Add Bernoulli's Principle Implementation

physics/bernoullis_principle.py

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+"""
+Title: Bernoulli's Principle Implementation
+
+Description:
+This Python script implements Bernoulli's Principle, which describes the behavior of
+a fluid under varying conditions of pressure, velocity, and height. Bernoulli's equation
+is applied to an incompressible, frictionless fluid to calculate the unknown variable
+(pressure, velocity, or height) when the others are known.
+
+Bernoulli's Equation:
+P1 + 0.5 * ρ * v1^2 + ρ * g * h1 = P2 + 0.5 * ρ * v2^2 + ρ * g * h2
+
+Where:
+- P1, P2 are pressures at points 1 and 2 (in Pascals),
+- v1, v2 are velocities at points 1 and 2 (in m/s),
+- h1, h2 are heights at points 1 and 2 (in meters),
+- ρ is the fluid density (in kg/m³, default is 1000 for water),
+- g is the acceleration due to gravity (default is 9.81 m/s²).
+
+The function `bernoullis_principle` calculates one unknown variable based on inputs and returns the result.
+"""
+
+
+def bernoullis_principle(P1, v1, h1, P2=None, v2=None, h2=None, density=1000, g=9.81):
+    """
+    Apply Bernoulli's Principle to calculate unknown variables.
+
+    Parameters:
+    P1 : float -> Pressure at point 1 (in Pascals)
+    v1 : float -> Velocity at point 1 (in m/s)
+    h1 : float -> Height at point 1 (in meters)
+    P2 : float -> Pressure at point 2 (in Pascals) (optional)
+    v2 : float -> Velocity at point 2 (in m/s) (optional)
+    h2 : float -> Height at point 2 (in meters) (optional)
+    density : float -> Fluid density (in kg/m^3) (default is 1000 for water)
+    g : float -> Acceleration due to gravity (default is 9.81 m/s²)
+
+    Returns:
+    - If one unknown is provided (P2, v2, or h2), the function calculates the missing value.
+    """
+
+    if P2 is None:
+        # Calculate Pressure at point 2 (P2)
+        P2 = P1 + 0.5 * density * (v1**2 - v2**2) + density * g * (h1 - h2)
+        return P2
+    elif v2 is None:
+        # Calculate Velocity at point 2 (v2)
+        v2 = ((2 * (P1 - P2 + density * g * (h1 - h2))) / density + v1**2) ** 0.5
+        return v2
+    elif h2 is None:
+        # Calculate Height at point 2 (h2)
+        h2 = h1 + (P1 - P2 + 0.5 * density * (v1**2 - v2**2)) / (density * g)
+        return h2
+    else:
+        return "Please provide at least one unknown (P2, v2, or h2)."
+
+
+# Example Usage
+# Given: P1 = 101325 Pa, v1 = 5 m/s, h1 = 10 m, v2 = 10 m/s, h2 = 5 m
+P1 = 101325  # Pressure at point 1 in Pascals
+v1 = 5  # Velocity at point 1 in m/s
+h1 = 10  # Height at point 1 in meters
+v2 = 10  # Velocity at point 2 in m/s
+h2 = 5  # Height at point 2 in meters
+
+# Calculate pressure at point 2 (P2)
+P2 = bernoullis_principle(P1, v1, h1, v2=v2, h2=h2)
+print(f"Pressure at point 2: {P2} Pascals")