Intermediate
Fluid Mechanics: Bernoulli's Theorem
Along a streamline, faster flow means lower pressure.
STEP 1 · CONCEPT
For steady, incompressible, frictionless flow, the total energy per unit volume stays constant along a streamline.
STEP 2 · THREE ENERGIES
Pressure energy, kinetic energy (velocity) and potential energy (height). If one goes up, another must go down.
STEP 3 · APPLICATIONS
Venturi meters, aircraft wings, carburettors and pitot tubes all use Bernoulli's principle.
WORKED EXAMPLE
Water speeds up in a narrow pipe section. Since velocity rises, the pressure there drops — which is exactly what a venturi meter measures.
Formulas
Bernoulli equation
P + ½ρv² + ρgh = constant
P pressure, ρ density, v velocity, h height
Continuity
A₁v₁ = A₂v₂
A area, v velocity
Practice questions
Q1.Bernoulli's equation is based on conservation of…
Fluid Mechanics: Bernoulli's Theorem · Easy
Q2.Pipe area halves. Velocity becomes…
Fluid Mechanics: Bernoulli's Theorem · Medium
Q3.Bernoulli's equation does NOT assume…
Fluid Mechanics: Bernoulli's Theorem · Hard