Bernoullis equations

physics/archimedes_principle.py

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+"""
+Calculates buoyant force on object submerged within static fluid.
+Discovered by greek mathematician, Archimedes. The principle is named after him.
+
+Equation for calculating buoyant force:
+Fb = ρ * V * g
+
+Source:
+- https://en.wikipedia.org/wiki/Archimedes%27_principle
+"""
+
+
+# Acceleration Constant on Earth (unit m/s^2)
+g = 9.80665
+
+
+def archimedes_principle(
+    fluid_density: float, volume: float, gravity: float = g
+) -> float:
+    """
+    Args:
+        fluid_density: density of fluid (kg/m^3)
+        volume: volume of object / liquid being displaced by object
+        gravity: Acceleration from gravity. Gravitational force on system,
+            Default is Earth Gravity
+    returns:
+        buoyant force on object in Newtons
+
+    >>> archimedes_principle(fluid_density=997, volume=0.5, gravity=9.8)
+    4885.3
+    >>> archimedes_principle(fluid_density=997, volume=0.7)
+    6844.061035
+    """
+
+    if fluid_density <= 0:
+        raise ValueError("Impossible fluid density")
+    if volume < 0:
+        raise ValueError("Impossible Object volume")
+    if gravity <= 0:
+        raise ValueError("Impossible Gravity")
+
+    return fluid_density * gravity * volume
+
+
+if __name__ == "__main__":
+    import doctest
+
+    # run doctest
+    doctest.testmod()

physics/bernoullis_equation.py

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+"""
+
+
+Source:
+- https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/14-6-bernoullis-equation/
+"""
+
+# Acceleration Constant on Earth (unit m/s^2)
+g = 9.80665
+
+
+def bernoulli_static_equation(
+    fluid_density: float, h: float, gravity: float = g, initial_pressure: float = 0
+) -> float:
+    """
+    Bernoulli's equation for static fluids.
+    Calculate pressure from static fluid at given depth.
+
+    Pascals law, "a pressure change at any point in a confined incompressible fluid,
+    is transmitted throughout the fluid such that the same change occurs everywhere"
+    According to Pascals law, the pressure will be the same at a given depth,
+    regardless of whether this is a submerged object or a force on container wall.
+
+    This function models:
+    P (pressure) = h (depth) * ρ (density) * g (gravity)
+    P = hρg
+
+    In addition to this equation being used independently to calculate pressure at a depth,
+    It is a component of bernoulli's principle.
+
+
+    Args:
+        fluid_density: Density of fluid within which pressure is being calculated
+        h: depth at which pressure is being calculated.
+        gravity: Acceleration from gravity. Default is Earth Gravity
+        initial_pressure: represents any external pressure acting on system (Pa)
+    returns:
+        Pressure at given depth in Pa (Pascals)
+
+
+    >>> bernoulli_static_equation(fluid_density=997, h=5)
+    48886.15025
+
+    >>> bernoulli_static_equation(fluid_density=997, h=5, gravity=9.8)
+    48853.0
+
+    >>> bernoulli_static_equation(fluid_density=997, h=5, gravity=9.8, initial_pressure=3.7)
+    48856.7
+    """
+
+    if fluid_density <= 0:
+        raise ValueError("Impossible fluid density")
+    if h < 0:
+        raise ValueError("Impossible depth")
+    if gravity <= 0:
+        raise ValueError("Impossible Gravity")
+
+    return fluid_density * h * gravity + initial_pressure
+
+
+def bernoulli_fluid_equation(
+    fluid_density: float, fluid_velocity: float, initial_pressure: float = 0
+) -> float:
+    """
+     Calculates pressure/fluids-kinetic-energy - work of a dynamic non-compressible fluid through a tube
+
+     Bernoulli's Equation:
+         W = P1 + 0.5*ρ*v^2
+
+     Args:
+         fluid_density: Density of fluid within which pressure is being calculated
+         fluid_velocity: Velocity at which the fluid is travelling at
+         initial_pressure: represents any external pressure acting on system (Pa)
+    Returns:
+         Pressure of system in Pa (Pascals)
+
+     >>> bernoulli_fluid_equation(fluid_density=997, fluid_velocity=0.7)
+     244.26499999999996
+     >>> bernoulli_fluid_equation(fluid_density=997, fluid_velocity=0.7, initial_pressure=2)
+     246.26499999999996
+    """
+
+    if fluid_density <= 0:
+        raise ValueError("Impossible fluid density")
+
+    return 0.5 * fluid_density * fluid_velocity**2 + initial_pressure
+
+
+def bernoulli_full_equation(
+    fluid_density: float,
+    fluid_velocity: float = 0,
+    h: float = 0,
+    gravity: float = g,
+    initial_pressure: float = 0,
+) -> float:
+    """
+     Bernoulli's equation represents the relation of (Pressure, KE, and GPE) of a non-compressible,
+     frictionless fluid within a container.
+
+     P1 + 0.5*ρ*v1^2 + ρgh1 = P2 + 0.5*ρ*v2^2 + ρgh2
+     or
+     P + 0.5*ρ*v^2 + ρgh = constant
+
+     Equation is often rearranged to solve for different variables
+
+     Args:
+         fluid_density: Density of fluid within which pressure is being calculated
+         fluid_velocity: Velocity at which the fluid is travelling at
+         h: height difference between two pressures being compared
+         gravity: Acceleration from gravity. Default is Earth Gravity
+         initial_pressure: represents any external pressure acting on system (Pa), Default = 0
+    Returns:
+         Pressure of system in Pa (Pascals)
+
+
+     >>> bernoulli_full_equation(fluid_density=997, fluid_velocity=0.2, h=5, gravity=9.8, initial_pressure=7)
+     48879.94
+     >>> bernoulli_full_equation(fluid_density=997, fluid_velocity=0.2, h=5, gravity=9.8)
+     48872.94
+     >>> bernoulli_full_equation(fluid_density=997, fluid_velocity=0.2, h=5)
+     48906.09025
+     >>> bernoulli_full_equation(fluid_density=997, h=9)
+     87995.07045
+    """
+
+    return (
+        bernoulli_fluid_equation(
+            fluid_density=fluid_density, fluid_velocity=fluid_velocity
+        )
+        + bernoulli_static_equation(fluid_density=fluid_density, h=h, gravity=gravity)
+        + initial_pressure
+    )
+
+
+if __name__ == "__main__":
+    import doctest
+
+    # run doctest
+    doctest.testmod()