Question

If \( V \) is the velocity of fluid flow, \( V_1 \) and \( V_2 \) are velocity at inlet and outlet of the pipe, respectively, and \( k \) is the value of the coefficient depending on the fittings, then which of the following options has the correct match of case and loss of head?

• A. (i) – (b), (ii) – (c), (iii) – (d), (iv) – (a)
• B. (i) – (c), (ii) – (d), (iii) – (b), (iv) – (a)
• C. (i) – (a), (ii) – (c), (iii) – (b), (iv) – (d)
• D. (i) – (b), (ii) – (c), (iii) – (a), (iv) – (d)

Hint:

Understanding the head loss in pipes is important for designing efficient fluid systems. Different cases like sudden enlargement, pipe fittings, and entrances have different formulas for calculating head loss.

Answer 1

The Correct Option is C

The correct match of head loss and cases are: 
- (i) Sudden enlargement → \( \frac{V_1^2}{2g} \) 
- (ii) Entrance of the pipe → \( \frac{V_2^2}{2g} \) 
- (iii) Exit of the pipe → \( 0.5 \frac{V_2^2}{2g} \) 
- (iv) Pipe fittings → \( k \frac{V_2^2}{2g} \)