BSA Flow Software Installation and User's Guide - CSI

In this particular example we get:
⎧
⎪
⎪1
⎪
⎧u
⎫ ⎪
⎪ ⎪ ⎪
⎨v
⎬ = ⎨0
⎪ ⎪ ⎪
⎩w⎭
⎪
⎪
⎪0
⎪
⎩
7.8.2 Example: Symmetrical 3D setup
0
sinα
2
−
sin( α −α
)
cosα
2
sin( α −α
)
1
1
2
2
⎫
⎪
0 ⎪
⎪
sinα
1 ⎪ ⎧u1
⎫
sin( α ⎪ ⎪ ⎪
1 −α
2 )
⎬ ⋅ ⎨u
2 ⎬
⎪ ⎪ ⎪
cosα
⎪ ⎩u3
⎭
1
sin( α − ⎪
1 α 2 )
⎪
⎪
⎭
In case α1 = - α2 = α/2 the expression becomes
⎧
⎪1
⎪
⎧u
⎫ ⎪
⎪ ⎪ ⎪
⎨v
⎬ = ⎨0
⎪ ⎪ ⎪
⎩w⎭
⎪
⎪0
⎪⎩
0
1
2cos(
α )
2
1
2sin(
α )
2
⎫
0 ⎪
⎪
⎪ ⎧u1
⎫
1 ⎪ ⎪ ⎪
⎬ ⋅ ⎨u
2 ⎬
2cos(
α )
2 ⎪ ⎪ ⎪
⎪ ⎩u3
⎭
1
− ⎪
2sin(
α )
2
⎪⎭
7.8.3 Example: 3D setup with 2D probe axis aligned with w
(7-19)
(7-20)
In Figure 7-74, the 2-D probe aligned with the w-axis and the 1-D probe is
positioned at an off-axis angle α.
BSA Flow Software:Reference guide 7-97