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Bernoulli's Equation

Applied Science: BTEC Level 3 National Extended Diploma, topic 4.11.5

Bernoulli's Equation

The relationship between pressure and velocity in fluids is described quantitatively by Bernoulli's equation.

Bernoulli's equation

Bernoulli's equation

  • Bernoulli's equation states that for an incompressible, frictionless fluid, at points 1 and 2 along a path that a part of the fluid takes, the following equation holds:
  • P1+ρgy1+12ρν12=P2+ρgy2+12ρν22P_1 +\rho g y_1 + \frac{1}{2}\rho \nu_1^2 =P_2 +\rho g y_2 + \frac{1}{2}\rho \nu_2^2
  • Where P is the absolute pressure, ρ\rho is the absolute density, ν\nu is the velocity of the fluid, yy is the height above some reference point, and g is the acceleration due to gravity.
Conservation of energy

Conservation of energy

  • Bernoulli's equation is a form of the conservation of energy principle.
  • Note that the second and third terms on each side are the kinetic and potential energy per unit volume.
  • The pressure terms also have units of energy per unit volume as P=FA=WA×d=WVP=\frac{F}{A}=\frac{W}{A\times d}=\frac{W}{V}.

Test yourself on Bernoulli's Equation

  • What does the term ρgy\rho g y represent?

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