Question

The tank shown in the accompanying figure is being filled by pipes 1 and 2. If the water level is to remain constant, what is the volumetric flow rate of water leaving the tank at 3? What is the average velocity of the water leaving the tank?

Answer 1

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.