I was going through a worked example in book "Concepts in Thermal Physics" by S.J. Blundell and K.M.Blundell. The example talks about measuring viscosity of a gas between two coaxial cylinders. 1. The problem statement, all variables and given/known data Two vertical coaxial cylinders. Outer cylinders is rotated by a motor at constant angular speed, while the inner one is suspended by a torsion wire. The torque is transmitted from rotating cylinder to suspended one via the gas. Find torque on the inner cylinder (i.e. couple on inner cylinder required to keep it from rotating) and show how can you measure viscosity using this set up. 2. Relevant equations The momentum flux of x momentum in z direction is Πz = -η duz/dz Momentum flux is equal to - shear stress Force = stress * area Linear velocity us related to angular velocity as u(r) = r*ω(r) 3. Solution To find the force on the on inner cylinder we just need to find the flux of momentum in radial direction to find shear stress. Then should be easy to find torque and so on and so forth. So authors solve the problem by first considering the velocity gradient. They say that that molecules of gas will be travelling in a circular motion and consider the velocity as u(r) = r*ω(r) . The do not actually find the velocity profile of the flow, they just consider the velocity gradient of the flow. So they find: du/dr = ω + r dω/dr (1)But then the next part of their solution has me completely stuck. They completely ignore the first term. They state (referring to equation (1) ): "but the first term on the right hand side simply corresponds to the velocity gradient due to rigid rotation and does not contribute to the viscous shearing stress which thus is just ηrdω/dr". This does not make sense to me. ω is a function of r, I really struggle to understand the reasoning to ignore the first term. Shearing stress is related to velocity gradient. du/dr is the velocity gradient in radial direction. Why would you completely a term in it? Does anyone have a nice explanation? I found an article which considers a similar problem, but goes to find the actual velocity profile of the flow: http://www.syvum.com/cgi/online/serve.cgi/eng/fluid/fluid301.html There again, it just says: From the velocity profile, the momentum flux (shear stress) is determined as:s I imagine the reason it uses such a weird term r d/dr(vθ/r) is because of the same logic of ignoring the "velocity gradient due to rigid rotation", but is there a "mathematical" explanation? Is my understanding of shear stress and momentum flux too simplistic? Can this be shown mathematically by properly considering the stress tensor? The rest of the example makes sense - they find force from stress. the torque from force, integrate between two cylinders and integrate between ω0 and 0.