Step 1: Understanding the Concept:
A centrifugal (turbine) pump spins water outward and this spinning motion, not friction, is what raises the water's pressure head. Ignoring blade curvature means we treat the whole tip speed of the impeller as doing useful work on the water, which is the simplest form of Euler's pump theory.
Step 2: Key Formula or Approach:
Under this assumption the manometric head links directly to the tip speed as $H_m = \eta_{man}\, u_2^2 / g$. Once $u_2$ is found, convert it to a diameter through the angular speed of rotation, $\omega = 2\pi N/60$, using $u_2 = \omega r$ where $r$ is the impeller radius.
Step 3: Detailed Explanation:
Rearranging the head formula for tip speed: $u_2 = \sqrt{H_m g / \eta_{man}} = \sqrt{(60)(9.81)/0.70} = \sqrt{840.86} = 29.00\ m/s$.
The angular speed at 2000 rpm is $\omega = 2\pi (2000)/60 = 209.44\ rad/s$.
The impeller radius is then $r = u_2/\omega = 29.00/209.44 = 0.1385\ m$.
Doubling for the diameter, $D = 2r = 0.2769\ m$, which is $27.69\ cm$.
Step 4: Final Answer:
Working through the angular speed and radius gives the same impeller diameter, about 27.69 cm.