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Bernoulli Equation – Pipe Flow
Parameters
Inlet velocity v₁:
2.0
m/s
Inlet diameter D₁:
100
mm
Throat diameter D₂:
50
mm
Inlet height h₁:
0
m
Throat height h₂:
1
m
P₁ + ½ρv₁² + ρgh₁ = P₂ + ½ρv₂² + ρgh₂
Continuity: A₁v₁ = A₂v₂
v₂ (throat):
—
P₁:
—
Pa
P₂:
—
Pa
ΔP:
—
Pa
Bernoulli: along a streamline, total energy (pressure + kinetic + potential) is conserved for inviscid, incompressible flow. Narrowing increases velocity, which DECREASES pressure (Venturi effect). Used in carburetors, pitot tubes, airplane wings.