An engineer is designing a water filter that works by forcing water through a circular plate that has many identical holes in it. The plate is to be welded into a pipe so the water stream and the plate have the same 2.54-cm diameter. Before it hits the filter, the water is to be traveling at 75.0 cm/s. The holes are planned to be circular and 0.100 mm in diameter.

(a) If the holes are to cover of the total plate area, how many of them will you need?
(b) Assuming that initially none of the holes are plugged, what is the flow speed just after the water leaves the holes?
(c) Later, if of the holes are completely plugged with gunk and the water speed before the filter has not changed, what will be the flow speed of the water upon leaving the filter area?
(d) Compare the flow rate in this system (in liters per minute) before and after some of the holes plug up.