To study the drop of pressure in pipes, several variables are considered. These include the pressure gradient (dp/ dx), the diameter of the pipe (d), the density (p) and viscosity (µ) of the fluid,...

To study the drop of pressure in pipes, several variables are considered. These include the pressure gradient (dp/ dx), the diameter of the pipe (d), the density (p) and viscosity (µ) of the fluid, the fluid velocity ( V), and the roughness of the pipe wall (e). Relate the pressure gradient to other parameters using the Ti-theorem.

Using dimensional analysis, show chat the power P required to operate a test tunnel is given by
 where pis the density, I is a characteristic linear dimension of the tunnel, Vis the velocity of the fluid relative to the tunnel, and R,, is the Reynolds number.