How Do Fluid Dynamics Affect Medical and Environmental Applications?

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Fluid dynamics play a crucial role in medical and environmental applications, as demonstrated by calculations involving hypodermic needles, bronchial airflow, and water transport in pipes. For a hypodermic needle with specific dimensions, the required excess pressure for a flow rate of 1 g/s must be calculated in Pascals. Additionally, the pressure drop through a bronchial constriction can be determined by analyzing the change in airflow speed, assuming incompressible flow. Lastly, to ensure a minimum volume flow rate from a water tank over a significant distance, the appropriate pipe radius must be calculated using the viscosity of water at 20°C. Accurate calculations and adherence to the provided homework template are essential for effective assistance.
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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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