Problem $7\mathrm{.}5.$

$7\mathrm{.}9$ A hydraulic cylinder is to be used to move a workpiece in a manufacturing operation through a distance of $50$ mm in $10$ s $.$ A force of $10$ kN is required to move the worlpiece. Determine the required working pressure and hydraulic liquid flow rate if a cylinder with a piston diameter of $100$ mm is available.

$7\mathrm{.}10$ An actuator has a stem movement which at full travel is $40$ mm $.$ It is mounted with a linear plug process control valve which has a minimum flow rate of $0$ and a maximum flow rate of $0\mathrm{.}20\frac{m^3}{s}.$ What will be the flow rate when the stem movement is $($a$)10$ mm $,($b$)20$ mm $?$

$7\mathrm{.}11$ An actuator has a stem movement which at full travel is $40$ mm $.$ It is mounted on a process control valve with an equal percentage plug and which has a minimum flow rate of $0\mathrm{.}2\frac{m^3}{s}$ and a maximum flow rate of $4\mathrm{.}0\frac{m^3}{s}.$ What will be the flow rate shen the stem movement is $($a$)10$ mm $,($b$)20$ mm $?$

$7\mathrm{.}12$ What is the process control valve size for a valve that is required to control the flow of water when the maximum flow required is $0\mathrm{.}002\frac{m^3}{s}$ and the permissible pressure drop across the valve at this flow rate is $100$ kPa $?$ The density of water is $1000g\frac{g}{m^3}.$