Statement of a problem № 10692


Two hoses are connected to the same outlet using a Y-connector, as the drawing shows. The hoses A and B have the same length, but hose B has the larger radius. Each is open to the atmosphere at the end where the water exits. Water flows through both hoses as a viscous fluid, and Poiseuille s law [Q = πR4(P2 - P1)/(8ηL)] applies to each. In this law, P2 is the pressure upstream, P1 is the pressure downstream, and Q is the volume flow rate. The ratio of the radius of hose B to the radius of hose A is RB/RA = 1.50. Find the ratio of the speed of the water in hose B to the speed in hose A.

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