Vascular endothelial cells are cultured on the inside of a 10-cm long hollow tube that has aninternal diameter of 3 mm. Culture medium flows through the tube at Q= 1 ml/s. The cells produce a cytokine, EDGF, at a rate nEDGF (production rate per cell area) that depends on the local wall shear stressaccording to nEDGF = kτwall, wherek is an unknown constant with units of ng/dyne per s. The flow in the tubeis not fully developed, such that the shear stress is known to vary with axial position according toτwall = τ0(1 –βx), where β= 0.02 cm−1, τ0= 19 dyne/cm2, and x is the distance from the tubeentrance. Under steady conditions a sample of medium is taken from the outlet of the tube, and theconcentration of EDGF is measured to be 35 ng/ml in this sample. What isk?

Flow occurs through a layer of epithelial cells that line the airways of the lung due to avariety of factors, including a pressure difference across the epithelial layer(ΔP = P0) and, in the case of transientcompression, to a change in the separation between the two cell membranes, w2, as a function of time. We consider these cases sequentially below. Note that the depthof the intercellular space into the paper is L, and the transition in cellseparation from w1 to w2 occurs over alength δ much smaller than H1 andH2. (See the figure overleaf.)