We have set up a base on mars, where we want to transport water weve mined from surface ice. This water travels downhill from a tank at the mining site (Tank 1) to a settling and distribution tank (Tank 2) before it is pumped to a tank in our settlement. To make sure the water remains liquid, we have heated and pressurized our storage system. The pressures, diameters and free surface heights in each of our tanks are given in the image below. This image is not to scale. The gravitational acceleration on mars is given by gmars = 3.7 m/s2 , and the surface roughness of the iron pipes were using is 1 mm. You can use values of = 1000 kg/m3 and = 0.001 Pas for water. Ignore minor losses.

a) Calculate the flow rate (in m3 /s) and average velocity (in m/s) in the pipe from Tank 1 to Tank 2.

b) Imagine we wanted to regulate the flow through the pipe by changing the pressure in Tank 2. What would the pressure in Tank 2 have to be to stop the flow through the pipe? Give your answer in kPa.

c) We have a centrifugal pump moving the water from Tank 2 to Tank 3. The vapour pressure of our water is 2 kPa. If our pump is moving 0.01 m3 /s from Tank 2, calculate the net positive suction head available (, in meters) of this pump. You can assume a fanning friction factor of 0.01 here.

d) What is the suction head and discharge head of this pump at the this flow rate (0.01 m3 /s)?

e) If the pump has a mechanical efficiency of 65% at this flow rate, how much (brake) power do we need to supply to the pump? Assume your discharge head is equal to the pump head.