Variable mass calculation of thrust for a water rocket

In summary, the conversation discusses deriving a formula for time varying thrust using known initial values for a water rocket. The Bernoullis equation and isentropic expansion formula are mentioned as possible methods for solving the problem. The main focus is on deriving a differential equation for velocity and pressure using a small mass ejected in a given time frame.
  • #1
Engn_sam
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0

Homework Statement



I am trying to derive the formula for time varying thrust given that I know the initial mass/volume of water in a water rocket. Knowns will include initial pressure, initial volume of water, and nozzle cross sectional area.

Homework Equations



Bernoullis equation: (p/ρg) + (2V2/g) + z = c

Isentropic expansion: pvγ = c

The Attempt at a Solution


[/B]
I derived the formula for the exit velocity of the water from the nozzle using the Bernoullis equation,
https://www.dropbox.com/s/gnatjasgb2fjx5i/Photo%202015-02-05%2C%203%2050%2055%20PM.jpg?dl=0
https://www.dropbox.com/s/gnatjasgb2fjx5i/Photo 2015-02-05, 3 50 55 PM.jpg?dl=0

I know that I am supposed to derive a differential equation for the velocity and pressure but I can't seem to setup the equation using the isentropic flow formula.

any help will be appreciated. thank you.
 

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  • #2
Welcome to PF;
this is something that is normally done by taking a small dm ejected in time dt, and working out the dp that results.
 

Related to Variable mass calculation of thrust for a water rocket

What is a water rocket?

A water rocket is a type of rocket that uses water as its propellant. It works by filling a plastic bottle partially with water and then pressurizing it with air. When the pressure is released, the water is forced out of the bottle, creating thrust that propels the rocket upwards.

Why is variable mass calculation important for a water rocket?

Variable mass calculation is important for a water rocket because it allows for more precise control over the rocket's flight. By taking into account the changing mass of the rocket as the water is expelled, the calculation can determine the optimal amount of water to use for maximum thrust and altitude.

How is variable mass calculated for a water rocket?

The variable mass of a water rocket is calculated by taking into account the initial mass of the rocket (before water is added), the mass of the water added, and the mass of the rocket after the water has been expelled. This calculation can be done using the rocket equation, which takes into account the change in mass and the specific impulse of the propellant.

What factors can affect the variable mass calculation of thrust for a water rocket?

The variable mass calculation of thrust for a water rocket can be affected by factors such as the initial pressure inside the rocket, the amount of water added, the shape and size of the rocket, and external factors like wind and air resistance. These factors can impact the amount of thrust produced and the overall altitude and flight trajectory of the rocket.

How can variable mass calculation be used to improve the performance of a water rocket?

By accurately calculating the variable mass of a water rocket, it is possible to optimize its performance and achieve higher altitudes and longer flight times. This calculation can help determine the ideal amount of water to use for maximum thrust, as well as inform design choices for the rocket to minimize air resistance and improve overall performance.

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