In some applications, elbow-type flow meters like the one shown in Fig. P5–115 are used to measure flow rates. The pipe radius is R, the radius of curvature of the elbow is λ, and the pressure difference ΔP across the curvature inside the pipe is measured. From the potential flow theory, it is known that V r = C, where V is the fluid velocity at a distance r from the center of curvature O, and C is a constant. Assuming frictionless steady-state flow and thus the Bernoulli equation across streamlines to be applicable, obtain a relation for the flow rate as a function of ρ, g, ΔP, λ, and R.

FIGURE P5–115

Transcribed Image Text:

R Ροζ ΔΡ