Pressure in Garden Hose: Solving P + (1/2)pv^2 + pgh

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SUMMARY

The discussion focuses on calculating the gauge pressure inside a garden hose using the equation P + (1/2)pv^2 + pgh. The scenario involves a hose connected to a faucet with a nozzle turned off, resulting in water spraying vertically from a leak to a height of 0.82 meters. The gauge pressure is determined by comparing the energy density inside the hose to that at the top of the spray, confirming that the correct approach involves using the energy density equation effectively. The conclusion reached is that the gauge pressure can be accurately calculated using the principles of fluid mechanics.

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  • Understanding of fluid mechanics principles
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  • Knowledge of the energy density equation in fluid dynamics
  • Ability to perform basic calculations involving height and pressure
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  • Study the Bernoulli's equation in fluid dynamics
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Am I substituting other variables into P + (1/2)pv^2 + pgh in this problem?

A garden hose is attached to a water faucet on one end and a spray nozzle on the other end. The water faucet is turned on, but the nozzle is turned off so that no water flows through the hose. The hose lies horizontally on the ground, and a stream of water sprays vertically out of a small leak to a height of 0.82 m. What is the gauge pressure inside the hose? (Gauge pressure is the amount by which the pressure exceeds atmospheric pressure.)
 
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That is the correct equation. All you have to do is compare between a point inside the hose (energy density in hose = P_in ) and the point at the top of the vertical spray (energy density at top = pgh + Po).
 
Great, got the answer, thanks!
 

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