# Would this idea of a water rocket to pass the Karman line work?

When I fly my water rockets as a hobby I use this formula to calculate the height of the flight so I get an idea of how high my water rocket will fly. My idea is to make a theoretical water rocket out of graphene (https://www.nanowerk.com/what_is_graphene.php). It would have around 50 - 100 layers of graphene and the air pressure would be brought up to 6000 bars. Then I would add some shampoo in the water to change the density (Best case scenario the density would be dropped by half but that is not fully possible). The rocket length would be around 4m and 16 cm in diameter. It would be filled up to 30% with water.

In this case then:

Mi = 400 cm / 3 * 8² * π = 26 808,257... cm³ = 26,808257 kg water

Mr = 0,16 * π * 4 * 50 * 0,00077 + 26,808257 = 26,885665 kg in total

Here 0,16 * π * 4 is the area made out of graphene. 50 is the numbers of layers of graphene. 0,00077 is the weight of a square meter. 26,808257 is the weight of the water.

Pi = 6000 bars = 600 000 000 pascal

p = 600 (kg/m³)

g = 9,81 m/s²

Then adding it to the formula: (26,808257 / 26,885665)² * (600 000 000 / 600 * 9,81) = 101 350,6604788 m =~ 101,35 km

This formula is leaving out the air resistance so the height it would fly is definitely lower, but if you increased the pressure by another 1000 bars or so then it would fly high enough to pass the Karman line.

Have I made any mistakes in my calculations or the method I used to calculate the height of the flight?

• Again, you can't use that formula to simulate your water rocket design, your chosen parameters are far outside the assumptions the formula makes. Jul 30, 2022 at 10:51
• @notovny then which formula can I use? Jul 30, 2022 at 11:00
• Remember the maximum energy you can get from this system is its internal energy, i.e. the pressurized gas cools as it discharges and soon becomes liquid and loses all its pressure. BTW at 600MPa air is already supercritical at room temperature so this nitrogen-oxygen-water mixture doesn't behave the way you have imagined. Jul 30, 2022 at 11:28
• I love the combination of "I'm going to make a 600MPa pressure chamber out of layered graphene" and "then I would add some shampoo to the water to change its density". Truly schizo tech. Jul 31, 2022 at 8:50