A centrifugal pump is to be used to circulate water between two reservoirs with an altitude difference of 36.6m. A 400 m long tube having a diameter of 0.35 m

connects the two reservoirs. The Darcy friction factor in the tube is f = 0.028. The pump performance can be modeled by the equation below: \boldsymbol{H}_{\text {pump }}=150-22.5 \boldsymbol{Q}^{2} \quad\left(Q \text { in } \mathrm{m}^{3} / \mathrm{s} \text { and } H_{\text {pump }} \text { in } \mathrm{m}\right) a) Explain in detail and using your own words the functioning principle of a centrifugal pump. b) Calculate the volume flow rate and the head in the circuit above. c) Provide an answer to question (b) using a different method. d) Without doing any calculations, explain what would happen to the flow rate if the tube is replaced by another that is half the length and half the diameter, while keeping other parameters constant. (5 pts.)