Two hoses are connected to the same outlet using a Y - connector, as the drawing

Question

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 = piR4(P2 - P1) 8etaL 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 = 1.55. Find the ratio of the speed of the water in hose B to the speed in hose A. vB/vA=

Explanation / Answer

As the fluid enters both the tubes form the same source, the volume flow rate of the fluid in both hoses will be same QA = QB The volume flow rate Q = Av A is the cross-sectional area v is the speed vB/vA = AA/AB vB/vA = (pi)RA^2/(pi)RB^2 vB/vA = 1/[(RB/RA)^2] vB/vA = 1/1.55^2 vB/vA = 0.4162

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.