Problem #$3$ HGL and EGL

A diffuser in a pipe flow is basically a slow expansion of the pipe diameter, which slows down the fluid velocity and increases the pressure $($the Bernoulli effect$).$ Water at room temperature flows with a flowrate of $0\mathrm{.}025\frac{m^3}{s}$ through a horizontal diffuser in which the pipe diameter increases gradually from $D_1=6$ to $D_2=11cm.$ The irreversible head loss through the diffuser is estimated to be $0\mathrm{.}45m.$ The flow is turbulent, and the kinetic energy correction factors at both the inlet and outlet of the diffuser are assumed to be $1\mathrm{.}05.$

a Calculate the pressure difference $P_2-P_1$ in units kPa.

b Calculate the change in energy grade line $($DEGL$)$ and the change in hydraulic grade line $($DHGL$).$ Does EGL go up or down? Does HGL go up or down?

c Conceptual question $-$ how would the EGL and HGL lines look if we had no losses in our system?