2 (35pts) A continuous bottle filling operation is to rely on a gravitational feed system to deliver equal volumetric flow rates through each of 3 dispensing tubes as shown in the figure. The manifold is fed from a surge tank that maintains the liquid kitchen cleanser at roughly a constant height of 5m. The overall flow rate in the system is 2104m3/s (about 3gal/min ). Given the dimension shown in the figure, determine the diameter of the center pipe to ensure that the flow rate is equal in all three dispensers. The fluid density is 1000kg/m3 and its viscosity is 0.001Pas