Create bernoullis_principle.py

searches/bernoullis_principle.py

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+"""
+Title: Bernoulli's Principle
+
+Description:
+This algorithm implements Bernoulli's Principle to calculate the unknown pressure
+at a second point in a fluid system using the Bernoulli equation. Bernoulli's equation
+states that for an incompressible, frictionless fluid, the total mechanical energy
+(remains constant) as the fluid flows.
+
+The equation used:
+P1 + 0.5 * ρ * v1^2 + ρ * g * h1 = P2 + 0.5 * ρ * v2^2 + ρ * g * h2
+
+Where:
+- P1 and P2 are the pressures at point 1 and point 2 (Pascals)
+- v1 and v2 are the fluid velocities at point 1 and point 2 (m/s)
+- h1 and h2 are the heights at point 1 and point 2 (m)
+- ρ is the density of the fluid (kg/m^3)
+- g is the gravitational constant (9.81 m/s^2)
+
+This algorithm solves for P2, the unknown pressure at point 2.
+
+Example:
+>>> bernoullis_principle(10, 101325, 0, 15, 5)
+100732.64
+"""
+
+
+def bernoullis_principle(
+    velocity1: float,
+    pressure1: float,
+    height1: float,
+    velocity2: float,
+    height2: float,
+    density: float = 1.225,
+) -> float:
+    """
+    Calculate the unknown pressure at a second point in a fluid system using Bernoulli's equation.
+
+    Parameters:
+    velocity1 (float): velocity at point 1 in m/s
+    pressure1 (float): pressure at point 1 in Pascals
+    height1 (float): height at point 1 in meters
+    velocity2 (float): velocity at point 2 in m/s
+    height2 (float): height at point 2 in meters
+    density (float): density of the fluid in kg/m^3 (default is 1.225, for air)
+
+    Returns:
+    float: Pressure at point 2 in Pascals
+
+    Example:
+    >>> bernoullis_principle(density=1000, velocity=5, height=10, pressure=101325)
+    144413.5
+    >>> bernoullis_principle(density=500, velocity=10, height=5, pressure=0)
+    25000.0
+    >>> bernoullis_principle(density=997, velocity=0, height=0, pressure=101325)
+    101325.0
+    """
+    g = 9.81  # gravitational constant in m/s^2
+
+    # Bernoulli's equation to solve for pressure at point 2
+    pressure2 = (
+        pressure1
+        + 0.5 * density * (velocity1**2)
+        + density * g * height1
+        - 0.5 * density * (velocity2**2)
+        - density * g * height2
+    )
+
+    return round(pressure2, 2)
+
+
+# Example usage
+if __name__ == "__main__":
+    # Example doctest
+    import doctest
+
+    doctest.testmod()
+
+    # Manual test
+    pressure_at_point_2 = bernoullis_principle(10, 101325, 0, 15, 5)
+    print(f"Pressure at point 2: {pressure_at_point_2} Pascals")