Consider the circular pipe in figure $3,$ having a variable cross section in the axial direction $($see figure $3).$ The fluid is incompressible and ideal.

We know: $d_1=20cm,d_2=40cm,d_3=25cm,z_1=4m,z_2=3m,z_3=1m,V_1=5\frac{m}{s},p_1=1$ bar, $=1000k\frac{g}{m^3}.$ Determine:

a$)$ the discharge through the pipe;

b$)$ the mean velocity in section $2$ ;

c$)$ the pressure in section $2$ ;

d$)$ the mean velocity in section $3$ ;

e$)$ the total head in section $2$ ;

f$)$ the pressure in section $3$ ;

g$)$ the hydraulic head $($piezometric head$)$ in section $3.$

$2$