Consider a large axial flow pump that provides a pressure rise of $150$ kPa and a flow rate of $0\mathrm{.}5$ m$^3/$s$.$ The impeller hub diameter ddd and the outer diameter DDD are $0\mathrm{.}5$ m and $0\mathrm{.}3$ m$,$ respectively, with a rotational speed of $1200$ RPM$.$ Perform the following calculations:

$($A$)$ Estimate the pump's total pressure efficiency considering the Reynolds number effect based on the Cordier diagram efficiency.

Using the Cordier efficiency, estimate the pump's efficiency while accounting for the influence of the Reynolds number.

$($B$)$ Draw the velocity triangle at the mean radius based on the efficiency calculated in part $($A$)$ to generate the given pressure.

Utilize the efficiency obtained in part $($A$)$ to plot the velocity triangle at the mean radius to produce the given pressure rise.

$($C$)$ Sketch the blade profile at the mean radius based on the velocity triangle calculated in part $($B$).$

Using the velocity triangle from part $($B$),$ draw the blade shape at the mean radius.

$($D$)$ Evaluate the diffusion ratio $($de Haller ratio$)$ at this section.

Assess the diffusion ratio, or de Haller ratio, at this cross$-$section of the pump.

This translation maintains the technical context of the original task.