Question

Match List-I with List-II

List-I (Formula)	List-II (Purpose)
(A) Kennedy	(I) Open channel flow
(B) Chezy	(II) Friction factor
(C) Darcy-Weisbach	(III) Design of open channels
(D) Manning's	(IV) Estimates on seepage loss in canal systems

• (A) - (II), (B) - (III), (C) - (IV), (D) - (I)
• (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
• (A) - (I), (B) - (IV), (C) - (II), (D) - (III)
• (A) - (IV), (B) - (I), (C) - (II), (D) - (III)

Hint:

To quickly solve this:
- Darcy-Weisbach is synonymous with pipe friction and the friction factor (C \(\rightarrow\) II).
- Manning's equation is the standard for the design of open channels (D \(\rightarrow\) III).
- Chezy's is the classic open channel flow equation (B \(\rightarrow\) I).
These three matches immediately point to Option 4.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Fluid flow through pipes and open channels is governed by various empirical and theoretical formulas.
These equations are used by engineers to design stable canal networks, estimate water losses, and calculate friction losses.

Step 2: Detailed Explanation:
Let us match the formulas in List-I with their primary purposes in List-II:
- (A) Kennedy's Formula: R.G. Kennedy developed a theory for designing stable, non-silting, non-scouring alluvial channels.
The critical velocity equation (\(V_0 = 0.55 D^{0.64}\)) is also historically used in irrigation engineering to evaluate canal performance and estimates on seepage loss in canal systems through design iterations.
Hence, (A) matches with (IV).
- (B) Chezy's Formula: Developed by Antoine de Chézy for calculating flow velocity in open channels:
\[ V = C \sqrt{R S} \]
This is a fundamental equation for open channel flow.
Hence, (B) matches with (I).
- (C) Darcy-Weisbach Equation: Used to calculate the head loss due to friction in pipe flow:
\[ h_f = \frac{f L V^2}{2 g D} \]
It is directly used to calculate and evaluate the dimensionless friction factor (\(f\)).
Hence, (C) matches with (II).
- (D) Manning's Formula: The most widely used empirical formula for uniform flow in open channels:
\[ V = \frac{1}{n} R^{2/3} S^{1/2} \]
It is extensively used in the design of open channels and canals.
Hence, (D) matches with (III).
This gives the correct sequence: (A)-(IV), (B)-(I), (C)-(II), (D)-(III).

Step 3: Final Answer:
The correct option is (D).