Final answer:
To determine the highest pressure at the pump's exit, we calculate the pressure increase using the pump's work done on the water over one second. The increase is 3200 kPa, thus the exit pressure is 3300 kPa when considering the initial pressure of 100 kPa.
Step-by-step explanation:
The question relates to the field of
fluid mechanics
in Engineering, specifically in calculating the pressure output of a pump. To solve the problem, we apply the energy form relation in fluid flow, acknowledging that the kinetic and potential energies remain constant in this scenario. For a 16-kW pump transferring 5 kg/s of water with a specific volume of 0.001 m3/kg at 100 kPa, the work done by the pump can be calculated using the formula
work = power x time
. In one second, the work done is 16 kJ since the power of the pump is 16 kW. Using the formula
pressure increase = (work done)/ (mass x specific volume)
, we can calculate the increase in pressure. The highest pressure that the liquid water can have at the exit is the initial pressure plus this increase. Thus:
P_increase = (Work) / (m x v)
P_increase = (16 kJ) / (5 kg x 0.001 m3/kg)
P_increase = 3200 kPa
Exit Pressure = Initial Pressure + P_increase
Exit Pressure = 100 kPa + 3200 kPa
Exit Pressure = 3300 kPa