You have not given me all of the information that may be relevant, especially the viscosity of the polymer, but I will assume that the viscosity is much higher than water.  The problem becomes more about how you mix a viscous fluid with a low viscosity one, which is difficult in either a stirred vessel or a static mixer.  The very long residence time (15 minutes) you report for a 500 ml sample is probably a result of poor (slow) mixing, not a dissolution of the polymer.  I would expect a much faster rotational speed than 60 rpm (1 revolution per second) in a 500 ml sample.  I could have believed 300 rpm, although you did not provide the beaker and stir bar dimensions.
 
Regardless of the solubility of the polymer in water, which may require an extended residence time, the mixing needs to be effective.  You have indicated a flow rate of 7 cu.m per hour of water and 0.5 cu.m per hour of polymer for a total flow of 7.5 cu.m per hour.  By my calculation, that flow rate gives you a 0.44 m/s velocity through a 3-inch pipe.  You most likely want a 2.0 to 2.5 m/s velocity through a static mixer to get good mixing.  You definitely do not want to increase the mixer diameter to 4 inches and further slow the flow velocity.  You have tried to get a low flow velocity for a long residence time at the expense of getting good mixing, or even any mixing at all.  You probably need to be using a 1-1/4 inch diameter pipe and mixer.
 
The length of the mixer will depend on the type of mixer being used.  A six-element twisted-element static mixer may be adequate to get initial mixing, provided a good injector is used.  With any static mixer, especially with viscous polymer addition to water, the polymer injection needs to be near the centerline of the pipe and away from the tank wall.  With a twisted-element mixer, two injection points, one ahead of each side of the first element will maximize the turbulent mixing and minimize viscous flow attachment to the pipe wall or mixing element.  Once the mixing is accomplished, a downstream length of pipe (perhaps 100 pipe diameters or more) may be necessary for additional residence time to complete the dissolution of the polymer in the water.  Multi-finger, structured-packing type, static mixers may work even better for handling large viscosity differences.  Large viscosity differences are some of the most difficult mixing problems.  In the extreme, some mixers specially designed for polymer addition to water, with small flow channels and rotating cores, may be needed to accomplish your mixing task.
 
As with most mixing problems, getting good mixing is the essential part of the process.  Residence time may be needed to complete the process, but without good mixing the process will always fail.

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