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In fluid dynamics, there are many key questions relating to nozzles to consider that could benefit the human race. For example, a burning question on the forefront of everyone's mind is "Would it be theoretically possible to use a water gun to shoot the moon?"
Well, there are several factors to consider when attempting to answer this question:
The distance required to the Earth's outer atmosphere.
The velocity required from the gun to have sufficient velocity to escape from Earth's outer atmosphere.
The pressure required by the gun.
The distance from the surface of the Earth to Earth's outer atmosphere, or Kármán line, is approximately 100 km, as shown in the following diagram. The escape velocity from Earth is 11.186 kms-2.
Figure 1 - The layers of Earth's atmosphere - (En.wikipedia.org, 2019)
Step 1: Draw a diagram of the problem.
Step 2: With an assumption of constant acceleration, calculate the velocity from the water gun.
Step 3: To maximise the possibility of reaching the moon, the output diameter of the nozzle could be the smallest hole ever drilled, at 0.022mm (Piquepaille, 2019). A sensible estimate for the input diameter to the nozzle could be 1m.
Step 4: Now calculate the pressure of the water going into the nozzle. Assume that the change in height of the nozzle is zero, as in reality, the nozzle height is negligible when compared to the distance to the moon.
Challenge:
In reality, this is an over-simplification; other factors would need to be brought into consideration. As a challenge, consider the following:
The change in gravity over distance
The change of temperature in space
The change in gravity over distance can be calculated using Newton's Law of Universal Gravitation:
F = (Gm1m2) / d2
where G is the gravitational constant of 6.674×10−11 m3kg−1s−2, m1 and m2 are the masses of the Earth and water respectively and d is the distance between the Earth and the Earth's outer atmosphere.
The change in temperature may have some impact on the flow. When water is released into space, first it undergoes a violent boiling process, due to the drop in pressure. Then the vapour immediately solidifies, known as sublimation.
Figure 2 - Water in a Vacuum - (Think About: What Happens to Water in a Vacuum?, 2019)
Although the mass of the water would remain the same, a change in state to small crystals could cause the movement of water in space to vary slightly due to an increase in volume.
En.wikipedia.org. (2019). Atmosphere of Earth. [online] Available at: https://en.wikipedia.org/wiki/Atmosphere_of_Earth#/media/File:Earth%27s_atmosphere.svg [Accessed 25 Mar. 2019].
Piquepaille, R. (2019). The world's smallest drilled hole | ZDNet. [online] ZDNet. Available at: https://www.zdnet.com/article/the-worlds-smallest-drilled-hole/ [Accessed 24 Mar. 2019].
Think About: What Happens to Water in a Vacuum?. (2019). [video] Available at: https://www.youtube.com/watch?v=UG7nsZkVZc0 [Accessed 25 Mar. 2019].
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