

BERNOULLI EFFECT (BERNOULLI PRESSURE DIFFERENCE)

Description 

If in a steadystate situation, along a horizontal flow line in a nonviscous fluid, the flow speed is not the same at two different points, the fluid pressure will be different at these points. We can say that speed changes require (or establish) pressure differences.




Relations 

Left: Venturi pipe with pressure sensors; air is blown into the pipe on the right side.
Right: Narrowing of pipe leads to increase of flow speed and to a reduction of the fluid pressure (see Continuity Equation):
delta_pB = – 0.5*rho*(v2^2 – v1^2)
delta_pB: pressure difference because of speed change; v: flow speed; rho: density of fluid; p: fluid pressure.
If there is no friction (or no other process between Points 1 and 2), the pressure difference delta_pB equals the actual pressure difference p2–p1.




Remarks 

Bernoulli's theorem can be found by integrating the momentum equation along a flow line. Alternatively, it can be derived based on an inputoutput analysis using the balance of energy of the participating systems.
It holds for gases (air) if the density does not vary too greatly.




Symbols 

p, delta_p, rho, v 
Units 

[p] = Pa, [rho] = kg/m^3, [v] = m/s 
Synonyms 


Related to 

Bernoulli theorem 
Translations 

(German) BernoulliEffekt



