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Fluids Formula

What is Bernoulli's Equation?

Along a streamline in steady, incompressible, non-viscous flow, the total mechanical energy per unit volume is constant.

Formula: P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}

Plain-English Meaning

Along a streamline in steady, incompressible, non-viscous flow, the total mechanical energy per unit volume is constant.

Mechanics questions usually become easier once you identify whether the problem is about force balance, kinematics, energy, or conservation.

Deeper Explanation

Along a streamline in steady, incompressible, non-viscous flow, the total mechanical energy per unit volume is constant.

Worked Example

Problem: Water (ρ=1000 kg/m³) flows at 2 m/s at P₁=200 kPa, h₁=0. Pipe rises to h₂=3 m, v₂=1 m/s. Find P₂.

  • P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
  • 200000 + ½(1000)(4) + 0 = P₂ + ½(1000)(1) + 1000(9.8)(3)
  • 202000 = P₂ + 500 + 29400
  • P₂ = 202000 − 29900 = 172100 Pa ≈ 172.1 kPa

Result: P₂ ≈ 172.1 kPa

At A Glance

Category: Fluids

Levels covered:

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.