1.3. Stagnation Point

Now, there is something called a stagnation point. So, this is a very interesting point. So, a point of interest in the study of kinematics of fluid is the occurrence of the points where the fluid flow stops. So, as the name suggests stagnation, stagnation means something is stagnant or stopped.

A stagnation point is identified as a location in a fluid flow where the velocity of the fluid is zero. This occurs when the fluid encounters an obstruction, such as a solid object. The term 'stagnation' refers to this stop in flow. Understanding stagnation points is essential in fluid dynamics as they play a crucial role in various applications, including aerodynamics and hydraulic engineering.

Imagine placing a flat hand against a steady stream of water, like a water fountain. The point on your palm where the water initially touches and stops moving is a stagnation point. The water directly pressing against your hand has zero velocity because it cannot move past your hand.

So, one of the stagnation point could also be the plate for example, because there also the fluid flow stops right. So, when a stationary body is immersed in a fluid, the fluid is brought to stop at the nose of the bound nodes of the body, such a point, where the fluid flow is brought to the rest is known as stagnation point.

A stagnation point occurs when a fluid encounters a stationary object. The fluid particles adjacent to the object cannot move past it, and their velocity becomes zero. This is particularly important in understanding how the shape of an object affects the flow of a fluid around it. For example, on an airfoil (airplane wing), the stagnation point is where air hits the front edge; the airflow stops at this point before moving around the wing.

Consider a car driving into a strong wind. The point at the front of the car where the air hits is a stagnation point. The air in direct contact with the car has zero velocity relative to the car because it can't flow past it.

My one question to you is, what creates, what physical phenomenon helps or is related to the occurrence of the stagnation point? Suppose, there is a solid object which is kept fixed in the fluid flow when the fluid touches this body that point is called stagnation point. Why? Because last lecture, we read about a concept that was called no slip condition because of the no slip condition, the adjacent fluid velocity fluid particle, the velocity will also be zero because of no slip condition.

The no slip condition is a fundamental concept in fluid dynamics that states that fluid in direct contact with a solid surface has zero velocity relative to that surface. This condition is what creates stagnation points when fluid flows over or against a stationary object. The surrounding fluid particles match the velocity of the surface they contact, leading to the stagnation effect.

Think about butter melting on a hot pan. As the pan heats up, the butter closest to the surface stays in contact and essentially 'stops' moving. The part of the butter that is still sliding around is not in contact with the pan and thus can flow freely. This 'zero movement' at the contacted surface can be likened to stagnation in fluid dynamics.

Thus, a stagnation point is defined as a point in the flow field where the velocity is, this is the key point is identically zero. This means, that the all the components of the velocity V that is u, v, and w, are identical is zero at this stagnation point.

At a stagnation point, not only is the velocity of the fluid zero, but this applies to all velocity components (u, v, and w in three-dimensional flow). This complete stop of flow at that specific point allows for analysis of pressures and forces acting on the body. Understanding the pressure at these points is crucial for design considerations in fluid systems.

When designing a bridge, engineers need to consider the impact of the wind on the structure. The point where air stops before it hits the bridge is a stagnation point. Knowing where these points are helps engineers design for the forces acting on the bridge, ensuring safety and stability.

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