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BSA Flow Software Installation and User's Guide - CSI

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2-D Probe<br />

1-D Probe<br />

u3<br />

u2<br />

Figure 5-73 Possible geometry of a 3D LDA system.<br />

u1<br />

u<br />

v 30° w<br />

Velocities u1 <strong>and</strong> u2 correspond directly to the ortogonal velocities u <strong>and</strong> v,<br />

but due to restricted optical access the third component w cannot be<br />

measured directly, but must be calculated from u2 <strong>and</strong> u3. With an angle of α<br />

between the two probes, <strong>and</strong> u3 lying in the v-w-plane, the w-component can<br />

be calculated from u2 <strong>and</strong> u3:<br />

u2 u3<br />

w = −<br />

tanα sinα<br />

– in the matrix-formulation including all velocity-components <strong>and</strong> with<br />

α=30° inserted this yields:<br />

⎡<br />

⎤<br />

⎢<br />

1 0 0<br />

⎥ ⎡ 1000 . 0. 000 0. 000 ⎤<br />

⎢<br />

⎥ ⎢<br />

⎥<br />

C = ⎢ 0 1 0 ⎥ = ⎢ 0. 000 1000 . 0. 000 ⎥<br />

⎢<br />

⎥ ⎢<br />

⎥<br />

⎢ 1 −1<br />

0<br />

⎥ ⎣⎢<br />

0. 000 1732 . −2.<br />

000 ⎦⎥<br />

⎣⎢<br />

tanα sinα<br />

⎦⎥<br />

– corresponding to the values shown in Figure 5-72.<br />

5-80 <strong>BSA</strong> <strong>Flow</strong> <strong>Software</strong>: Project explorer objects

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