Ventilation 1 - Program

1
Ventilation 1 - Program

• Presented by Training Staff
• Bureau of Deep Mine Safety
• Basic Math Problem Solving

2
Review of Formula Terms

• a sectional area of airway, in square feet
  (ft.2)
• l length of airway, in feet (ft.)
• o perimeter of airway, in feet (ft.)
• s rubbing surface, in square feet (ft2)
• v velocity of air current, in feet per minute
  (fpm)
• q quantity of air, in cubic feet per minute
  (cfm)

3
COMMON AREA FORMULAS

• Rectangular or Square Dimension
• Area Height X Width
• Note Please remember to convert inches into the
  decimal equivalent of one foot - inches divided
  by 12

4
Practice Problems Area Rectangle

• Determine the area of a mine entry that is 19
  feet wide and 7 feet high

• Solution
• A W x H
• A 19 x 7
• A 133 sq. ft.

7
19
5
Practice Problems Area Rectangle

• Determine the area of a mine entry that is 18
  feet wide and 5 feet, 6 inches high

• Solution
• A W x H
• A 5.5 x 18
• A 99 sq. ft.

56
18
6
Practice Problems

• Determine the area of a mine entry that is 17
  feet 3 inches wide and 6 feet 9 inches high

• Solution
• A W x H
• A 17.25 x 6.75
• A 116.44 sq. ft.

69
173
7
COMMON AREA FORMULAS

• Trapezoid

Area Top Width Bottom Width X Height
2
8
Practice Problems Area Trapezoid

• Determine the area of a mine entry that is 6 foot
  high, and 18 feet wide across the top, and is 19
  feet wide across the bottom.

• Solution
• Area Top Width Bottom Width X Height
• 2
• A 18 19 x 6
• 2
• A 37 x 6
• 2
• A 18.5 x 6
• A 111.00 sq. ft.

18
6
19
9
Practice Problems Area Trapezoid

• Determine the area of a mine entry that is 5 foot
  high, and 20 feet wide across the top, and is 22
  feet wide across the bottom.

• Solution
• Area Top Width Bottom Width X Height
• 2
• A 20 22 x 5
• 2
• A 42 x 5
• 2
• A 21 x 5
• A 105 sq. ft.

20
5
22
10
Practice Problems

• Determine the area of a mine entry that is 4 foot
  6 inches high, and 17 feet wide across the top,
  and is 20 feet wide across the bottom.

• Solution
• Area Top Width Bottom Width X Height
• 2
• A 17 20 x 4.5
• 2
• A 37 x 4.5
• 2
• A 18.5 x 4.5
• A 83.25 sq. ft.

17
46
20
11
COMMON AREA FORMULAS - Circle

• Circular
• A x D2
• 4
• or
• A x R2
• Please use the following
• For Pi
• 3.1416

diameter
radius
12
Practice Problems Area Circle

• Determine the area of a circle that has an
  diameter of 20 feet 9inches.

• Solution
• A x R2
• R 20.75 10.375
• 2
• A 3.1416 x 10.3752
• A 3.1416 x 107.640
• A 338.16 sq. ft.

R
13
Area - Circle

• Determine the area of a circular air shaft with a
  diameter of 20 feet

• Solution
• A x R2
• R 20 10
• 2
• A 3.1416 x 102
• A 3.1416 x 100
• A 314.16 sq. ft.

20
14
Practice Problems

• Determine the area of a circle that has an
  diameter of 17 feet.

• Solution
• A x r2
• R 17 8.5
• 2
• A 3.1416 x 8.52
• A 3.1416 x 72.25
• A 226.98 sq. ft.

17
15
Perimeters

• Square or Rectangle
• o Top Width Bottom Width Side 1 Side 2
• Remember, perimeter measured in linear feet

16
Practice Problem Perimeter Rectangle

• Determine the perimeter of an entry 7 feet high
  and 22 feet wide.

• Solution
• o Top Width Bottom Width Side 1 Side 2
• o 22 22 7 7
• o 58 feet

7 ft.
22 ft.
17
Practice Problem Perimeter Rectangle

• Solution
• o Top Width Bottom Width Side 1 Side 2
• o 6.5 6.5 20.25 20.25
• o 53.5 feet

• Determine the perimeter of an entry 6 feet 6
  inches high and 20 feet 3 inches wide.

6ft.6in.
20ft.3in.
18
Perimeters - Circle

• o x Diameter
• 3.1416

Diameter
19
Perimeter - Circle

• Determine the perimeter of a circular air shaft
  with a diameter of 17 feet, 6 inches.

• Solution
• o x Diameter
• o 3.1416 x 17.5 ft.
• o 54.978 ft.

176
20
Perimeter - Circle

• Determine the perimeter of a circular air shaft
  with a diameter of 20 feet

• Solution
• o x Diameter
• o 3.1416 x 20 ft.
• o 62.83 ft.

20
21
Perimeter - Circle

• Determine the perimeter of a circular air shaft
  with a radius of 9 feet.

• Solution
• D 2 x r
• D 2 x 9 ft.
• D 18 ft.
• 3.1416
• o x Diameter
• o 3.1416 x 18.0 ft.
• o 56.548 ft.

9
22
Formula Equations

• Quantity of Air (cfm)
• Q AV
• Quantity Area X Velocity
• Velocity of air (fpm)
• V _ Q_
• A
• Velocity Quantity ? Area
• Area (when velocity and quantity a known)
• A _Q_
• V
• Area Quantity ? Velocity

Algebraic Circle
Q
A
V
23
Practice Problem - Quantity

• Find the quantity of air passing thru an entry
  17 feet 6 inches wide and 9 feet high, with 180
  fpm registered on the anemometer.
• A WH
• Q AV

• Solution
• A WH
• A 17.5 x 9
• A 157.5 sq. ft.
• Q AV
• Q (157.5 sq.ft.)(180 fpm)
• Q 28,350 CFM

24
Practice Problem - Quantity

• Find the quantity of air passing thru and entry
  18 feet wide and 6 feet 6 inches high, with 110
  fpm registered on the anemometer.
• A WH
• Q AV

• Solution
• A WH
• A 18 x 6.5
• A 117 sq. ft.
• Q AV
• Q (117 sq.ft.)(110 fpm)
• Q 12,870 CFM

25
Practice Problem - Velocity

• What is the velocity in a entry 10 feet high and
  22 feet wide, with a quantity of 11,380 CFM?
• A WH
• V _Q_
• A

• Solution
• A WH
• A 22 ft. x 10 ft.
• A 220 sq. ft.
• V _Q_
• A
• V 11,380 CFM
• 220 sq.ft.
• V 51.72 fpm

26
Practice Problem - Area

• An entry has 12,500 CFM of air with a velocity
  of 150 fpm. What is the area of the entry?
• A _Q_
• V

• Solution
• A _Q_
• V
• A 12,500 CFM
• 150 fpm
• A 83.33 sq. ft.