Water flows into end A of a cylindrical tube AB at a speed v₁ and exits from end B at a speed v₂ . The tube remains entirely full of water at all times. Consider three cases: in case I, the tube lies horizontally; in case II, it stands vertically with end A facing upward; and in case III, it stands vertically with end B facing upward. The relation v₁ = v₂ is valid for

Step-by-step solution

By the equation of continuity for an incompressible fluid, the volume flow rate remains constant throughout the tube. A₁ v₁ = A₂ v₂ Since the tube is cylindrical, its cross-sectional area is uniform, so A₁ = A₂ . Therefore, v₁ = v₂ . This relation depends only on the conservation of mass and the incompressibility of water, and is independent of the orientation of the tube. Thus, v₁ = v₂ is valid for each case.