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1. For the case of question 7.6, what is the force required to pull the rod through the axis, per unit length? In 7.9, what is the net downward shear force on the pipe? Does the simple answer surprise you? Why not?

2. 7.4. Argue your answer. In what terms would you ballpark the answer? What is the importance of the pressure level? Of the flow velocity? What are the relevant values involved? What are the most important uncertainties?

3. 7.1a Assume only that the velocity only depends on $r$, $\vec v=\vec v(r)$, that $p=p(r,\theta,z,t)$ is arbitrary, and that the pipe is horizontal. Use the effective pressure. Show that two velocity components must be zero. (You should be able to show that the effective pressure is independent of $\theta$ from the appropriate momentum equation by noting that $p$ at $\theta=2\pi$ must be the same as at $\theta=0$; otherwise just assume it is. Also note that the velocity can obviously not be infinitely large on the pipe centerline.)

4. 7.1b Continuing the previous question, derive the velocity and pressure fields.