A viscous fluid is flowing through a cylindrical tube. The velocity distribution of the fluid is best represented by the diagram

Options

A.
B.
C.
D. None of these

Explanation

To solve the problem of determining the velocity distribution of a viscous fluid flowing through a cylindrical tube, we can follow these steps:

### Step 1: Understand the Flow Characteristics
In a cylindrical tube, the flow of a viscous fluid is characterized by a velocity gradient. The fluid moves in layers (or laminae), and due to the viscosity, the velocity of the fluid is not uniform across the cross-section of the tube.

**Hint:** Remember that in viscous flow, layers of fluid close to the wall move slower than those in the center.

### Step 2: Identify the Velocity Profile
The velocity of the fluid is maximum at the center of the tube and decreases as you move towards the walls. This is because the fluid in contact with the wall experiences a no-slip condition (velocity = 0 at the wall).

**Hint:** Visualize the tube and think about how the fluid layers interact with the wall.

### Step 3: Sketch the Velocity Distribution
You can sketch a graph where the x-axis represents the distance from the center of the tube and the y-axis represents the velocity of the fluid. The graph will show a parabolic shape, peaking at the center and tapering off to zero at the walls.

**Hint:** The shape of the graph is crucial; it should reflect that the velocity decreases smoothly from the center to the edges.

### Step 4: Identify the Correct Option
Based on the description and the sketch of the velocity distribution, you can identify the correct option from the given choices. The correct representation will show a maximum velocity at the center and a gradual decrease towards the walls.

**Hint:** Look for a graph that has a peak at the center and approaches zero at the edges.

### Conclusion
The velocity distribution of a viscous fluid flowing through a cylindrical tube is best represented by a parabolic curve, indicating that the velocity is highest at the center and decreases towards the walls of the tube. The correct option is C.