Measuring the Hydraulic Diameter of a Pore or Conduit

Abstract

A method for estimating the hydraulic diameter of a pore or conduit having a noncircular opening is presented with special reference to plant anatomy. An ellipse or a rectangle is inscribed within the opening, and the length of the short axis (a) is measured. The hydraulic diameter (Dh) is estimated for the ellipse (Dh = 1.4a) or rectangle (Dh = 2a). Use of these equations often gives a more accurate estimate of the hydraulic diameter of a pore or conduit than does averaging the lengths of the short and long axes (Dh = [a + b]/2, b is the long axis) or assuming that the opening is circular (Dh = a). A table of the error in each method is included, and the errors inherent in the use of Dh are discussed. Because fewer measurements are required, estimation based on the measurement of one axis is much faster than calculation using both the short and long axes. The equations and table should permit anatomists and physiologists to rapidly determine the best method for estimating the hydraulic diameter of a pore or conduit, and to more accurately and quickly estimate the hydraulic diameters of large numbers of openings. However, because of potential pitfalls in applying theoretical fluid dynamics equations to real-world functional anatomy, botanists must ensure that their applications of hydraulic diameter are appropriate in each case.