Streamline motion is that motion in which there is-

Options

A. only longitudinal velocity gradient
B. only radial velocity gradient
C. longitudinal as well as radial velocity gradient
D. neither longitudinal nor radial velocity gradient

Answer

To solve the question regarding streamline motion, we need to analyze the characteristics of such motion in fluid dynamics. Here’s a step-by-step solution:

### Step 1: Understand Streamline Motion
Streamline motion refers to the flow of fluid in such a way that the fluid particles follow smooth paths, known as streamlines. In this type of motion, the velocity of the fluid particles at any given point is constant over time.

### Step 2: Identify Velocity Gradients
In streamline motion, we can have different types of velocity gradients:
- **Longitudinal Velocity Gradient**: This occurs along the direction of the flow (longitudinal direction).
- **Radial Velocity Gradient**: This occurs perpendicular to the direction of flow (radial direction).

### Step 3: Analyze the Given Options
The question provides four options regarding the presence of velocity gradients in streamline motion:
1. Only longitudinal velocity gradient
2. Only radial velocity gradient
3. Longitudinal as well as radial velocity gradient
4. Neither longitudinal nor radial velocity gradient

### Step 4: Apply the Concept of Continuity
According to the principle of continuity in fluid dynamics, the product of cross-sectional area and velocity at one point must equal the product at another point (A1V1 = A2V2). If the cross-sectional area decreases, the velocity must increase.

### Step 5: Conclusion
In streamline motion, there is a longitudinal velocity gradient because the velocity changes along the direction of flow (as seen in the funnel example). However, there is no radial velocity gradient since the particles do not cross each other's paths. Therefore, the correct answer is:
**Only longitudinal velocity gradient.**

### Final Answer
The correct option is **Option A: Only longitudinal velocity gradient.**

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