Task $2$

An oil hydraulics system is presented in figure $1.$ Figure $2$ is a schematic drawing of the same oil

hydraulic system. The hydraulic motor works as a turbine by extracting energy from the oil. The oil in

the system has a density of $897,4k\frac{g}{m^3}$ The pressure increase over the pump is $p_{\text{p}\text{u}\text{m}\text{p}}=$

$180,\frac{16}{b}ar.$ The pressure decrease over the hydraulic motor is $p_{h-m}=-180,\frac{16}{b}ar,$ and the flow

in the line is $0,000158\frac{m^3}{s}.$ The pipe diameter is $50mm$ for all pipes, and we assume there is no

friction loss in the pipe. The heights of the different positions are given below:

$z_1=z_8=0m$

$z_2=z_7=0,5m$

$z_3=z_6=0,7m$

$z_4=z_5=1,5m$

a$)$ Draw the streamline that describe the trajectory of the flow in the system.

b$)$ Calculate the pressure and the velocity at each point. Fill in the following table:

TIPS: Gauge pressure is the pressure difference between the pressure at the point and the air

pressure at the reservoirs.

c$)$ Draw the EGL and the HGL of the system in the same graph. Calculate the value of the EGL

and $HGL$ at each point.

d$)$ How would the EGL change, if the system is in a horizontal configuration, where all the parts

are at the same elevation? The pressure increase over the pump is the same. Sketch the new

EGL.