Consider the figure of a fountain with four holes given below : Which one of the holes in the fountain will throw the water farthest ?

1. Basics of Pressure in Fluids (basic)

To understand how fluids behave, we must start with the fundamental definition of pressure. In physics, pressure is not just a "push"; it is defined as the force acting per unit area. Mathematically, we express this as: Pressure = Force / Area. Because area is in the denominator, a small area results in much higher pressure for the same amount of force. This is why a sharp needle pierces skin easily while a blunt finger does not. The SI unit for pressure is the Pascal (Pa), which is equal to one newton per square metre (N/m²) Science, Class VIII, Chapter 6, p.82.

When we apply this concept to fluids (a term that includes both liquids and gases), a unique characteristic emerges: fluids exert pressure in all directions. Unlike a solid book resting on a table that only exerts pressure downwards, a liquid exerts pressure against the bottom and the side walls of its container Science, Class VIII, Chapter 6, p.84. This is why if you poke a hole in the side of a plastic bottle filled with water, the water squirts out horizontally—the fluid is pushing outward against the walls.

The most vital rule to remember for this topic is that fluid pressure increases with depth. Imagine a column of water: the layer at the bottom has to support the entire weight of the water stacked above it. As you move deeper, the "weight" of the fluid column increases, leading to higher pressure Science, Class VIII, Chapter 6, p.94. This is known as hydrostatic pressure. In practical terms, this means that water will exit a hole near the bottom of a tank with much more force and speed than it would from a hole near the top.

Sources: Science, Class VIII, Chapter 6: Pressure, Winds, Storms, and Cyclones, p.82; Science, Class VIII, Chapter 6: Pressure, Winds, Storms, and Cyclones, p.84; Science, Class VIII, Chapter 6: Pressure, Winds, Storms, and Cyclones, p.94

2. Hydrostatic Pressure and Depth (basic)

In our previous hop, we understood that Pressure is defined as the force acting per unit area (P = F/A) Science, Class VIII, Pressure, Winds, Storms, and Cyclones, p.94. When we apply this to liquids, things get interesting. Unlike a solid block that primarily exerts pressure downwards due to its weight, a liquid is fluid—it flows and takes the shape of its container. Because liquid particles are nearly incompressible Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.148, they transmit force in all directions: against the bottom, the sides, and even upwards Science, Class VIII, Pressure, Winds, Storms, and Cyclones, p.85.

The most critical rule of hydrostatic pressure (pressure in a liquid at rest) is that it increases with depth. Imagine a column of water: a point at the bottom must support the weight of all the water stacked above it. The deeper you go, the heavier that column becomes, and the greater the pressure exerted. This is why deep-sea submarines must have incredibly thick hulls, and why you feel a "squeeze" in your ears when you dive to the bottom of a swimming pool.

This pressure manifests as speed when the liquid is allowed to escape. According to Torricelli’s Law, the speed (v) at which water spurts out of a hole depends on the depth (h) of that hole below the surface, following the formula v = √(2gh). Therefore, a hole near the bottom of a tank shoots water out much faster than a hole near the top. However, horizontal range (how far the water travels before hitting the ground) is a balancing act between speed and time to fall. While the bottom hole has the most speed, it has the least time to travel before hitting the floor. Conversely, the top hole has plenty of time to fall but very little speed. Mathematically, the "sweet spot" that yields the maximum horizontal range is exactly at the mid-depth of the liquid column.

Sources: Science, Class VIII, Pressure, Winds, Storms, and Cyclones, p.84-85, 94; Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.148

3. Atmospheric Pressure and its Measurement (intermediate)

Imagine you are standing at the bottom of a vast ocean, but instead of water, you are surrounded by a sea of air. Although air seems weightless, it is composed of various gases that possess mass and are pulled toward the Earth by gravity. This results in Atmospheric Pressure, defined as the weight of a column of air contained in a unit area extending from mean sea level to the very top of the atmosphere NCERT Class XI, Fundamentals of Physical Geography, p.76. At sea level, this pressure is quite substantial—averaging about 1,013.2 millibars or roughly 1,034 grams per square centimeter PMF IAS, Pressure Systems and Wind System, p.304. We don't feel crushed because the internal pressure of our bodies balances this external force.

One of the most critical features of atmospheric pressure is how it changes with altitude. As you ascend a mountain or fly in a plane, the pressure decreases. This happens for two primary reasons: first, there is simply less air above you to press down; and second, gravity is strongest near the surface, making the air denser at lower levels GC Leong, Weather, p.117. This is why mountaineers often feel breathless—the air becomes "thin" or rarefied, meaning there are fewer oxygen molecules in every breath you take NCERT Class XI, Fundamentals of Physical Geography, p.76.

