Home Repair. You need to extend a 2.50-inch-diameter pipe, but you have only a 1.00-inch-diameter pipe on hand. You make a fitting to connect these pipes end to end. If the water is flowing at 6.00 cm/s in the wide pipe, how fast will it be flowing through the narrow one?

(I) Engine oil (assume SAE 10, Table 13–3) passes through a fine 1.80-mm-diameter tube that is 10.2 cm long. What pressure difference is needed to maintain a flow rate of 5.8 mL/min?

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(II) Poiseuille’s equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the Reynolds number, Re, exceeds approximately 2000. Re is defined as

Re = 2υ¯rρ /η ,

where υ¯ is the average speed of the fluid, ρ is its density, is its viscosity, and r is the radius of the tube in which the fluid is flowing.

(a) Determine if blood flow through the aorta is laminar or turbulent when the average speed of blood in the aorta ( r = 1.2 cm) during the resting part of the heart’s cycle is about 35 cm/s.