Hydraulics of microtube emitters: a dimensional analysis approach

Abstract

Dimensional analysis is a simple, clear and intuitive method for determining the functional dependence of physical quantities that are of importance to a certain process. Buckingham’s pi theorem is used to derive a dimensionally homogeneous equation for predicting the discharge of the microtube as a function of gravitational acceleration (g), microtube diameter (D), operating pressure head (H) and microtube length (L). Experimental investigations were conducted at College of Agricultural Engineering and Technology, Junagadh, to determine (a) the variation in Q with L, D and H and (b) the coefficients (K, y and z) of the developed model. The L and D of microtube were varied from 5 to 250 cm and 1.2 to 2 mm. The operating pressure was varied from 0 to 1.5 m. The L, H and D combinations selected in the study suit most of the manufacturer’s recommendations for microtube drip irrigation systems. The discharge of microtube decreased with increase in microtube length for particular microtube diameter and operating pressure. The discharge increased with increase in the microtube diameter for a particular operating pressure and microtube length. The values of K, y and z are 4.476, 1 and 0.5, respectively. Goodness of fit and efficiency coefficient reduced with increase in the microtube diameter. The dimensionally homogeneous equation (Eq. 25) developed for all flow regimes can predict discharge with good accuracy for less than 2-mm microtube diameter. The microtube diameter was found to be 1.2 mm based on the dominance of viscous forces over inertial forces.