55
If we use the above equation, but consider the flow through two different orifices that are in series with
each other, we get the following equation.
Qm1 = 0.09970190
X
C
1
X
Y
1
X
d
1
2
X
h
w1
x
p
1
1
-
B
1
4
= 0.09970190
X
C
2
X
Y
2
X
d
2
2
X
h
w2
x
p
2
1
-
B
2
4
The mass flow through the first orifice must be equal to the mass flow through the second orifice or else
mass is being accumulated somewhere (or there is leakage, but we will assume zero leakage for this
analysis).
Since the expansibility factor Y and the 0.09970190 terms are essentially constants on both sides of the
equation, we can simplify it to:
C
1
X
d
1
2
X
h
w1
x
p
1
1
-
B
1
4
= C
2
X
d
2
2
X
h
w2
x
p
2
1
-
B
2
4
The terms C1, C2, D1, D2, B1 and B2 terms do not change with changes in atmospheric conditions, and
the above equation can be simplified even further to:
K
1
X
h
w1
x
p
1
= K
2
X
h
w2
x
p
2
At low speeds it is appropriate to assume that air is incompressible, and p1 = p2. This is true at speeds
below 100 m/s, which is roughly the equivalent velocity of escaping air with a differential pressure of
25 inches of water. At speeds above this, there are some air density corrections, but the amount of the
correction is far smaller than the actual air density change. Using this incompressible assumption, we can
now define the differential pressure at the orifice plate as a function of the differential pressure at the test
article:
h
w1
= K
X
h
w2
As you can see, this equation has no air density reference. So, if you have a test pressure of 25 inches
of H20, the orifice pressure is simply a multiple of this, regardless of the air density. To be absolutely
technically correct, there are some minor factors such as Expansibility and Discharge Coefficient that do
change with air density changes, but these effects are extremely small, usually much less than 0.25% so
it is normally safe to ignore these effects as the accuracy of the pressure measurement is typically less
accurate.
7.0 Flowbench Theory
