Flow over a cylinder: Variation in pressure and velocity

When an ideal fluid flows over a cylinder, there are certain points of interest that are important to consider. One such point is the front stagnation point, which is the point on the cylinder where the fluid flow velocity is zero. In this context, the correct answer to the given question is option 'B', which states that the velocity first decreases and then increases.

Explanation:

The flow over a cylinder can be analyzed using the Bernoulli's equation, which relates the pressure, velocity, and elevation of a fluid in a steady flow. Based on the Bernoulli's equation and the flow pattern over a cylinder, the following observations can be made:

1. Pressure distribution:
At the front stagnation point, the pressure is maximum, which is also known as stagnation pressure. As the fluid flows around the cylinder, the pressure gradually decreases due to the increase in velocity. At the rear stagnation point, the pressure is minimum, which is also known as dynamic pressure.

2. Velocity distribution:
At the front stagnation point, the velocity is zero, and as the fluid flows around the cylinder, the velocity increases due to the decrease in pressure. The maximum velocity is reached at a point known as the separation point, beyond which the flow becomes turbulent and unpredictable.

3. Variation in pressure and velocity:
Based on the above observations, it can be concluded that the velocity first decreases and then increases as the fluid flows over a cylinder. This is because the pressure decreases as the fluid flows from the front stagnation point to the separation point, which leads to an increase in velocity. However, beyond the separation point, the flow becomes turbulent and unpredictable, and the velocity may vary in different directions.

Conclusion:

In summary, the flow over a cylinder is a complex phenomenon that involves the interplay between pressure and velocity. While the pressure decreases as the fluid flows around the cylinder, the velocity first decreases and then increases due to the Bernoulli's equation. Therefore, the correct answer to the given question is option 'B'.