Rates of pressure and volume change

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SUMMARY

The discussion centers on calculating the speed of water flowing out of a hose connected to a sealed cylindrical tank under varying water heights. When the water height is 3.0m and 2.0m, the absolute pressure of the compressed air is 4.20 x 10^5 Pa, with atmospheric pressure at 1.00 x 10^5 Pa. The problem requires the application of Bernoulli's Equation to determine the flow speed and the height at which the water ceases to flow.

PREREQUISITES
  • Understanding of Bernoulli's Equation
  • Familiarity with the Ideal Gas Law (PV = nRT)
  • Knowledge of fluid dynamics principles
  • Basic calculus for relating volume and height changes
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  • Study Bernoulli's Equation applications in fluid flow
  • Explore the Ideal Gas Law and its implications in pressure-volume relationships
  • Research fluid dynamics concepts related to pressure differentials
  • Learn about the relationship between flow speed and height in fluid systems
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Students in physics or engineering courses, particularly those studying fluid dynamics, as well as educators seeking to explain concepts related to pressure and flow in liquids.

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Homework Statement


A large tank of water has a hose conected to. The tank (a cylinder) is 4.0 m in height and the tank is sealed at the top and has compressed air between the water surface and the top. When the water height h has the value 3.50m, the absolute pressure p of the compressed air is 4.20*10^5Pa. Assume that the air above the water expands at constant temp. and take the atmospheric pressure to be 1.00*10^5Pa. What is the speed at which the water flows out of the hose at h = 3.0m and h = 2.0m? at what value h does the water stop flowing?




Homework Equations


I'm pretty sure this involves the ideal gas equation of state PV = nrT and maybe the fact that the volume increase or decrease dV with respect to time is equal to the height increase or decrease dh with respect to time...




The Attempt at a Solution



I have tried quite a few things but to be honest I am stumped at how to approach this problem so please help...i strongly appreciate it...
 
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Have you had Bernoulli's Equation yet? The fact that the problem asks for the speed of water flow and gives you pressure differences leads me to suspect that they want you to apply that. (Otherwise we'll have to work this out from basic principles...)
 

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