Frictional Pressure Losses
Frictional losses in pipes are due to the viscosity of the fluid. A viscous fluid develops shear stresses in the fluid and along the wall of the pipe. When drawn on a control volume the wall viscous shear stresses appear similar to the way that friction forces are drawn on a free body diagram. Thus the wall shear forces are commonly called friction forces.
The example used in the dimensional analysis chapter showed that the pressure loss in a straight pipe was related to the Reynolds number and the diameter to length ratio.
This equation can be rewritten by rearranging the terms and dividing through by the density and gravitational acceleration
where hf is the head loss due to viscous or frictional losses in the pipe.
Not included in the dimensional analysis that gave this equation was a roughness parameter, ε, that is equal to the average height of the asperities on the inside of the pipe. The roughness parameter gives rise to another Π-Group called the relative roughness.
The frictional head loss can then be written as
Note that this equation has units of distance (i.e. m or ft).