1. The problem statement, all variables and given/known data I have a tutorial question I have been struggling with. The problem is: The ﬂow through a closed, circular sectioned pipe may be metered by measuring the speed of rotation of a propeller having its axis along the pipe central line. Derive a relation between the volume ﬂow rate and the rotational speed of the propeller in terms of the diameter of the pipe and the propeller and the density and viscosity of the ﬂuid. A propeller of 75mm diameter installed in a 150mm pipe carrying water at 42.5 l/s is found to rotate at 20.7rps. If a geometrically similar propeller of 375mm diameter rotates at 10.9rps in air ﬂow through a pipe of 750mm diameter, estimate the volume ﬂow rate of the air. (The air density is 1:28kg/m3 with viscosity of 1.93E-05 Ns/m2 as and the viscosity of water is 1:145E-03 Ns/m2). 3. The attempt at a solution I think my main problem is just finding all the pertinent variables to start with. After that I should be able to use the Buckingham Pi theorem, form dimensionless groups the use similarity to find the value of volume flow rate for air. The variables I can think of are: Volume flow rate, Q pipe diameter, D propeller diameter, d density, ρ viscosity, μ rotational speed, N I have a feeling I should also include angular velocity or just theta for the angle but I'm cant figure it out.