” wg
  • Corrected Volumetric Flow rate = N / A
  • Corrected Velocity = N / A
  • Corrected Velocity Pressure = N / A
  • Resultant Velocity Pressure = N / A

Duct Segment Identification: HI

  • Target Volumetric Flow rate (Design) Q = 1169 cfm (Given)
  • Minimum Transport Velocity (Vt) = 2500 fpm (Given)
  • Maximum Duct Diameter = 9.26”
  • Selected Duct Diameter = 9”
  • Duct Area = 0.442 sq. ft.
  • Actual Duct Velocity = 2644.8 fpm
  • Duct Velocity Pressure, VP = 1.15” wg
  • Maximum Slot Area = N / A
  • Slot Area Selected = N / A
  • Slot Velocity Pressure = N / A
  • Slot Loss Coefficient = N / A
  • Acceleration Factor = N / A
  • Slot Loss per VP = N / A
  • Slot Static Pressure = N / A
  • Duct Entry Loss Factor = N / A
  • Acceleration Factor = N / A
  • Duct Entry Loss per VP = N / A
  • Duct Entry Loss = N / A
  • Other Losses = N / A

Hood Static Pressure (SPh) = N / A

  • Straight Duct Length = 4’ (Given)
  • Friction Factor (Hf) = 0.0278
  • Friction Loss per VP = 0.1112
  • No. of 900 degree elbows = N / A
  • Elbow Loss Coefficient = N / A
  • Elbow Loss per VP = N / A
  • No. of Branch Entries = N / A
  • Entry Loss Coefficient = N / A
  • Special Fittings Loss Factors = N / A
  • Duct Loss per VP = 0.1112
  • Duct Loss = 0.049
  • Duct SP Loss = 0.049
  • Other Losses = N / A
  • Cumulative Static Pressure = 0.049
  • Governing Static Pressure =
  • Corrected Volumetric Flow rate = N / A
  • Corrected Velocity = N / A
  • Corrected Velocity Pressure = N / A
  • Resultant Velocity Pressure = N / A

CALCULATION OF BRAKE HORSE POWER (BHP):

FAN SP = SPout - SPin - VPin

= 0.049 – (-10.11) – 0.44 = 9.72” wg

FAN TP = SPout + VPout - SPin - VPin

= 9.72 + 0.049 – (-10.11) – 0.44 = 10.16

BHP = FAN TP * Q / (6362 * η)

Where:

η = mechanical efficiency (generally taken as 0.9)

BHP = 10.16 * 1169 / (6362 * 0.9) = 2.07