Definition and Formula
Definition of pressure: Liquid pressure is the type of pressure that happens inside a liquid. It refers to how much force is being applied by the liquid on each unit of area. This force comes from the weight of the liquid and how it presses on the surfaces around it. The pressure can push in all directions, not just downwards.
Basic formula (P = F/A): Pressure can be calculated using a simple formula: Pressure (P) equals Force (F) divided by Area (A). This means that if a large force is applied over a small area, the pressure is high. For example, if you press your finger against a balloon, the small contact area causes high pressure and may pop it.
Liquid pressure formula: To find out how much pressure a liquid makes at a certain depth, we use this formula: P = hρg. This special formula helps us understand how pressure increases when you go deeper into a liquid.
Formula terms explained:
- h (depth): This means how deep you are in the liquid. The deeper you go, the more liquid is above you, which makes more pressure.
- ρ (rho, density): This stands for how heavy or thick the liquid is. A thick liquid like honey has more density than a light liquid like water.
- g (gravity): This is the strength of gravity pulling the liquid down. On Earth, it’s about 9.8 m/s². Gravity causes the weight of the liquid, which leads to pressure.
Factors Affecting Liquid Pressure
Depth (h): The more you go down into a liquid, the more pressure you feel. That’s because there’s more liquid above you, and all that liquid has weight. The weight pushes down and increases the pressure as you go deeper.
Depth experiments: If you punch small holes at different heights in a bottle full of water, you will see water coming out faster and farther from the lower holes. This shows that pressure increases as the depth increases.
Density (ρ): Liquids that are denser create more pressure. This is because dense liquids have more mass packed into the same space. At the same depth, a heavy liquid like syrup will exert more pressure than a light one like alcohol.
Density comparison experiments: By filling three containers with alcohol, water, and glycerine, and using the same depth, we can measure the pressure and see that glycerine (the densest) produces the most pressure. This proves that higher density equals higher pressure.
Gravitational acceleration (g): Gravity helps create pressure because it pulls the liquid downward. The stronger the gravity, the more the liquid weighs, and the more pressure it creates.
Gravity variations: If gravity were to increase, like on Jupiter, the pressure in the liquid would be higher. If gravity were weaker, like on the Moon, liquid pressure would be less, even at the same depth and density.
Direction and Behavior of Pressure
Omnidirectional pressure: Pressure in a liquid doesn’t just push down. It pushes in every direction — up, down, and sideways. This is why when you’re underwater, you feel pressure all around you, not just from the top.
Demonstrating direction: If you take a can and punch holes on all sides, then fill it with water, you’ll see water coming out in all directions. This experiment shows that liquid pressure acts in every direction equally at a certain depth.
Calculating Pressure
Using P = hρg: To calculate how much pressure there is at a certain depth, you simply multiply the depth of the liquid by its density and by the gravitational pull. For example, if you know the depth is 2 m, the density is 1000 kg/m³, and g is 9.8 m/s², then P = 2 × 1000 × 9.8 = 19,600 Pa.
Gauge vs absolute pressure: Gauge pressure is the pressure from the liquid only. But in real life, there’s also air pressure above the liquid. To find the total or absolute pressure, you have to add the air (atmospheric) pressure to the liquid’s pressure.
Units of Pressure
Standard unit – Pascal: The most common unit for measuring pressure is the Pascal (Pa). One Pascal is the same as one newton of force acting on one square metre (1 Pa = 1 N/m²).
Other units: There are also other ways to measure pressure:
- N/m²: Another name for Pascal.
- Millibar (mbar): Often used for weather reports.
- mmHg and cmHg: These are used in medical tools like blood pressure monitors.
- mH₂O: Used to describe how high water can be pushed up by the pressure.
Applications
Water tanks in buildings: Water tanks are often placed at high places in buildings because water flows from high to low places due to gravity. The height helps create strong enough pressure to make water reach all the taps in the building.
Intravenous fluid bags: In hospitals, IV bags are hung high above the patient’s body. This height creates pressure that helps the fluid flow gently into the patient’s veins without needing a pump.
Dams and wall thickness: The deeper the water in a dam, the higher the pressure on the walls. That’s why dam walls are built thicker at the bottom — they need to be strong enough to handle the greater pressure from the deep water.
Siphons for liquid transfer: A siphon is a simple tool that lets you move a liquid from a higher container to a lower one. It works because pressure pushes the liquid through the tube from the higher side to the lower side using gravity.
Pressure Demonstration Experiments
Depth-pressure experiments: If you put a manometer (a tool that measures pressure) into water at different depths, you’ll see that the readings go up as you go deeper. This proves that liquid pressure increases with depth in a straight-line pattern.
Density-pressure experiments: You can also use manometers filled with different liquids to compare how density affects pressure. The denser the liquid inside the manometer, the higher the pressure it will show at the same depth.