The pressure drop, \(\Delta p\), over a certain length of horizontal pipe is assumed to be a function of the velocity, \(V\), of the fluid in the pipe, the pipe diameter, \(D\), and the fluid density and viscosity, \(ho\) and \(\mu\).

(a) Show that this flow can be described in dimensionless form as a "pressure coefficient," \(C_{p}=\Delta p /\left(0.5 ho V^{2}\right)\) that depends on the Reynolds number, \(\operatorname{Re}=ho V D / \mu\).

(b) The following data were obtained in an experiment involving a fluid with \(ho=2\) slugs \(/ \mathrm{ft}^{3}\), \(\mu=2 \times 10^{-3} \mathrm{lb} \cdot \mathrm{s} / \mathrm{ft}^{2}\), and \(D=0.1 \mathrm{ft}\). Plot a dimensionless graph and use a power law equation to determine the functional relationship between the pressure coefficient and the Reynolds number.

(c) What are the limitations on the applicability of your equation obtained in part (b)?

Transcribed Image Text:

V, ft/s Ap, lb/ft 3 192 11 704 17 1088 20 1280