|
| 1 | +""" |
| 2 | +Title : Computing the terminal velocity of an object falling |
| 3 | + through a fluid. |
| 4 | +
|
| 5 | +Terminal velocity is defined as the highest velocity attained by an |
| 6 | +object falling through a fluid. It is observed when the sum of drag force |
| 7 | +and buoyancy is equal to the downward gravity force acting on the |
| 8 | +object. The acceleration of the object is zero as the net force acting on |
| 9 | +the object is zero. |
| 10 | +
|
| 11 | +Vt = ((2 * m * g)/(ρ * A * Cd))^0.5 |
| 12 | +
|
| 13 | +where : |
| 14 | +Vt = Terminal velocity (in m/s) |
| 15 | +m = Mass of the falling object (in Kg) |
| 16 | +g = Acceleration due to gravity (value taken : imported from scipy) |
| 17 | +ρ = Density of the fluid through which the object is falling (in Kg/m^3) |
| 18 | +A = Projected area of the object (in m^2) |
| 19 | +Cd = Drag coefficient (dimensionless) |
| 20 | +
|
| 21 | +Reference : https://byjus.com/physics/derivation-of-terminal-velocity/ |
| 22 | +""" |
| 23 | + |
| 24 | +from scipy.constants import g |
| 25 | + |
| 26 | + |
| 27 | +def terminal_velocity( |
| 28 | + mass: float, density: float, area: float, drag_coefficient: float |
| 29 | +) -> float: |
| 30 | + """ |
| 31 | + >>> terminal_velocity(1, 25, 0.6, 0.77) |
| 32 | + 1.3031197996044768 |
| 33 | + >>> terminal_velocity(2, 100, 0.45, 0.23) |
| 34 | + 1.9467947148674276 |
| 35 | + >>> terminal_velocity(5, 50, 0.2, 0.5) |
| 36 | + 4.428690551393267 |
| 37 | + >>> terminal_velocity(-5, 50, -0.2, -2) |
| 38 | + Traceback (most recent call last): |
| 39 | + ... |
| 40 | + ValueError: mass, density, area and the drag coefficient all need to be positive |
| 41 | + >>> terminal_velocity(3, -20, -1, 2) |
| 42 | + Traceback (most recent call last): |
| 43 | + ... |
| 44 | + ValueError: mass, density, area and the drag coefficient all need to be positive |
| 45 | + >>> terminal_velocity(-2, -1, -0.44, -1) |
| 46 | + Traceback (most recent call last): |
| 47 | + ... |
| 48 | + ValueError: mass, density, area and the drag coefficient all need to be positive |
| 49 | + """ |
| 50 | + if mass <= 0 or density <= 0 or area <= 0 or drag_coefficient <= 0: |
| 51 | + raise ValueError( |
| 52 | + "mass, density, area and the drag coefficient all need to be positive" |
| 53 | + ) |
| 54 | + return ((2 * mass * g) / (density * area * drag_coefficient)) ** 0.5 |
| 55 | + |
| 56 | + |
| 57 | +if __name__ == "__main__": |
| 58 | + import doctest |
| 59 | + |
| 60 | + doctest.testmod() |
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