Pressure, speed, and height relationship

Summary

Bernoulli’s principle describes how pressure, speed, and height (elevation) are related in fluid flow. For steady, incompressible, low-friction (negligible viscous effects) and essentially isentropic flow, the total energy per unit mass along a streamline is constant. In a horizontal flow, this implies that when the fluid speeds up, its static pressure decreases; when it slows down, its static pressure increases. The relationship is commonly expressed by Bernoulli’s equation: v^2/2 + gz + p/ρ = constant. Here v is flow speed, g is gravitational acceleration, z is elevation above a reference plane, p is static pressure, and ρ is density. The equation shows that increases in kinetic energy (speed) must be balanced by decreases in potential energy (height term gz) and/or pressure energy (p/ρ). In terms of “head,” the same idea can be written as velocity head + elevation head + pressure head = constant, making it clear how changes in height and pressure trade off with changes in speed.

Key Points

• 1

  In horizontal, steady, incompressible, low-viscosity flow, higher speed corresponds to lower static pressure, and lower speed corresponds to higher static pressure.

• 2

  Bernoulli’s equation links speed, elevation, and pressure through conservation of energy along a streamline: v^2/2 + gz + p/ρ = constant.

• 3

  The height (gz) term represents gravitational potential energy, while p/ρ represents pressure energy; changes in one require compensating changes in the others.