Estimating fluid parameter

A system for estimating an air mass flow (WTAP) of air flowing in a fan duct, the system comprising:

• a plurality of instruments operable to measure a property of the fluid flowing in the passage, the plurality of instruments being disposed in the passage and arranged within a common measurement plane;
• and
• a computer adapted to communicate with the plurality of instruments and to:
• receive measured values of the one or more properties of the fluid air measured by the plurality of instruments, the one or more properties comprising each of static pressure Ps and total pressure Pt;
• assign a stream tube to each instrument, wherein each stream tube represents a region of space in the common measurement plane within the passage and each stream tube surrounds one of the plurality of instruments, wherein the stream tubes together correspond to the cross-sectional shape and area of the passage in the common measurement plane;
• use the measured value(s) for each stream tube to estimate the air mass flow in an annulus of the common measurement plane from the measurement for each stream tube according to the equation:
• W
• ⁢
• ⁢
• T
• ⁢
• ⁢
• A
• ⁢
• ⁢
• P
• =
• W
• 1
• ⁢
• ⁢
• A
• ×
• T
• t
• ⁢
• ⁢
• 1
• ⁢
• ⁢
• A
• P
• t
• ⁢
• ⁢
• 1
• ⁢
• ⁢
• A
• ×
• A
• 1
• ⁢
• ⁢
• A
• =
• (
• P
• s
• ⁢
• ⁢
• 1
• ⁢
• A
• P
• t
• ⁢
• ⁢
• 1
• ⁢
• ⁢
• A
• )
• (
• 1
• γ
• )
• ×
• 2
• ⁢
• ⁢
• γ
• R
• ⁡
• (
• γ
• -
• 1
• )
• [
• 1
• -
• (
• P
• s
• ⁢
• ⁢
• 1
• ⁢
• A
• P
• t
• ⁢
• ⁢
• 1
• ⁢
• ⁢
• A
• )
• (
• γ
• -
• 1
• γ
• )
• ]
• *
• cos
• ⁢
• ⁢
• α
• where:
• W=mass flow,
• y=a ratio of specific heats of air,
• R=a gas constant,
• A=an area of the stream tube, and
• α=an angle between a longitudinal direction through the annulus and a flow vector;
• and
• sum the air mass flow across all of the stream tubes.