Contents
The laws of Physics Topics are used to explain everything from the smallest subatomic particles to the largest galaxies.
Fluid Pressure : Definition, Formula, Factors
Water is a liquid. When we pour some water on a table, it ‘flows’. Air is a gas (or rather a mixture of gases). Air flows from one place to another. Those substances which can flow easily are called fluids. All the liquids and gases are fluids. Water and air are the two most common fluids. We have already studied that solids exert pressure on a surface due to their weight. Fluids also have weight. So, fluids (liquids and gases) also exert pressure on the container in which they are enclosed. A fluid (liquid or gas) exerts pressure in all directions – even upwards ! We will now discuss buoyancy which is a property exhibited by fluids.
Buoyancy
When an object is placed in a liquid, the liquid exerts an ‘upward force’ on it. For example, when a piece of cork is held below the surface of water by applying the force of our thumb and then released, the cork immediately rises to the surface (see Figure). It appears as if some upward force is exerted by water on the cork which pushes it to the surface.
If we lift a stone lying at the bottom of a pond, it appears to be light as long as it is being lifted inside water. But as soon as the stone is lifted out of water into air, the same stone feels to be much heavier. This means that some upward force acts on the stone when it is immersed in water and makes it feel lighter. Let us take another example. While taking bath, we find that as long as the mug filled with water remains immersed in the bucket full of water, it appears to be light and hence easy to lift. But as soon as the mug filled with water is lifted out of the bucket of water, it feels much heavier. This observation also shows that as long as the mug filled with water is inside the water surface, some upward force acts on it which reduces its effective weight and makes it appear lighter. In general, whenever an object (or body) is immersed in water (or any other liquid), it appears to lose some weight and feels lighter.
From all the above examples, we conclude that the objects appear to be less heavy when submerged
in water than they are in air. The objects appear to be less heavy in water because the water exerts an
upward force on them. It is not only water which exerts an upward force on the objects immersed in it. In fact, every liquid exerts an upward force on the objects immersed in it. The tendency of a liquid to exert an upward force on an object placed in it, is called buoyancy. Even the gases exhibit the property of buoyancy. We will now discuss the buoyant force.
Buoyant Force
When an object is immersed in a liquid, it experiences an upward force. This upward force is called buoyant force. Thus, the upward force acting on an object immersed in a liquid is called buoyant force. It is due to the upward ‘buoyant force’ exerted by a liquid that the weight of an object appears to be less in the liquid than its actual weight in air. The upward force exerted by a liquid is also known as ‘upthrust’. In other words, the buoyant force is also known as upthrust. It is due to the upward force (‘buoyant force’ or ‘upthrust’) exerted by water that we are able to swim in water and ships float in water. If there were no upward force of water, we would not be able to swim, and the ships would also sink. It is the buoyant force which makes the heavy objects seem lighter in water. We will now discuss the cause of buoyant force.
Cause of Buoyant Force
In order to understand why liquids exert an upward buoyant force, let us consider a mug filled with water immersed in a bucket containing water as shown in Figure. Water exerts force on the sides of the mug as well as on its top and bottom (shown by arrows). The sideways forces exerted by water on the mug, being equal and opposite, cancel out. Now, there is a force of water acting on the top of the mug (which acts in the downward direction), and a force of water acting on the bottom of the mug (which acts in the upward direction) (see Figure).
It is known that the pressure exerted by a liquid increases with depth and acts in all directions (even upwards). Now, as the top A of the mug is at a lower depth in water, it experiences less force downwards. The bottom B of the mug is at a greater depth in water, so it experiences more force in the upward direction. Thus, there is a net force on the mug in the upward direction. The net upward force on the mug is equal to the difference in the upward force acting on its bottom and the downward force acting on its top. This net upward force acting on the mug is the buoyant force (which reduces the effective weight of mug and makes it feel lighter inside the water).
From this discussion we conclude that : As we lower an object into a liquid, the greater m St tidy gear upward pressure of liquid underneath it provides an upward force called the buoyant force (or upthrust).
We will now describe an experiment to study the magnitude of buoyant force acting on a body when the body is gradually dipped in a liquid like water.
Experiment to Study the Magnitude of Buoyant Force
The experiment to study the magnitude of buoyant force can be performed as follows :
1. We take a small metal cylinder C and suspend it from the hook of a spring balance B as shown in Figure. The reading of spring balance will give the weight of metal cylinder in air. We can see from Figure that the weight of metal cylinder in air is 150 grams. This is the real weight of the metal cylinder (because it has been taken in air).
2. Let us lower the cylinder attached to the spring balance in a container of water in such a way that only a small volume of the cylinder is immersed in water [see Figure]. We will find that the reading on spring balance decreases, it becomes 140 grams. This means that when a small part of the cylinder is immersed in water, its weight appears to decrease from 150 grams to 140 grams, and it becomes lighter.