To measure this invisible force, we use instruments called barometers. The traditional mercury barometer, invented by Torricelli in 1643, uses a column of liquid mercury in a glass tube; the height of the mercury rises or falls depending on the weight of the atmosphere pressing down on it GC Leong, Weather, p.116. However, because carrying a tube of liquid mercury is impractical for field research, scientists often use an aneroid barometer. This device contains a small metal box with a partial vacuum inside. Since there is no air inside to push back, the box's lid is extremely sensitive to external pressure changes, moving inward when pressure rises and outward when it falls GC Leong, Weather, p.117.

Sources: Fundamentals of Physical Geography, NCERT Class XI, Atmospheric Circulation and Weather Systems, p.76; Certificate Physical and Human Geography, GC Leong, Weather, p.116-117; Physical Geography by PMF IAS, Pressure Systems and Wind System, p.304

4. Buoyancy and Archimedes' Principle (intermediate)

Have you ever noticed how you feel much lighter when you're in a swimming pool, or how it’s surprisingly difficult to push an empty plastic bottle deep under the water? This isn't your imagination; it's a fundamental property of fluids. When any object is placed in a liquid, the liquid exerts an upward force on it. This force is known as upthrust or the buoyant force Science, Class VIII, Exploring Forces, p.77. This force acts in the opposite direction to gravity, which is why objects appear to lose weight when submerged.

To understand exactly how much force this is, we look to Archimedes' Principle. The great Greek scientist Archimedes discovered that the upward buoyant force acting on an object (whether fully or partially submerged) is exactly equal to the weight of the liquid the object displaces Science, Class VIII, Exploring Forces, p.76. If you drop a stone into a full glass of water, the water that spills over represents the "displaced liquid." If you weigh that spilled water, you know the exact magnitude of the upward force pushing on the stone.

Whether an object sinks or floats depends on the battle between its own weight (pulling it down) and the buoyant force (pushing it up). We can summarize these conditions as follows:

This explains why a solid iron nail sinks, while a massive iron ship floats. The ship is designed with a hollow hull, allowing it to displace a huge volume—and thus a huge weight—of water. Once the weight of the displaced water equals the weight of the ship, it floats Science, Class VIII, Exploring Forces, p.76. In terms of density, an object will float if it is less dense than the liquid it is in, which is why oil (less dense) floats on top of water Science, Class VIII, The Amazing World of Solutes, Solvents, and Solutions, p.150.

Sources: Science, Class VIII (NCERT Revised ed 2025), Exploring Forces, p.76; Science, Class VIII (NCERT Revised ed 2025), Exploring Forces, p.77; Science, Class VIII (NCERT Revised ed 2025), The Amazing World of Solutes, Solvents, and Solutions, p.150

5. Bernoulli's Principle and Fluid Dynamics (intermediate)

At the heart of fluid dynamics lies Bernoulli’s Principle, which reveals a counter-intuitive truth: within a horizontal flow of a fluid, points of higher fluid speed will have less pressure than points of slower fluid speed Physical Geography by PMF IAS, Tropical Cyclones, p.358. This principle explains everything from how airplane wings generate lift to why high winds can rip roofs off houses. When fluid (like air or water) speeds up, its internal pressure drops because some of its energy is converted from "pressure energy" into "kinetic energy" (motion).

A practical application of these energy conversions is seen in hydrostatic pressure. In a container of water, the pressure isn't uniform; it increases with depth because of the weight of the water column above. If you poke a hole in the side of a tank, this pressure forces the water out. According to Torricelli’s Law (a specific application of Bernoulli’s), the speed of the water jet (v) depends on the depth (h) of the hole below the surface, calculated as v = √(2gh). Thus, a hole at the bottom of a tank will always have a higher exit speed than a hole at the top Science, Class VIII, Pressure, Winds, Storms, and Cyclones, p.85.

However, the horizontal range (how far the water lands from the tank) depends on two competing factors: the speed of the exit and the time the water has to fall before hitting the ground. While the bottom hole has the highest speed, it has the shortest time to travel horizontally before hitting the floor. Conversely, the top hole has plenty of time to fall but very little exit speed. This leads to a fascinating result: the water jet from the middle hole (at half the total height of the water column) typically reaches the farthest horizontal distance because it achieves the perfect balance between velocity and falling time.

