You are drinking a milk shake through a straw that is $8 \mathrm{in.}$ long and $0.3 \mathrm{in}$. in diameter. The milk shake has the properties of a Bingham plastic, with a yield stress of $300 \mathrm{dyn} / \mathrm{cm}^{2}$, a limiting viscosity of $150 \mathrm{cP}$, and a density of $0.8 \mathrm{~g} / \mathrm{cm}^{3}$.

(a) If the straw is inserted 5 in. below the surface of the milk shake, how hard must you suck to get the shake flowing through the entire straw (e.g., how much vacuum must you pull, in psi)?

(b) If you pull a vacuum of $1 \mathrm{psi}$, how fast will the shake flow (in $\mathrm{cm}^{3} / \mathrm{s}$ )?