3. We now lower the cylinder further down in water so that a large volume of ‘cylinder is immersed in water [see Figure]. We will find that the reading on spring balance decreases further, it becomes 130 grams. This means that when a large volume of cylinder is dipped in water, its weight decreases further to 130 grams and it becomes more lighter in water.
4. We again lower the cylinder further so that the cylinder gets fully immersed in water [see Figure]. We will find that the reading on spring balance decreases still further, it becomes 120 grams. This means that when the cylinder is fully immersed in water, its weight decreases further to 120 grams, and it becomes still more lighter in water.
5. Once the cylinder is fully immersed in water, then the maximum loss in the weight of cylinder takes place. Any further lowering of cylinder in water does not reduce the weight of cylinder. In the above experiment, the maximum loss in weight of cylinder on fully immersing in water is 150 – 120 = 30 grams. Now, even if we lower the fully immersed cylinder more and more in water, there will be no further loss in its weight.
From the above discussion we conclude that as more and more volume of an object is immersed in a liquid, the apparent weight of the object goes on decreasing and it seems to become more and more lighter. But once the object is completely immersed under the liquid, then further lowering it in liquid does not make it any more lighter. This means that the maximum loss in weight of an object takes place when it is fully immersed in a liquid.
We know that an object immersed in a liquid appears to lose weight and become lighter due to the upward buoyant force of the liquid. This means that as more and more volume of the object is immersed in a liquid, the upward buoyant force acting on it increases. But once the object is completely immersed in a liquid, then lowering it further in the liquid does not increase the buoyant force. This means that the maximum upward ‘buoyant force’ acts on an object when it is completely immersed in the liquid. We will now discuss the factors which affect the buoyant force.
Factors Affecting Buoyant Force
The magnitude of buoyant force acting on an object immersed in a liquid depends on two factors :
- volume of object immersed in the liquid, and
- density of the liquid.
Let us discuss these two factors in somewhat detail, one by one.
1. The buoyant force exerted by a liquid depends on the volume of the solid object immersed in the liquid
As the volume of solid object immersed inside the liquid increases, the upward ‘buoyant force’ also increases. And when the object is completely immersed in the liquid, the buoyant force becomes the maximum and remains constant. Please note that the magnitude of buoyant force acting on a solid object does not depend on the nature of the solid object. It depends only on its volume. For example, if two balls made of different metals having different weights but equal volumes are fully immersed in a liquid, they will experience an equal upward ‘buoyant force’ (and undergo an equal loss in weight). This is because both the balls displace equal weight of the liquid due to their equal volumes.
2. The buoyant force exerted by a liquid depends on the density of the liquid in which the object is immersed
The liquid having higher density exerts more upward buoyant force on an object than another liquid having lower density. Thus, as the density of liquid increases, the buoyant force exerted by it also increases. For example, sea-water has higher density than fresh water, therefore, sea-water will exert more buoyant force on an object immersed in it than the fresh water. It is easier to swim in sea-water because sea-water
exerts a greater buoyant force on the swimmer (due to its higher density). The fresh-water in a swimming pool, however, exerts a comparatively smaller buoyant force on the swimmer (due to its lower density than sea-water). Mercury is a liquid having very high density. So, mercury will exert a very great buoyant force on an object immersed in it. Even a very heavy material like an iron block floats in mercury because mercury exerts a very high buoyant force on iron block due to its very high density.
Before we go further and study Archimedes’ principle, we should know the meaning of the term ‘displaced liquid’. This is discussed below. Suppose we have a bucket filled with water upto the brim. Now, if we immerse an object into this bucket full of water, then the object will occupy some of the volume in the bucket which was earlier occupied by water. Due to this the object will ‘push out’ some of the water from the bucket. This ‘pushed out water’ is the ‘displaced water’. So, we can now say that when an object is immersed in a bucket filled with water, it displaces some of the water which overflows from the bucket. And when an object is completely immersed in water, then the volume of water displaced will be equal to the volume of the object itself.
Please note that water can flow out from a bucket on immersing an object in it only when the bucket is filled to the brim. If, however, we immerse an object in a bucket of water which is not filled to the brim, then the object will displace water due to which the level of water will rise in the bucket but no water will flow out. The Archimedes’ principle which we will study now gives a relationship between the buoyant force exerted by a liquid on an object and the weight of liquid displaced by it. Please note that the mass of water (or any other liquid) is expressed in kilograms (or grams) but the weight of water is a force and hence it should be expressed in the unit of force called ‘newton’ (N). The weight of 1 kilogram mass of water is about 10 newtons (or 10 N).