ANS:B - V₂ > V₁ and V₂ > V₃

For flow through a venturi tube at a particular discharge, the correct relationships among velocities at points X, Y, and Z are typically: V1 > V2 > V3

Explanation:

1. Venturi Tube:
   • A venturi tube is a device used to measure fluid flow by creating a pressure differential between its throat (point Y) and the entrance (point X).
   • The velocity of the fluid varies along the length of the venturi tube due to changes in cross-sectional area.
2. Velocities at Points X, Y, and Z:
   • Point X: Velocity is highest at the entrance (point X) where the cross-sectional area is largest, according to the principle of continuity.
   • Point Y (Throat): Velocity decreases at the throat (point Y) where the cross-sectional area is smallest. This is where the velocity is maximized due to the principle of conservation of mass and Bernoulli's principle.
   • Point Z: Velocity increases again after the throat (point Z) as the cross-sectional area expands, but it remains less than the velocity at point X.
3. Relationship:
   • At a particular discharge rate, the velocity at point X (entrance) is greater than the velocity at point Y (throat), and the velocity at point Y (throat) is greater than the velocity at point Z (exit).
   • Therefore, the correct relationship among velocities at points X, Y, and Z in a venturi tube is typically V1 > V2 > V3, where V1 represents velocity at point X, V2 at point Y, and V3 at point Z.

Conclusion:

Hence, the correct answer describing the relationships among velocities at points X, Y, and Z in a venturi tube for a particular discharge is V1 > V2 > V3. This sequence reflects the expected velocity distribution due to changes in cross-sectional area along the length of the venturi tube.