Three measurements are made of the x-component velocity in the diffuser of an incompressible plane flow to be 32 m/s, 28 m/s and 20 m/s. The measurement points are
Along the centerline of the symmetrical diffuser and are 4 cm apart. The y-component of the
Velocity 2 cm above the centerline is approximated to be:

Question

Quizplus · Accepted Answer

$3 \mathrm {~m} / \mathrm { s }$
$\text {We chose to use the more accurate central difference to approximate the derivative }$$\text {since the information given allows such an approximation:}$
$$\frac { \partial u } { \partial x } \cong \frac { \Delta u } { \Delta x } = \frac { 20 - 32 } { 0.08 } = - 150 \frac { \mathrm { m } / \mathrm { s } } { \mathrm { m } }$$
$\text {The continuity equation then provides}$
$$\frac { \partial v } { \partial y } = - \frac { \partial u } { \partial x } = 150 \quad \text { or } \quad \frac { \partial v } { \partial y } \cong \frac { \Delta v } { \Delta y } = \frac { v _ { 2 } - 0 } { 0.02 } = 150 . \quad \therefore v _ { 2 } = \underline { 3 \mathrm {~m} / \mathrm { s } }$$

Three Measurements Are Made of the X-Component Velocity in the Diffuser