The velocity field for a plane source located distance \(h=1 \mathrm{~m}\) above an infinite wall aligned along the \(x\) axis is given by

\[\begin{aligned} \vec{V}= & \frac{q}{2 \pi\left[x^{2}+(y-h)^{2}\right]}[x \hat{i}+(y-h) \hat{j}] \\ & +\frac{q}{2 \pi\left[x^{2}+(y+h)^{2}\right]}[x \hat{i}+(y+h) \hat{j}] \end{aligned}\]

where \(q=2 \mathrm{~m}^{3} / \mathrm{s} / \mathrm{m}\). The fluid density is \(1000 \mathrm{~kg} / \mathrm{m}^{3}\) and body forces are negligible. Derive expressions for the velocity and acceleration of a fluid particle that moves along the wall, and plot from \(x=0\) to \(x=+10 h\). Verify that the velocity and acceleration normal to the wall are zero. Plot the pressure gradient \(\partial p / \partial x\) along the wall. Is the pressure gradient along the wall adverse (does it oppose fluid motion) or not?

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P6.6 h X-