1.3. Pressure is always perpendicular to the surface

One of the other important feature of pressure is that pressure is always perpendicular to the surface, this is very important as you can see, if this is a surface we have a perpendicular like this, on this surface like this, on this surface like this. Here we have already indicated by the red thick red arrows here.

Pressure acts perpendicular to any surface it touches. This means that if you have a flat surface, the force exerted by the fluid on that surface will be directed straight out from the surface and not at an angle. This characteristic of pressure is crucial in fluid mechanics and helps explain how forces are applied by fluids to surfaces.

Imagine a basketball being pushed against a wall. The force from the basketball is directed straight outward, just like how pressure acts on a surface. If you were to measure the force, you'd feel it pushing straight out, not sideways. Similarly, pressure pushes perpendicular to surfaces in fluids.

And the pressure does depend only on depth we are going to see that will do some basic derivation later in this lecture, where you will see that the dependence of pressure is only on depth is very important to note.

Pressure in a fluid increases with the depth of the fluid. This means that if you go deeper into a body of water, the pressure felt increases due to the weight of the water above. This relationship is important because it helps predict how much pressure will be exerted at any specific depth in a fluid.

Think of scuba diving again. As a diver descends from the surface into the water, they feel more pressure on their bodies. This is because each layer of water above them adds to the total weight and pressure. For example, if you swim down to 10 meters, you feel more pressure than when you're at 5 meters due to the additional water above.

See, this is one of the animated examples which everybody of you must have encountered in your real life. So, there is a tap and this is a tank with some holes in it or some stopper valve. The valves are here, here, and here. So, we start filling the water. Let us suppose water gets filled. If we open this one this valve, you see the water trajectory is going to be something like this. Similarly, the one above it will have a trajectory like this. The third one will have another trajectory like this, what does it say the distance that each one of them is covering is decreasing as the valve is going up.

When water is released from different holes at varying depths in a tank, the trajectories of the water will differ. The deeper the hole, the farther the water will travel because the pressure at greater depths is higher, resulting in a higher velocity for the water exiting the hole. This phenomenon illustrates how pressure varies with depth and influences fluid speed and direction.

Consider a water fountain with multiple outlets at different heights. The water that comes out from the lowest outlet shoots the furthest because it has the highest pressure behind it, pushing it out with more force than the water from higher outlets, which has less pressure.

Now, some definitions and applications, in fluid statics as we have seen there is no relative motion between the adjacent fluid layers, therefore, the shear stress is 0 as we have already seen this in our previous lecture. So, what can be acting on the fluid surface? So, only pressure can be acting in that case on the fluid surface there is no shear only pressure forces.

In fluid statics (the study of fluids at rest), the only force acting on a stationary fluid is pressure. Since there is no motion between the layers of fluid, shear stress, which typically arises from movement, is absent. This leads to significant implications for how we analyze forces acting within fluids and their interactions with surfaces.

Think of a still lake. The water surface is calm and not moving. The only forces acting on the water at that moment are the pressures from the water above it pushing down. If you were to place a rock in the water, the pressure would change, but the layers would remain still in relation to one another, illustrating the absence of shear stress.

Gravity force acts on the fluid and that is called the body force.

The gravitational force must be considered in fluid mechanics because it acts downwards on the fluid, influencing the pressure experienced at different depths. This gravitational force is referred to as a body force since it affects the entire mass of the fluid, rather than just the surface.

When you hold a gallon of water, you feel its weight because gravity is acting on that mass. In a larger body of water, like an ocean, the same principle applies; the weight of the water above any given point increases as you go deeper due to gravity, which explains why pressure increases with depth.

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