Change in pressure with fluids

In summary, the conversation discusses the speed and pressure of water in a garden hose with a diameter of 0.66 in and a nozzle with a diameter of 0.25 in. The water is flowing at a speed of 0.65 m/s and has a pressure of 1.0 atmospheres. The goal is to find the speed and pressure at the end of the nozzle. The speed is easily determined using the given information, but the pressure requires the use of an equation and may be affected by the density of water.
  • #1
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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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  • #2
The pressure will come out of your equation. Don't forget that being on Earth and having an atmosphere, we have an initial pressure.
 
  • #3


I would like to clarify a few things before providing a response. Firstly, it is important to note that the equation you used, P1+1/2 pv1^2=P2+1/2 pv2^2, is known as Bernoulli's equation and is used for incompressible fluids, which includes water. However, this equation assumes steady flow, which may not be the case in this scenario as the water is flowing through a nozzle.

Secondly, the density of water is not a constant value and can vary depending on factors such as temperature and pressure. In this case, the density of water should be calculated using the ideal gas law, which takes into account the pressure and temperature of the water.

Now, to answer your questions, the speed of water in the nozzle can be calculated using the continuity equation, which states that the mass flow rate at any given point in a pipe is constant. This can be expressed as A1v1=A2v2, where A is the cross-sectional area and v is the velocity. Using this equation, we can find the speed of water in the nozzle to be approximately 2.6 m/s.

To find the pressure in the nozzle, we can use the Bernoulli's equation, but we need to make some assumptions. Firstly, we can assume that the height of the nozzle is the same as the height of the garden hose, so the change in elevation is zero. Secondly, we can assume that the pressure at the surface of the water in the hose is atmospheric pressure (1.0 atmospheres). With these assumptions, we can rearrange the Bernoulli's equation to solve for P2, which gives us a pressure of approximately 1.6 atmospheres in the nozzle.

However, as mentioned earlier, this calculation assumes steady flow and neglects factors such as friction and turbulence, which can affect the pressure in the nozzle. To accurately determine the pressure, we would need to take into account these factors and use more advanced equations and techniques.
 

1. How does pressure change with depth in a fluid?

The pressure in a fluid increases with depth. This is because the weight of the fluid above a certain depth exerts a force on the fluid below, causing an increase in pressure.

2. How does the density of a fluid affect pressure?

The density of a fluid has a direct effect on pressure. The higher the density of the fluid, the greater the pressure it exerts. This is because a denser fluid contains more particles, which results in a higher force being applied per unit area.

3. Does the shape of a container affect the pressure of a fluid?

Yes, the shape of a container can affect the pressure of a fluid. The pressure at any point in a fluid is determined by the depth and density of the fluid above that point. Therefore, the shape of the container can affect the depth of the fluid at a certain point, and thus, the pressure.

4. What is the relationship between pressure and volume in a fluid?

According to Boyle's Law, the pressure of a fluid is inversely proportional to its volume. This means that as the volume of a fluid decreases, the pressure increases, and vice versa, as long as the temperature and amount of fluid remain constant.

5. Can changes in temperature affect the pressure of a fluid?

Yes, changes in temperature can affect the pressure of a fluid. According to Gay-Lussac's Law, the pressure of a gas (and therefore, a fluid) increases with an increase in temperature and decreases with a decrease in temperature, as long as the volume and amount of gas remain constant.

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