Final answer:
The other pump, with a discharge of 0.01 m³/s, will have an impeller diameter of 200 mm and operate against a head of 7.5 m.
Step-by-step explanation:
To determine the head and impeller diameter of the second pump, we can use the affinity laws for pumps. The affinity laws state that for geometrically similar pumps running at the same speed, the ratios of the impeller diameters, heads, and discharges are equal. In this case, the ratio of the discharges is given as 0.01 m3/s divided by 0.02 m³/s, resulting in 0.5.
Using the affinity law for the heads, we find that the other pump must operate against a head of 15 m multiplied by 0.5, giving a head of 7.5 m. Similarly, the impeller diameter ratio is the square root of the discharge ratio, which is the square root of 0.5. Multiplying the given impeller diameter of 300 mm by the square root of 0.5 yields the impeller diameter of the other pump as 200 mm.
In summary, the second pump, with a discharge of 0.01 m³/s, will have an impeller diameter of 200 mm and operate against a head of 7.5 m. These calculations are based on the affinity laws, providing a straightforward method for determining the characteristics of geometrically similar pumps running at the same speed.