- #1

Tanguy

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- Homework Statement
- I have to do a presentation about water rocket and the theoretical pressure needed to send me (a mass of 60kg) up in space

- Relevant Equations
- Simplified Newton's seconds law : Sum(F) = m.a

Bernouilli's theorem : ½.v^2+g.z+(roh).P=constant

Kepler's Laws

Hi ! I'm a French student in Terminale (12th grade equivalent) and I have to do an oral presentation of 5min (Grand Oral) for my baccalauréat linked with my professional project. As I want to become an engineer in astrophysics, I want to talk about water rocket and the theoretical possibility to send a human being up in space.

With a bunch of approximations and some equations found on the Internet, I came up with an approximation of the acceleration of the rocket at liftoff : m.a = -m.g + (volumic_mass_of_water).(area_of_the_neck).[(water_ejection_speed)]^2,

with (water_ejection_speed)=sqrt[2.([inside_pressure] - [atmospheric_pressure])/(volumic_mass_of_water)]

Using 5cm as the diameter of the neck, 9.81 as and 60kg as m, then by integrating the expression of a, I come up with

velocity(t) = v(t) = 6,5*10^(-5)*P*(t)-9,81*(t), with P the searched initial air pressure in the rocket.

I know that a rocket needs a velocity of 11,2*10^(3)m/s in order to espace earth attraction.

But I have absolutely no idea about how to link the expression of velocity (with 2 variables) I found and this given velocity of reference.

Does someone have any idea about it ? Should I simplify the expression of velocity by choosing a value for (t) ? If so, which value should I take ?

Thanks your for your answers,

Have a good day

Tanguy

With a bunch of approximations and some equations found on the Internet, I came up with an approximation of the acceleration of the rocket at liftoff : m.a = -m.g + (volumic_mass_of_water).(area_of_the_neck).[(water_ejection_speed)]^2,

with (water_ejection_speed)=sqrt[2.([inside_pressure] - [atmospheric_pressure])/(volumic_mass_of_water)]

Using 5cm as the diameter of the neck, 9.81 as and 60kg as m, then by integrating the expression of a, I come up with

velocity(t) = v(t) = 6,5*10^(-5)*P*(t)-9,81*(t), with P the searched initial air pressure in the rocket.

I know that a rocket needs a velocity of 11,2*10^(3)m/s in order to espace earth attraction.

But I have absolutely no idea about how to link the expression of velocity (with 2 variables) I found and this given velocity of reference.

Does someone have any idea about it ? Should I simplify the expression of velocity by choosing a value for (t) ? If so, which value should I take ?

Thanks your for your answers,

Have a good day

Tanguy