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

AI Thread Summary
To find the speed of water in the nozzle, apply the principle of conservation of mass, which indicates that the flow rate must remain constant. Using the diameters and initial speed of the water, the speed in the nozzle can be calculated. For pressure in the nozzle, Bernoulli's equation is used, but care must be taken to include the initial atmospheric pressure in the calculations. The density of water is correctly taken as 1000 kg/m³, but ensure that all units are consistent when applying the equation. The final pressure should not be negative if all values are accurately substituted.
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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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