In Eqn. 2 , sap velocity is estimated from four types of quantities: a ratio of temperature increases between two probes (δ j/δ i), the thermal diffusivity k , the positions of the two probes (x i, x j,y i, y j), and the time elapsed since the heat pulse length (t ). If the two probes are parallel to one another (i.e., at identical azimuthal positions relative to the flow axis), then y i =y j, giving