Homework 3 Solutions

It can be modeled as constant the fluid level does not

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Unformatted text preview: of the IV liquid ρ, and the acceleration due to gravity g. It can be modeled as constant (the fluid level does not decrease because the bag is very large). • Assume that neither the fluid, nor the catheter or the IV bag are compressible. The catheter is an inelastic cylindrical tube of radius r and length d. • The density and the viscosity of the fluid are both significant to the problem. The catheter will present a hydraulic resistance Rh and hydraulic inertance Lh. a) Draw the equivalent circuit to this model. b) Find the analytic expression for the steady state flow, Q, of liquid through the catheter in terms of height of ρ, g, x, d, r, PAC, PDC, and viscosity of the fluid μ. c) How high must you hang the IV bag to prevent the patient from bleeding out through the catheter? d) How high must you hang the IV bag to prevent any temporary backflow? Problem 3: Doppler Flow Estimation. An ultrasonic Doppler blood velocity transducer is positioned near an artery as shown below: Assume that the transducer is highly directional, in that the beams from the emitter and towards the detector are very narrow (almost paraxial). This angle θ for the emitted...
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