Question:
Figure shows the steady and incompressible flow of a fluid in the direction of 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 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?
Figure shows the steady and incompressible flow of a fluid in the direction of 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 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?
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?
Show Hint
When analyzing pipe flow sections, always check TEL/HGL behavior:
- Drop in pressure + velocity increase $\Rightarrow$ converging.
- Flat/parallel behavior $\Rightarrow$ constant area.
- Pressure recovery + velocity drop $\Rightarrow$ diverging.
Updated On: Aug 27, 2025
- Converging, Constant area, Diverging
- Diverging, Constant area, Converging
- Constant area, Constant area, Constant area
- Constant area, Converging, Diverging
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The Correct Option is A
Solution and Explanation
Step 1: Observe the figure.
The given figure shows a pipe carrying steady incompressible fluid. Between points A and D, the Total Energy Line (TEL) and Hydraulic Grade Line (HGL) are drawn. The slope of TEL and HGL reflects changes in velocity head and pressure head due to varying pipe geometry.
Step 2: From A to B.
The TEL and HGL show a steep drop between A and B. This indicates that velocity increases while pressure decreases. According to Bernoulli’s principle, such a rise in velocity occurs when the pipe converges. So, A–B is a converging section.
Step 3: From B to C.
Between B and C, the TEL and HGL remain nearly parallel and constant in slope. This suggests velocity and pressure are not changing significantly. Hence, the pipe cross-sectional area must be constant. So, B–C is a constant area section.
Step 4: From C to D.
Between C and D, the TEL and HGL rise relative to the flow direction, showing a reduction in velocity and recovery of pressure. This corresponds to a diverging section. So, C–D is a diverging section.
Step 5: Match with options.
Thus, the sequence is: \[ \text{A–B: Converging, B–C: Constant area, C–D: Diverging}. \] This matches option (A). Final Answer:
\[ \boxed{\text{Converging, Constant area, Diverging}} \]
The given figure shows a pipe carrying steady incompressible fluid. Between points A and D, the Total Energy Line (TEL) and Hydraulic Grade Line (HGL) are drawn. The slope of TEL and HGL reflects changes in velocity head and pressure head due to varying pipe geometry.
Step 2: From A to B.
The TEL and HGL show a steep drop between A and B. This indicates that velocity increases while pressure decreases. According to Bernoulli’s principle, such a rise in velocity occurs when the pipe converges. So, A–B is a converging section.
Step 3: From B to C.
Between B and C, the TEL and HGL remain nearly parallel and constant in slope. This suggests velocity and pressure are not changing significantly. Hence, the pipe cross-sectional area must be constant. So, B–C is a constant area section.
Step 4: From C to D.
Between C and D, the TEL and HGL rise relative to the flow direction, showing a reduction in velocity and recovery of pressure. This corresponds to a diverging section. So, C–D is a diverging section.
Step 5: Match with options.
Thus, the sequence is: \[ \text{A–B: Converging, B–C: Constant area, C–D: Diverging}. \] This matches option (A). Final Answer:
\[ \boxed{\text{Converging, Constant area, Diverging}} \]
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