Hydraulic Diameter of a Tube within a Tube

The hydraulic diameter, abbreviated d_h, is used to calculate the Reynolds Number, friction factor or for calculating pressure drop across two points.  For most geometries, the hydraulic diameter, or characteristic length, is not equal to the diameter of the shape.  The calculation below is an example of the hydraulic diameter when the shape is a circular shape with a circular, tube running through the flowing area.  This equation can be used for a tube if the inside radius is set to zero.

 

Hydraulic Diameter of a Tube within a Tube formulas
\( d_h =   4\; ( \pi\; r_{o}{^2} - \pi \;r_{i}{^2} )  \;/\;  2 \;\pi \;r_o +  2\; \pi\; r_i  \)  \( d_h =   4\; \pi  \; ( r_{o}{^2}  -  r_{i}{^2} )  \;/\;  2\; \pi  \; ( r_o +  r_i )  \)
Symbol	English	Metric
\( d_h \) = hydraulic diameter	\(in\)	\(mm\)
\( \pi \) = Pi	\(3.141 592 653 ...\)	\(3.141 592 653 ...\)
\( r_o \) = pipe inside radius of the outside tube	\(in\)	\(mm\)
\( r_i \) = pipe outside radius of the inside tube	\(in\)	\(mm\)