Apump increases the water pressure from 70 kpa at the inlet to 700 kpa at the outlet. water enters this pump at 15 °c through a 1-cm-diameter opening and exits through a 1.5-cm-diameter opening. determine the velocity of the water at the inlet and outlet when the mass flow rate through the pump is 0.5 kg/s. how much work is required to operate the pump?

Explanation:

First, we are going to need the water specific volume at 15ºC: v=0.001001 . The density '' of the water is the inverse of the specific volume:

First, consider the mass flow, which is related to the volumetric flow (density and velocity) and the area:

The area of each cross-section is:

(in square meters). Here, the radius was not used but the diameter, which means a division by 4 (2 squared).

From mass flow isolate the velocity and calculate it:

The work of the pump is calculated considering an energy balance on the pump:

Considering the isentropic process may give us the relation:

Applying that to the pump,

Multiplying it by the mass flow:

The work is negative because it is entering to the system, but the required is positive. (It is just a standard rule)