Barker effect

The Barker effect is an effect in fluid mechanics that can lead to measurement errors when using pitot tubes and Prandtl tubes with low Reynolds numbers . The Barker effect was first described by Muriel Barker in 1922 .

The measurement with pitot tubes is based on the fact that the total pressure is measured at the stagnation point of a small tube placed in the flow . With a relatively high influence of the viscosity ( viscosity ) of the fluid , i.e. with low Reynolds numbers Re , a higher pressure than the total pressure of the undisturbed inflow is measured at the stagnation point. This can be explained by the fact that the stream filament, which is delayed towards the stagnation point, is subject to a viscous impulse transport, that is to say is "carried along and driven" by the viscosity of the surrounding fluid. ${\ displaystyle p _ {\ text {total}}}$

The effect plays a role for pitot tubes from and for Prandtl tubes from . The Reynolds number Re is formed with the outer diameter D of the Pitot or Prandtl tube. ${\ displaystyle Re <100}$ ${\ displaystyle Re <400}$

{\ displaystyle Re = {\ frac {u \ cdot D} {\ nu}}}

With

${\ displaystyle u}$ the speed of the undisturbed flow
${\ displaystyle D}$ the outside diameter of the Pitot or Prandtl tube
${\ displaystyle \ nu}$ the kinematic viscosity of the fluid

The deviation that occurs due to the Barker effect can be approximately described with

{\ displaystyle {\ frac {p _ {\ text {total}} - p _ {\ text {stat}}} {{\ frac {\ rho} {2}} u ^ {2}}} = 1 + {\ frac {6} {Re}}}

With

${\ displaystyle p _ {\ text {total}}}$ the total pressure,
${\ displaystyle p _ {\ text {stat}}}$ the static pressure
${\ displaystyle \ rho}$ the density of the fluid

literature

H. Eckelmann: Introduction to flow measurement technology. Teubner, Stuttgart 1997, ISBN 3-519-02379-2 .
H. Schlichting, K. Gersten: boundary layer theory. Springer, Berlin 1997, ISBN 3-540-55744-X .

Individual evidence

↑ Muriel Barker: On the Use of Very Small Pitot Tubes for Measuring Wind Velocity . In: Proceedings of the Royal Society of London. Series A . tape 101 , no. 712 , 1922, pp. 435-445 , doi : 10.1098 / rspa.1922.0055 .
↑ H. Eckelmann: Introduction to flow measurement technology. Teubner, Stuttgart 1997, ISBN 3-519-02379-2 .

[1] Muriel Barker: On the Use of Very Small Pitot Tubes for Measuring Wind Velocity . In: Proceedings of the Royal Society of London. Series A . tape 101 , no. 712 , 1922, pp. 435-445 , doi : 10.1098 / rspa.1922.0055 .

[2] H. Eckelmann: Introduction to flow measurement technology. Teubner, Stuttgart 1997, ISBN 3-519-02379-2 .