Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The Total Energy Line (TEL) in open channel or pipe flow is sum of pressure head, elevation head and velocity head of flowing fluid in respect to a reference line. Reason R: The Hydraulic Grade Line (HGL) under same conditions is obtained by subtracting velocity head from total energy line. In the light of the above statements, choose the most appropriate answer from the options given below

• A. Both A and R are correct and R is the correct explanation of A
• B. Both A and R are correct but R is NOT the correct explanation of A
• C. A is correct but R is not correct
• D. A is not correct but R is correct

Hint:

Important relations: \[ \boxed{ TEL = \frac{P}{\gamma} + \frac{V^2}{2g} + z } \] \[ \boxed{ HGL = \frac{P}{\gamma} + z } \] \[ \boxed{ TEL = HGL + \frac{V^2}{2g} } \]

Answer 1

The Correct Option is B

Concept: In fluid mechanics:
• Total Energy Line (TEL) represents total mechanical energy per unit weight of fluid.
• Hydraulic Grade Line (HGL) represents piezometric head. The Bernoulli equation forms the basis of these concepts.

Step 1: Understanding Total Energy Line (TEL). The total energy head of flowing fluid is: \[ \boxed{ \frac{P}{\gamma} + \frac{V^2}{2g} + z } \] where:
• \(\frac{P}{\gamma}\) = pressure head
• \(\frac{V^2}{2g}\) = velocity head
• \(z\) = elevation head This total head is represented graphically by: \[ \boxed{ \text{Total Energy Line (TEL)} } \] Thus Assertion A is correct.

Step 2: Understanding Hydraulic Grade Line (HGL). Hydraulic Grade Line includes: \[ \boxed{ \frac{P}{\gamma} + z } \] It excludes velocity head. Therefore: \[ \text{HGL} = \text{TEL} - \frac{V^2}{2g} \] Hence: \[ \boxed{ \text{Reason R is correct} } \]

Step 3: Analyzing whether Reason explains Assertion. Reason R gives relation between:
• TEL
• HGL But it does not explain why TEL consists of pressure, elevation and velocity heads. Therefore:
• Assertion A is true
• Reason R is also true
• But R is not the correct explanation of A

Step 4: Selecting the correct option. Hence the correct answer is: \[ \boxed{ (B) } \]

Step 5: Checking all options carefully. Option (A): Incorrect because R does not explain A. \[ \boxed{ \text{Option (A) is incorrect} } \] Option (B): Correct. \[ \boxed{ \text{Option (B) is correct} } \] Option (C): Incorrect because R is also true. \[ \boxed{ \text{Option (C) is incorrect} } \] Option (D): Incorrect because A is true. \[ \boxed{ \text{Option (D) is incorrect} } \] Final Conclusion: Both Assertion and Reason are true, but Reason is not the correct explanation of Assertion. Hence the correct answer is: \[ \boxed{ (B) } \]