Sources: Physical Geography by PMF IAS, Tropical Cyclones, p.358; Science, Class VIII, Pressure, Winds, Storms, and Cyclones, p.85

6. Torricelli's Law: Speed of Efflux (exam-level)

When we talk about Torricelli’s Law, we are exploring the physics of how liquids escape a container—a process known as efflux. Imagine a large tank filled with water. If you poke a hole in the side, the water doesn't just trickle out; it spurts out with a specific velocity. This happens because liquids exert pressure not just on the bottom of a container, but in all directions, including the side walls Science, Class VIII, Chapter 6, p.85. This pressure is fundamentally driven by gravity and the weight of the water column above the hole.

The core principle of Torricelli’s Law is strikingly simple: the speed of efflux (v) from a hole at a depth h below the free surface is exactly the same as the speed a solid object would acquire if it were dropped from the same height h under gravity. Mathematically, this is expressed as v = √(2gh). This tells us a crucial fact: the deeper the hole (the larger the value of h), the faster the water will exit. This is why a water tank is placed high on a roof—to maximize the vertical distance between the tank's surface and your tap, thereby increasing the pressure and flow speed Science, Class VIII, Chapter 6, p.95.

However, an interesting phenomenon occurs when we consider the horizontal range (R)—how far the water jet travels before hitting the ground. While a hole at the very bottom has the highest exit speed, the water has almost no time to travel horizontally before it hits the floor. Conversely, a hole near the top has a long time to fall but exits very slowly. To achieve the maximum horizontal range, there must be a balance. Using the kinematics of projectile motion, we find that the jet reaches its furthest point when the hole is positioned exactly at the mid-depth of the liquid column (h = H/2, where H is the total height of the water).

Sources: Science, Class VIII (NCERT 2025), Chapter 6: Pressure, Winds, Storms, and Cyclones, p.85; Science, Class VIII (NCERT 2025), Chapter 6: Pressure, Winds, Storms, and Cyclones, p.95

7. Horizontal Range of a Liquid Jet (exam-level)

When we poke a hole in a container filled with liquid, the resulting stream is called a liquid jet. The physics behind how far this jet travels involves a fascinating trade-off between pressure and time. As we understand from fundamental principles, liquid pressure increases with depth because of the weight of the liquid column above. This is why a water tank placed at a greater height 'H' provides more pressure at the ground floor Science, Class VIII. NCERT (Revised ed 2025), Chapter 6, p. 95.

According to Torricelli’s Law, the speed (v) at which water exits a hole at a depth h below the free surface is given by the formula v = √(2gh). This means the deeper the hole, the faster the water shoots out. However, once the water leaves the hole, it becomes a projectile. The time of flight (t)—how long it stays in the air—depends on the vertical distance from the hole to the ground. If the total height of the liquid is H, the distance from the hole to the ground is (H - h). Using the equations of motion, the time it takes to fall is t = √[2(H-h)/g].

The Horizontal Range (R) is the product of the horizontal exit speed and the time of flight: R = v × t. When you multiply these two square roots, the 'g' (acceleration due to gravity) cancels out, leaving us with the elegant formula R = 2√[h(H - h)]. This mathematical relationship reveals a beautiful symmetry: a hole at depth h from the top will have the exact same range as a hole at height h from the bottom.

Sources: Science, Class VIII. NCERT (Revised ed 2025), Chapter 6: Pressure, Winds, Storms, and Cyclones, p.85, 95

8. Solving the Original PYQ (exam-level)

This question perfectly illustrates the interplay between hydrostatic pressure and projectile motion. As you learned in your building blocks, the pressure of a liquid increases with depth, a concept detailed in Science, Class VIII, NCERT (Revised ed 2025). This pressure translates into exit velocity via Torricelli’s law: the deeper the hole from the surface, the faster the water shoots out. However, the horizontal distance (range) the water travels isn't just about speed; it also depends on the time of flight, which is determined by how high the hole is from the ground.

To arrive at the correct answer, you must find the "sweet spot" where speed and height are perfectly balanced. A hole at the very bottom has the maximum exit speed but hits the ground almost immediately because it has no height to fall through. Conversely, a hole at the very top has the most time to fall but exits with very little speed. Mathematically, the maximum range is achieved when the hole is located at the mid-depth of the water column. In the provided figure, Hole 2 is positioned closest to this central point, providing the optimal combination of velocity and falling time to throw the water the farthest.

UPSC often includes Option (A) 4 as a classic trap because students intuitively associate "highest pressure" with "greatest distance," overlooking the lack of falling time. Similarly, Option (D) 1 traps those who focus only on the height of the fountain. By selecting (C) 2, you demonstrate a nuanced understanding of how competing physical variables—speed and time—interact to create a maximum outcome at the midpoint.