Answer: 2.93 ft/sec
Explanation: Calculate the volume/sec entering from the two inlets (Pipes 1 and 2), add them, and then calculate the flow in Pipe 3.
The table illustrates the approach. I calculated the volume of each pipe for a 1 foot section with the indicated diameters, divided by 2 for the radius of each using V = πr²h. Units of V are in^3/foot length. Now we can multiply that volume by the flow rate, in ft/sec, to obtain the flow rate in in^3/sec.
Add the two rates from Pipes 1 and 2 (62.14 in^3/sec) to arrive at the flow rate for Pipe 3 necessary to keep the water level constant. Calculate the volume of 1 foot of Pipe 3 (21.21 in^3/foot) and then divide this into the inflow sum of 62.14 in^3/sec to find the flow rate of Pipe 3 (in feet/sec) necessary to keep the water level constant.
That is 2.93 ft/sec.
