A pipe system carrying water consists of two smaller pipes of different diameters connected to a larger tube. Pipe 1 has a diameter of 10 cm and a velocity of 1 m/s, and pipe 2 has a diameter of 5 cm and a velocity of 2 m/s. Pipes 1 and 2 merge at a junction and flow into pipe 3, which has a diameter of 20 cm. Neglecting all losses (friction, sudden expansion, etc.) and assuming uniform velocity profiles, calculate (a) the velocity in pipe 3, u3, and (b) the difference in pressure between pipe 1 and pipe 3.
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