4.2 Friction Losses: Atkinson Expression
93
So finally:
Q 2 = 42.09
m
3
s
4.3 Concept of Resistance of an Airway
The Atkinson equation can be expressed as a function of the square of the airflow
rate, and a coefficient (R) that groups together all the geometric parameters (O, L,
A), the properties of the conduit (K) and of the density of the fluid (ρ) (Eq. 4.9):
R = K 1.2
O
L + L eq
A 3
⎛
⎝ ρ
1.2
kg
m 3
⎞
⎠
(4.9)
So the Atkinson equation would appear as (Eq. 4.10). This expression is called
the mine characteristic curve as is discussed in detail in Sect. 4.4:
P = R Q
2
(4.10)
Thus, R is usually called the aerodynamic resistance (Atkinson resistance) of the
airway, which expressed in SI units is:
R =
P
Q 2 =
1
N
m 2
1
m 3
s
2 =
N s
2
m 8 ,
kg
m 7
This unit is called gaul and is defined as: “Resistance of the airway which causes
a pressure loss of 1 Pa when crossed by a quantity of 1 m
3 s
−1 at the standard air
density of 1.2 kg m
−3 ”. For the sake of simplicity, the gaul can often be seen as Pa
Q
−2 .
In Germany, the weisbach (Wb) is frequently used. Its definition is analogous to
the previous one with the particularity that instead of using the N m
−2 , the kgf m
−2
is employed, so 9.8 gauls = 1 Wb.
In spite of the diffusion that the SI currently has, the use of the English unit or
atkinson is still frequent.
5 Analogous to the previous one, it is defined as: “Resistance
of the airway which causes a pressure loss of 1l bf ft
−2 when crossed by an air quantity
of 1000 ft
3 s
−1 at the air density of 0.075 lbm ft
−3 ”, therefore:
5 Not to be confused with Atkinson friction factor.
93
So finally:
Q 2 = 42.09
m
3
s
4.3 Concept of Resistance of an Airway
The Atkinson equation can be expressed as a function of the square of the airflow
rate, and a coefficient (R) that groups together all the geometric parameters (O, L,
A), the properties of the conduit (K) and of the density of the fluid (ρ) (Eq. 4.9):
R = K 1.2
O
L + L eq
A 3
⎛
⎝ ρ
1.2
kg
m 3
⎞
⎠
(4.9)
So the Atkinson equation would appear as (Eq. 4.10). This expression is called
the mine characteristic curve as is discussed in detail in Sect. 4.4:
P = R Q
2
(4.10)
Thus, R is usually called the aerodynamic resistance (Atkinson resistance) of the
airway, which expressed in SI units is:
R =
P
Q 2 =
1
N
m 2
1
m 3
s
2 =
N s
2
m 8 ,
kg
m 7
This unit is called gaul and is defined as: “Resistance of the airway which causes
a pressure loss of 1 Pa when crossed by a quantity of 1 m
3 s
−1 at the standard air
density of 1.2 kg m
−3 ”. For the sake of simplicity, the gaul can often be seen as Pa
Q
−2 .
In Germany, the weisbach (Wb) is frequently used. Its definition is analogous to
the previous one with the particularity that instead of using the N m
−2 , the kgf m
−2
is employed, so 9.8 gauls = 1 Wb.
In spite of the diffusion that the SI currently has, the use of the English unit or
atkinson is still frequent.
5 Analogous to the previous one, it is defined as: “Resistance
of the airway which causes a pressure loss of 1l bf ft
−2 when crossed by an air quantity
of 1000 ft
3 s
−1 at the air density of 0.075 lbm ft
−3 ”, therefore:
5 Not to be confused with Atkinson friction factor.