Question

Match List-I with List-II
List-I & List-II
(A). Steady flow & (I). Velocity changes along the length
(B). Uniform flow & (II). Velocity and depth of flow changes with time
(C). Non-uniform flow & (III). Velocity and depth of flow remains constant with time
(D). Unsteady flow & (IV). Velocity remains constant along the length

Choose the correct answer from the options given below:

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

Hint:

To remember flow classifications:
- Steady vs. Unsteady \(\rightarrow\) Variation with respect to Time (\(t\)).
- Uniform vs. Non-uniform \(\rightarrow\) Variation with respect to Space/Length (\(s\)).

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Fluid flows are classified based on how flow parameters (such as velocity, depth, and discharge) vary with respect to time and space (position along the channel).

Step 2: Detailed Explanation:
Let us define each flow type and match them to the descriptions in List-II:
- (A) Steady Flow \(\rightarrow\) (III) Velocity and depth of flow remains constant with time:
By definition, steady flow occurs when the fluid properties (velocity, pressure, cross-section, depth) at any point do not change over time.
Mathematically, \(\frac{\partial v}{\partial t} = 0\) and \(\frac{\partial y}{\partial t} = 0\).
- (B) Uniform Flow \(\rightarrow\) (IV) Velocity remains constant along the length:
Uniform flow occurs when the velocity and depth of flow remain identical at every cross-section along the channel length at any given instant.
Mathematically, \(\frac{\partial v}{\partial s} = 0\).
- (C) Non-uniform Flow \(\rightarrow\) (I) Velocity changes along the length:
Also known as varied flow, it occurs when flow parameters (such as velocity or depth) vary from one cross-section to another along the channel length.
- (D) Unsteady Flow \(\rightarrow\) (II) Velocity and depth of flow changes with time:
Unsteady flow occurs when flow parameters at any given point change over time.
Mathematically, \(\frac{\partial v}{\partial t} \neq 0\).
This matches the sequence: (A) - (III), (B) - (IV), (C) - (I), (D) - (II), which corresponds to Option (D).

Step 3: Final Answer:
The correct matching is represented by Option (D).