The water$-$lifting experiment done during class on Sept. $19$ had a successful attempt for raising water to a height of $2-$storeys $(22\mathrm{.}9$ ft $)$ from human suction. The successful attempt raised the water to that height using a plastic tube of inside diameter $0\mathrm{.}17$ in $.$ This success was repeated with a larger tube of $0\mathrm{.}25$ in $.$ in diameter.

The upward velocity can be approximated as $2i\frac{n}{s}$ or $\frac{2}{12}f\frac{t}{s}.$ The density and dynamic viscosity of the water were $1\mathrm{.}94$ slugs $\frac{?}{f{t}^3}$ and $2\mathrm{.}34{10}^{-5}lb*\frac{s}{f}{t}^2,$ respectively. Use $14\mathrm{.}7$ psi for the atmospheric pressure and $32\mathrm{.}2f\frac{t}{s^2}$ for the gravitational constant. Recall that $1$ slug is $1lbf*\frac{s^2}{f}t.$

a$)$ Calculate the head loss due to friction for a length along the tube equal to the height of $22\mathrm{.}9$ ft $.$

b$)$ Calculate the vacuum pressure that was created at the end of the pipe to lift the water to a height of $22\mathrm{.}9$ ft $.$

Hint: Recall that a vacuum pressure is the opposite of a gage pressure. It is the atmospheric pressure minus the absolute pressure.