Figure P$1\mathrm{.}52$

HA$2-3$ A piston$-$cylinder assembly contains an unknown liquid. Pressure is applied to the piston

from above with a screw, and the piston is then pinned in place through the cylinder wall at

a height, $h_1=1m,$ from the bottom of the cylinder. Two absolute pressure gauges, located

at $h_2=0\mathrm{.}75m$ and $h_3=0\mathrm{.}25m,$ read $P_2=200$kPa and $P_3=206\mathrm{.}2$kPa, respectively. The

piston has a diameter, $d_p,$ of $30$ cm and a mass, $m_p,$ of $2$ kg $.$ The upper portion of the cylinder

is exposed to atmospheric pressure, $P_0,$ of $101$ kPa $.$

a$)$ Using Table A$.4$ as a reference, identify the unknown liquid.

b$)$ If a single pin can safely hold $2000$ N $,$ how many pins should be installed to hold the

piston in place as the screw pressure is removed?