Question

Figure shows the steady and incompressible flow of a fluid in the direction of the arrow from section A to section D. Three pipe connectors are to be placed between sections at A and D having Total Energy Line (TEL) and Hydraulic Grade Line (HGL) as depicted in the figure. Consider, \( g \), \( P \), \( Q \), \( V \), \( \gamma \), and \( Z \) denote gravitational acceleration, pressure, volume flow rate, velocity, specific weight, and elevation of the centerline of the pipe connectors from the datum, respectively. Which one of the following options, in sequence, indicates the correct nature of connectors between sections A and B, B and C, and C and D in the direction of flow?

• A. Converging, Constant area, Diverging
• B. Diverging, Constant area, Converging
• C. Constant area, Constant area, Constant area
• D. Constant area, Converging, Diverging

Hint:

When analyzing fluid flow through pipes, always consider how the energy lines (TEL and HGL) behave. Converging sections lead to increased velocity, constant area sections maintain steady conditions, and diverging sections lead to a decrease in velocity.

Answer 1

The Correct Option is A

In this problem, the fluid flow is steady and incompressible. The Total Energy Line (TEL) and Hydraulic Grade Line (HGL) are used to understand the nature of flow through the pipe sections.
- Section A to B: From the figure, we see that the hydraulic grade line (HGL) and total energy line (TEL) both decrease, and the velocity also decreases. This implies that the area is converging from section A to section B. In a converging section, the cross-sectional area decreases, leading to an increase in velocity and a decrease in pressure.
- Section B to C: Between sections B and C, the area remains constant as the total energy line (TEL) and the hydraulic grade line (HGL) both remain nearly unchanged. Thus, section B to C is a constant area section. In this case, the flow is steady, and the velocity and pressure do not change drastically.
- Section C to D: From section C to section D, the TEL and HGL again show a noticeable decrease, indicating that the area is diverging. A diverging section generally results in a decrease in velocity and an increase in pressure. This can be inferred by the increase in pressure head and the drop in velocity head as shown by the given diagram.
Thus, the correct sequence for the nature of the pipe connectors between sections A and B, B and C, and C and D is:
\[ {Converging, Constant area, Diverging} \]