You are discussing blood flow in dialysis machines with an engineer who designs them. The engineer has come up with a design where the flow rate is limited by a particular tube, and wants to know whether this tube in design A results in a better or worse flow rate than a different tube in design B.

Design A:

tube length: 25.0 cm

tube inside diameter: 0.45 cm

pressure difference between ends of tube: 15 Pa

Design B:

tube length: 10.0 cm

tube inside diameter: 0.30 cm

pressure difference between ends of tube: 36 Pa

a) Which design results in a better flow rate? Explain your answer.

b) What is the flow rate in the better design? Use a viscosity of 3.8 x 10-3 Pa s for the blood. (Note that the viscosity of blood depends on its flow rate and the radius of the tube it is moving in; it is not a Newtonian fluid.)

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