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61 lines
2.0 KiB
Python
61 lines
2.0 KiB
Python
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"""
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Title : Computing the terminal velocity of an object falling
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through a fluid.
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Terminal velocity is defined as the highest velocity attained by an
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object falling through a fluid. It is observed when the sum of drag force
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and buoyancy is equal to the downward gravity force acting on the
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object. The acceleration of the object is zero as the net force acting on
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the object is zero.
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Vt = ((2 * m * g)/(ρ * A * Cd))^0.5
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where :
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Vt = Terminal velocity (in m/s)
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m = Mass of the falling object (in Kg)
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g = Acceleration due to gravity (value taken : imported from scipy)
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ρ = Density of the fluid through which the object is falling (in Kg/m^3)
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A = Projected area of the object (in m^2)
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Cd = Drag coefficient (dimensionless)
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Reference : https://byjus.com/physics/derivation-of-terminal-velocity/
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"""
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from scipy.constants import g
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def terminal_velocity(
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mass: float, density: float, area: float, drag_coefficient: float
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) -> float:
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"""
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>>> terminal_velocity(1, 25, 0.6, 0.77)
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1.3031197996044768
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>>> terminal_velocity(2, 100, 0.45, 0.23)
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1.9467947148674276
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>>> terminal_velocity(5, 50, 0.2, 0.5)
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4.428690551393267
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>>> terminal_velocity(-5, 50, -0.2, -2)
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Traceback (most recent call last):
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...
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ValueError: mass, density, area and the drag coefficient all need to be positive
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>>> terminal_velocity(3, -20, -1, 2)
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Traceback (most recent call last):
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...
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ValueError: mass, density, area and the drag coefficient all need to be positive
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>>> terminal_velocity(-2, -1, -0.44, -1)
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Traceback (most recent call last):
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...
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ValueError: mass, density, area and the drag coefficient all need to be positive
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"""
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if mass <= 0 or density <= 0 or area <= 0 or drag_coefficient <= 0:
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raise ValueError(
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"mass, density, area and the drag coefficient all need to be positive"
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)
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return ((2 * mass * g) / (density * area * drag_coefficient)) ** 0.5
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if __name__ == "__main__":
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import doctest
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doctest.testmod()
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