19. Fluid Mechanics

(II) Suppose the top surface of the vessel in Fig. 13–58 is subjected to an external pressure P₂ in addition to atmospheric pressure P₀ .

(b) If P₂ = 0.85 atm and y₂ - y₁ = 2.4 m, determine v1 for water.

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(I) A gardener feels it is taking too long to water a garden with a 3/8 -in. - diameter hose. By what factor will the time be cut using a 5/8 - in. - diameter hose instead? Assume nothing else is changed.

You are watering your lawn with a hose when you put your finger over the hose opening to increase the distance the water reaches. If you are holding the hose horizontally, and the distance the water reaches increases by a factor of 4, what fraction of the hose opening did you block?

(II) If cholesterol buildup reduces the diameter of an artery by 25%, by what % will the blood flow rate be reduced, assuming the same pressure difference?

(II) Estimate the air pressure inside a category 5 hurricane, where the wind speed is 300 km/h (Fig. 13–56).

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(II) A viscometer consists of two concentric cylinders, 10.20 cm and 10.60 cm in diameter. A liquid fills the space between them to a depth of 15.0 cm. The outer cylinder is fixed, and a torque of 0.024 m · N keeps the inner cylinder turning at a steady rotational speed of 57 rev/min. What is the viscosity of the liquid?

(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.