BackA tree loses water to the air by the process of transpiration at the rate of 110 g/h. This water is replaced by the upward flow of sap through vessels in the trunk. If the trunk contains 2000 vessels, each 100 μm in diameter, what is the upward speed in mm/s of the sap in each vessel? The density of tree sap is 1040 kg/m³.
A nuclear power plant draws 3.0 x 106 L/min of cooling water from the ocean. If the water is drawn in through two parallel, 3.0-m-diameter pipes, what is the water speed in each pipe?
(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 where 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. 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.
Estimate the air pressure inside a category 5 hurricane, where the wind speed is 300 km/h (Fig. 13–56).
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(I) Calculate the average speed of blood flow in the major arteries of the body, which have a total cross-sectional area of about 2.0 cm2. Use the data of Example 13–14.
(II) Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.78 m/s through a pipe 5.0 cm in diameter. The pipe tapers down to 2.8 cm in diameter by the top floor, 16 m above (Fig. 13–57), where the faucet has been left open. Calculate the flow velocity and the gauge pressure in the pipe on the top floor. Assume no branch pipes and ignore viscosity.
(II) Water at a gauge pressure of 3.8 atm at street level flows into an office building at a speed of 0.78 m/s through a pipe 5.0 cm in diameter. The pipe tapers down to 2.8 cm in diameter by the top floor, 16 m above (Fig. 13–57), where the faucet has been left open. Calculate the gauge pressure in the pipe on the top floor. Assume no branch pipes and ignore viscosity.
(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. If P2 = 0.85 atm and y2 - y1 = 2.4 m, determine v1 for water.
A pump supplies water to a 1.59-cm inner diameter hose that tapers down to a 0.953-cm-diameter nozzle. The nozzle is aimed so water comes out at a 45° angle and lands 3.0 m away. The nozzle is 0.60 m above ground level, and the pump output is essentially at ground level. What pressure is supplied by the pump?
A fish tank has dimensions 36 cm wide by 1.0 m long by 0.60 m high. If the filter should process all the water in the tank once every 2.5 h, what should the flow speed be in the 3.0-cm-diameter input tube for the filter?