a) [20 pts] The Dean number is a non-dimensional parameter that measures the relative importance of inertia and centripetal forces vs. viscous forces and is useful for characterizing flows in curved pipes and channels. For our experimental setup it can be defined as: where Re is the Reynolds number: De = Re W 2R Re == puw μ and u is the mean axial velocity in the channel. When the Dean number is large, vortical flow structures or secondary flows are observed in the cross sections of the channel. But when the Dean number is small (say De <40), these structures do not form and the flow is unidirectional. To ensure that the flow in our experiment does not contain secondary flows, calculate the maximum steady flow rate Q through the channel that would produce a Dean number below a maximum value Dm. do b) [30 pts] Find the pressure P, that needs to be generated by the piston of the syringe in order to maintain the constant flow rate Q calculated in a). Neglect viscous losses in the flow chamber, and assume the syringe is large and the injection long enough so that steady flow conditions are a reasonable approximation for the duration of the experiment. c) [30 pts] For the conditions of a) and b), find the restraining force necessary to maintain the flow chamber fixed in place. Neglect viscous forces in the flow chamber. d) [20 pts] If the syringe has a length Lo before the needle, for how long can the flow in the experiment be maintained at the desired steady state value? Po + W d₁ >> Kn R d2- Lt Kv Figure 1 Pa