Liquid pressure increases with depth because the liquid above a point has weight. The deeper the point, the more liquid sits above it, so the pressure is greater. A full answer also says that pressure acts equally in all directions at a point.
This lesson builds on calculating liquid pressure. It turns the equation into the written reasoning that exam questions ask for.
What makes a good explanation?
A good explanation is a short chain of linked statements. For depth, the chain is:
- A liquid has weight because of gravity.
- The pressure at a point is caused by the weight of the liquid above it.
- At a greater depth there is a greater height of liquid above.
- So the pressure is greater. In the equation p = ρgh, p is directly proportional to h.
Two more facts are useful. At the same depth in the same liquid, pressure is the same in every direction. Also, a liquid is hard to compress, so its density stays almost constant with depth.
How to answer a depth question
- Name the comparison: which two points, and which has the greater depth.
- State the cause: weight of the liquid above.
- Link depth to pressure: more depth, more liquid above, more pressure.
- Add numbers only if asked, using p = ρgh or Δp = ρgΔh.
- Check that you did not mention container width or total volume as a cause.
Worked example
A diver in fresh water moves from a depth of 5.0 m to a depth of 12.0 m. Explain why the pressure is greater at 12.0 m, then find the increase in pressure caused by the water. Use ρ = 1000 kg/m³ and g = 10 N/kg. (Invented example data.)
Explanation: at 12.0 m there is a greater height of water above the diver. The weight of this water presses on each square metre, so the pressure from the water is larger.
Step 1, pressure at 5.0 m: 1000 × 10 × 5.0 = 50 000 Pa.
Step 2, pressure at 12.0 m: 1000 × 10 × 12.0 = 120 000 Pa.
Step 3, difference: 120 000 − 50 000 = 70 000 Pa.
Check with the change in depth: Δh = 12.0 − 5.0 = 7.0 m, and 1000 × 10 × 7.0 = 70 000 Pa. The two methods agree.
The mistake to watch for
A common explanation is to say that pressure is larger at the bottom because there is more water in total.
Mistaken answer: “The pressure is bigger at the bottom of the lake because the lake contains more water than a small pond.”
This compares the amount of water, not the depth.
The correction is to talk about the height of the liquid above the point: “There is a greater depth, so a greater weight of liquid above each square metre.” A wide shallow lake holds more water than a narrow deep tube, but the tube gives the greater pressure at its bottom.
Check yourself
Use g = 10 N/kg.
1. Three holes are made at depths of 10 cm, 20 cm and 30 cm in the side of a tall bottle of water. Which hole squirts furthest, and why?
Show answer
The lowest hole (30 cm) squirts furthest. The pressure is greatest there, because there is the greatest height of water above it, so the water is pushed out with the greatest speed.
2. The pressure caused by water at 40 m is how many times the pressure caused by water at 10 m?
Show answer
p is directly proportional to h, so the ratio is 40 ÷ 10 = 4 times. Check: 1000 × 10 × 40 = 400 000 Pa and 1000 × 10 × 10 = 100 000 Pa, and 400 000 ÷ 100 000 = 4.
3. Two containers of different shapes hold the same liquid to the same depth. Compare the pressures at their bases.
Show answer
The pressures are equal, because p = ρgh and the liquid, g and depth are the same. The shape and volume of the container do not matter.
Where this leads next
Next, use pressure differences in a diagram with manometer-style questions. If units still cause trouble, see avoiding mass where a force is required.
Explaining in the right order, with the right words, is a skill teachers can model and then check in your own answers. That is part of online one-to-one Physics tuition.