$8.$ The symbol at right represents a device called:

a$.$ Directional control valve

b$.$ Pressure relieve valve

c$.$ Pressure reducing valve

d$.$ Flow control valve

$9.(10$ points$)$ Which of the following two hydraulic circuits uses the pressure relieve valve correctly? Explain Whe?

$10.(20$ points$)$ A hydraulic pump is used to drive a conveyor belt system for transporting heavy metal components. The system operates continuously, and the pump is powered by an electric motor. The following specifications are:

Electric motor output torque: $\backslash (120\backslash$mathrm$\{$lb$\}-\backslash$mathrm$\{$ft$\}\backslash )$

Pump displacement volume: $\backslash (5\backslash$mathrm$\{$in$\}^\{3\}\backslash )$

Pump output flow rate: $30$ GPM$,$ pressure: $1500$ psi $,$ speed: $1800$ rpm

Calculate: $($Note: maintain $2$ digits after the decimal point$)$

a$)$ the volumetric efficiency of the pump

b$)$ the mechanical efficiency of the pump

c$)$ theoretical torque required to drive this pump in lb$-$ ft

d$)$ overall efficiency of the pump

$11.(20$ points$)$ A hydrostatic transmission operating at $\backslash ($ P$\_\{1\}=1500\backslash )$ psi pressure $($pump output pressure$),\backslash ($ P$\_\{2\}=10\backslash )$ psi $($motor output pressure$)$ has the following characteristics