... R∗/R∗res= 10 −2, and we keep the data used in the previous example, we findB ∼ 0.05. The product AB is of the order of 10 −3, suggesting a dilation of t by afactor 10 3(i.e. using hours instead of ... θ ∼ 10 −2, ε = 4 10 −5, the r.h.s. is ∼ 4 10 10 .With R∗∼ 2cm,S∗s∼ 1 mm, we eventually find κ∗∼ 2 10 −14m2. This correspondsto an apparent average permeability of the pipe of ... findQ∗(0)inq∗c=Q∗(0)outq∗c=12∂p(0)(0,t)∂x=12Pin(t)Csinh(2C)1 +cosh(2C). (31) Journal of Mathematics in Industry (2011) 1:8 DOI 10. 1186/2190-5983-1-8 RESEARCH Open AccessDesigning irrigation pipesAntonio Fasano ·...