What Gauge Pressure is Needed for a Water Jet to Reach 29.8 m/s?

In summary, the problem involves finding the required gauge air pressure in a fire extinguisher to achieve a water jet speed of 29.8 m/s when the water level is 0.515 m below the nozzle. The Bernoulli's equation is used, with atmospheric pressure as p1, density of water, v1 as 29.8 m/s, and height of 0.515 m. However, further clarification is needed as the diagram provided is of a tank with a water pipe in the middle. Adjustments to the variables may be necessary to obtain the correct solution.
  • #1
RED20
1
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Help! Physics Fluids problem

Homework Statement


Water is forced out of a fire extinguisher by air pressure. How much gauge air pressure in the tank (above atmospheric) is required for the water jet to have a speed of 29.8 m/s when the water level is d=0.515 m below the nozzle?


Homework Equations


I tried using bernoulli's equation, p1+ 1/2*p*v1^2 + p*g*y1= p2 + 1/2*p*v2^2 + p*g*y2
I am not sure what variables I am supposed to put in where, as the diagram i am given in the question is that of a tank with a water pipe in the middle of it.


The Attempt at a Solution


I attempted to solve for p2, using p1 as atmospheric pressure, density as the density of water, v1 as 29.8m/s^2, height as 0.515. The rest of the terms on the second half of the equation I thought would cancel because the height would be 0 and I thought the starting velocity is 0. I ended up getting -4.49 x 10^5 Pa...which isn't right...please help!
 
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  • #2
The height of the water in the jet is below the nozzle. I think you want to either make y1 negative, or make it zero and use the .515m for y2.
 
  • #3


I understand your frustration with this problem. It can be difficult to solve fluid dynamics problems, but with the right approach, it can be done. First, let's review Bernoulli's equation. It states that the total pressure at one point in a fluid is equal to the total pressure at another point in the fluid, plus the kinetic energy of the fluid, plus the potential energy of the fluid. In this case, we are dealing with a pressurized tank of air and water, so we can use this equation to find the pressure at the nozzle.

The first step is to determine the total pressure at the nozzle. This includes the atmospheric pressure (p1) and the gauge pressure (p2) from the air in the tank. We can assume that the air pressure is uniform throughout the tank, so we can use the height of the water (d) to calculate the gauge pressure. The equation for gauge pressure is p2 = ρgh, where ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water.

Next, we need to calculate the kinetic energy of the water jet. This can be done using the equation for kinetic energy, KE = 1/2 * ρ * v^2, where ρ is the density of water and v is the velocity of the water jet.

Finally, we need to calculate the potential energy of the water. This is done using the equation PE = ρ * g * y, where ρ is the density of water, g is the acceleration due to gravity, and y is the height of the water.

Now, we can plug these values into Bernoulli's equation and solve for the gauge pressure (p2). Keep in mind that the pressure at the nozzle (p1 + p2) is equal to the pressure at the bottom of the tank, which is atmospheric pressure (p1). This means that p1 + p2 = p1, or p2 = 0.

I hope this helps you solve the problem. Remember to always use the correct units and to double-check your calculations. If you are still having trouble, don't hesitate to seek help from your teacher or classmates. Good luck!
 

Related to What Gauge Pressure is Needed for a Water Jet to Reach 29.8 m/s?

1. What are some common types of fluid problems in physics?

Some common types of fluid problems in physics include calculating the flow rate of a fluid through a pipe, determining the pressure at various points in a fluid, and analyzing the buoyant force on an object submerged in a fluid.

2. How do I approach solving a fluid problem in physics?

The first step in solving a fluid problem in physics is to clearly define the given variables and known values. Then, use relevant equations and principles (such as Bernoulli's equation or Pascal's law) to determine the unknown variables. It may also be helpful to draw a diagram or use a visual aid to better understand the problem.

3. What is the difference between a fluid and a solid?

A fluid is a substance that can flow and take the shape of its container, while a solid has a fixed shape and volume. Additionally, fluids are generally considered to be incompressible, meaning their density remains constant under pressure, whereas solids can be compressed under pressure.

4. How does viscosity affect fluid behavior?

Viscosity is a measure of a fluid's resistance to flow. In general, fluids with higher viscosity (such as honey) flow more slowly than those with lower viscosity (such as water). Viscosity also plays a role in the creation of laminar or turbulent flow patterns.

5. Can fluid mechanics be applied to real-world situations?

Yes, fluid mechanics has many practical applications in various fields such as engineering, meteorology, and biology. For example, understanding the behavior of fluids is crucial in designing efficient pipes for water distribution, predicting weather patterns, and studying the flow of blood in the human body.

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