Bernoulli's Equation Calculator Formula

Understand the math behind the bernoulli's equation calculator. Each variable explained with a worked example.

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Formulas Used

Pressure at Point 2 (P2)

p2 = p1 * 1000 + 0.5 * density * (pow(v1, 2) - pow(v2, 2)) + density * 9.81 * (h1 - h2)

P2 in kPa

p2_kpa = (p1 * 1000 + 0.5 * density * (pow(v1, 2) - pow(v2, 2)) + density * 9.81 * (h1 - h2)) / 1000

Variables

VariableDescriptionDefault
p1Pressure at Point 1 (P1)(kPa)200
v1Velocity at Point 1 (V1)(m/s)2
h1Elevation at Point 1 (z1)(m)5
h2Elevation at Point 2 (z2)(m)0
v2Velocity at Point 2 (V2)(m/s)5
densityFluid Density (rho)(kg/m^3)1000

How It Works

Bernoulli's Equation

For steady, incompressible, frictionless flow along a streamline, the total energy per unit volume remains constant.

Formula

P1 + 0.5 rho V1^2 + rho g z1 = P2 + 0.5 rho V2^2 + rho g z2

Rearranging for P2:

P2 = P1 + 0.5 rho (V1^2 - V2^2) + rho g (z1 - z2)

This equation is the foundation of fluid mechanics, connecting pressure, velocity, and elevation energy.

Worked Example

Water (1000 kg/m^3) flows from point 1 (P1=200 kPa, V1=2 m/s, z1=5 m) to point 2 (V2=5 m/s, z2=0 m).

p1 = 200v1 = 2h1 = 5h2 = 0v2 = 5density = 1000
  1. 01Velocity term: 0.5 x 1000 x (4 - 25) = -10,500 Pa
  2. 02Elevation term: 1000 x 9.81 x (5 - 0) = 49,050 Pa
  3. 03P2 = 200,000 - 10,500 + 49,050 = 238,550 Pa = 238.55 kPa

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