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Deep water on Mars

Air and fluids · level 5, lesson 3 of 6

A question to start

Mars once had lakes and flowing rivers, and future bases may hold big tanks of water. How deep would you have to dive in a Mars tank to feel the same pressure as standing in Earth's air?

The idea

The pressure under water is \(p = \rho g h\). Water's density is the same on Mars. But \(g\) is smaller: 3.71 N/kg against 9.81 N/kg. So each metre of water adds only about 38% as much pressure on Mars.

Under water Mars Earth
Gravity, \(g\) 3.71 N/kg 9.81 N/kg
Extra pressure for each metre of water 3,710 Pa 9,810 Pa
Air pressure at the surface 636 Pa 101,400 Pa
Depth to reach a total of 101,400 Pa about 27 m at the surface
Earth: 10 mMars: 26 mboth add about 98 kPa

Worked examples

1. 10 m down on Mars. \(1000 \times 3.71 \times 10 = 37{,}100\) Pa from the water.

2. The same extra pressure. On Earth, 10 m adds 98,100 Pa. On Mars that needs \(98{,}100/(1000 \times 3.71) = 26.4\) m.

3. Earth's air pressure, under Mars water. Total \(= 636 + 3710h = 101{,}400\), so \(h = 100{,}764/3710 = 27.2\) m.

Try it

  1. Why does each metre of water add less pressure on Mars?
  2. Find the pressure from 5 m of water on Mars.
  3. A Mars base tank is 4 m deep. What is the total pressure at its bottom if the air inside the base is at 70,000 Pa?
  4. A diver on Earth goes 30 m down. How deep would they go on Mars for the same pressure from the water alone?
Answers
  1. Gravity is weaker, so the water above weighs less.
  2. \(1000 \times 3.71 \times 5 = 18{,}550\) Pa.
  3. \(70{,}000 + 1000 \times 3.71 \times 4 = 84{,}840\) Pa.
  4. \(30 \times 9.81/3.71 \approx 79\) m.

Common mistake

"Water is lighter on Mars, so it is less dense." Its mass per cubic metre, its density, is the same everywhere. Only its weight changes.

Where it leads