4.7 Equivalent Orifice
111
For a more detailed review of the empirical literature on these types of barriers,
see Crane Company (2013).
Question 4.2 It is necessary to double the air quantity in a mine of 3 m
2 of equivalent
orifice. Explain the effect that this has on the following:
(a) Pressure to be communicated by the fan, and
(b) Fan power.
Answer
(a)
For the first conditions, we have:
A 1 =
1.2
√
P 1
Q 1
Similarly, for the second conditions:
A 2 =
1.2
√ P 2
Q 2
According to the statement A 1 = A 2 = A = 3 m
2 , Q 1 = Q and Q 2 = 2Q 1 = 2Q.
Then, substituting the values and equalizing in the previous expresions:
A =
1.2
√ P 1
Q =
1.2
√
P 2
2Q
So:
P 2
P 1
= 2
Therefore:
P 2
P 1
= 4
Thus, according to the equivalent orifice expression, if you want to double the
airflow rate, you have to quadruple the pressure difference.
(b) The power is proportional to the product P Q, then you have:
Pw 1 = P 1 Q 1
Pw 2 = P 2 Q 2 = 8Pw 1
111
For a more detailed review of the empirical literature on these types of barriers,
see Crane Company (2013).
Question 4.2 It is necessary to double the air quantity in a mine of 3 m
2 of equivalent
orifice. Explain the effect that this has on the following:
(a) Pressure to be communicated by the fan, and
(b) Fan power.
Answer
(a)
For the first conditions, we have:
A 1 =
1.2
√
P 1
Q 1
Similarly, for the second conditions:
A 2 =
1.2
√ P 2
Q 2
According to the statement A 1 = A 2 = A = 3 m
2 , Q 1 = Q and Q 2 = 2Q 1 = 2Q.
Then, substituting the values and equalizing in the previous expresions:
A =
1.2
√ P 1
Q =
1.2
√
P 2
2Q
So:
P 2
P 1
= 2
Therefore:
P 2
P 1
= 4
Thus, according to the equivalent orifice expression, if you want to double the
airflow rate, you have to quadruple the pressure difference.
(b) The power is proportional to the product P Q, then you have:
Pw 1 = P 1 Q 1
Pw 2 = P 2 Q 2 = 8Pw 1