How to Find Pressure in a Nozzle Using Bernoulli's Equation?

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SUMMARY

The discussion focuses on calculating the pressure in a nozzle using Bernoulli's Equation, specifically for a garden hose scenario. The initial conditions include a hose diameter of 0.66 inches, water speed of 0.65 m/s, and an initial pressure of 1.0 atmospheres. The nozzle diameter is 0.25 inches. The user successfully calculated the speed of water in the nozzle but encountered difficulties determining the pressure, leading to negative results when applying the equation P1 + 1/2 pv1^2 = P2 + 1/2 pv2^2. The correct approach involves using the density of water (1000 kg/m³) and accounting for atmospheric pressure in the calculations.

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A garden hose with a diameter of 0.66 in has water flowing in it with a speed of 0.65 m/s and a pressure of 1.0 atmospheres. At the end of the hose is a nozzle with a diameter of 0.25 in.
(a) Find the speed of water in the nozzle.
(b) Find the pressure in the nozzle.

I found out the speed of the water, but I am not sure how to find the pressure. I tried using the equation P1+1/2 pv1^2=P2+1/2 pv2^2 and solving for P2 but the answer that I get is negative. I think the problem is that I'm not sure about what to plug in for p. I looked up the density of water and used that value (1000), but am I supposed to figure it out another way? Because the only other equation I found for density was m/v and I wouldn't be able to calculate that.
 
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The pressure will come out of your equation. Don't forget that being on Earth and having an atmosphere, we have an initial pressure.
 

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