A tank is to be added to a refinery to increase the storage capacity for a product such as home heating oil. The oil level in the new tank may be as much as a height H above that in the tank leading to it, which will have the same pressure in the head space (i.e., the same gas pressure). Thus, pumping will be required. Two identical centrifugal pumps, whose performance is described by Eq. (12.3- 6) with n = 2, are available for this purpose. You are asked to decide how best to configure them.

(a) If the pumps are arranged in series and the loss in the pipe that connects them is negligible, how will the total pressure increase |ΔP|_T generated by them be related to the flow rate Q? How large would H need to be to make both pumps necessary? When would the two pumps not be enough?

(b) Repeat part (a) for pumps connected in parallel, assuming again that losses in the pipes and fittings that connect them are negligible. If H is small enough that either a single pump or two in parallel could be used, what would be the functional advantage of the parallel arrangement?