How Do Fluid Dynamics Affect Medical and Environmental Applications?

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SUMMARY

This discussion focuses on the application of fluid dynamics principles in medical and environmental contexts. Key calculations include determining the excess pressure required for a hypodermic needle with a length of 3.2 cm and diameter of 0.32 mm to achieve a flow rate of 1 g/s, and analyzing the pressure drop in the bronchus during inhalation when air speed doubles through a constriction. Additionally, the discussion addresses calculating the necessary pipe radius for a water flow rate of 0.0500 m³/s over a distance of 315 km from a 25.0 m tall tank, utilizing the viscosity of water at 20°C.

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  • Understanding of Bernoulli's equation
  • Knowledge of fluid viscosity and flow rate calculations
  • Familiarity with the principles of incompressible flow
  • Basic skills in dimensional analysis and unit conversions
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  • Learn how to calculate pressure drops in various flow scenarios
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1.) A hypodermic needle is 3.2 cm in length and 0.32 mm in diameter. What excess pressure is required along the needle so that the flow rate of water through it will be 1 g/s?

answer should be in units Pa

2.) When a person inhales, air moves down the bronchus (windpipe) at 14 cm/s. The average flow speed of the air doubles through a constriction in the bronchus. Assuming incompressible flow, determine the pressure drop in the constriction.

answer should be in units Pa

3.) A pipe carrying water from a tank 25.0 m tall must cross 3.15 102 km of wilderness to reach a remote town. Find the radius of the pipe so that the volume flow rate is at least 0.0500 m3/s. (Use the viscosity of water at 20°C.)

answer should be in units of Meters
 
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