Maximum height of pumped water

In summary, the conversation discusses how to determine the maximum height that water can reach when pumped from a hydrant at a given rate and angle. The equations of continuity, Bernoulli's equation, and the concept of treating water as a projectile are mentioned as possible methods for finding the solution. Ultimately, it is determined that knowing the velocity of the water exiting the hose is sufficient for solving the problem.
  • #1
monicaalves
2
0

Homework Statement



There is a fire in a building, so the fireman connects a hose to a hydrant that pumps 2 litres of water per second. The exit of the hose has and area of 15cm^2.
Which is the maximum floor of the building that the water can reach considering that it exits the hose at an height of 1,5m from the ground with an angle of 75 degrees?


Homework Equations



The pressure in a fluid at depth h in the fluid: p = Po + dgh
Equation of continuity for fluids: A1.v1 = A2.v2
Bernoulli’s equation: p1 + 1/2dv1^2 + dgh = constant

The Attempt at a Solution



Assuming that the area of the exit of the hose is the same of the area where the water exist the hydrant, I can assume using the equation of continuity that the velocity that the water is being pumped will the the same at the exit of the hose and I can find that value.
In this case, should I imagine the water like a solid object being launched from the ground, or is there any other equation to use when we are dealing with fluids?
 
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  • #2
This is really a "projectile problem." Treat each little parcel of water exiting the hose as a separate (non-interacting) mass. You know the initial velocity of the projectile and the angle that it is launched. Determine the maximum height that the projectile reaches.
 
  • #3
If you know the velocity of water exiting the hose, do you really need to know anything else to find how high it can go?
 
  • #4
Thank you for you explanation Chestermiller, now I understand. I was looking at this as a pressure problem, but I just need to see water as a projectile and it's solved :)
 
  • #5


I would approach this problem by considering the principles of fluid mechanics and using relevant equations to determine the maximum height that the pumped water can reach. First, I would use the equation of continuity to determine the velocity of the water at the exit of the hose, assuming that the area of the exit is the same as the area where the water exits the hydrant. This will give me a starting point for further calculations.

Next, I would consider the Bernoulli's equation, which takes into account the pressure, velocity, and height of a fluid at different points in a system. By applying this equation at the exit of the hose and at the maximum height that the water can reach, I can determine the relationship between the pressure and velocity at these points. From there, I can solve for the maximum height using the known values for the pressure, velocity, and angle of the hose.

It is important to note that the behavior of fluids, such as water, is different from that of solid objects, so it is not appropriate to imagine the water as a solid object being launched from the ground. The equations and principles of fluid mechanics must be used to accurately determine the maximum height that the pumped water can reach.
 

What is the maximum height of water that can be pumped?

The maximum height of pumped water depends on several factors such as the power of the pump, the diameter and length of the pipe, and the density of the water. Generally, a pump can lift water up to 25 feet for every 1 horsepower of power.

What type of pump is best for pumping water to a high height?

The type of pump that is best for pumping water to a high height is called a high-pressure pump. This type of pump is designed to handle high pressure and can push water to a height of up to 1000 feet.

How does elevation affect the maximum height of pumped water?

Elevation affects the maximum height of pumped water as it increases the atmospheric pressure. As the atmospheric pressure increases, the maximum height of pumped water decreases. This means that at higher elevations, the maximum height of pumped water is lower compared to lower elevations.

What is the relationship between water flow rate and maximum height of pumped water?

The higher the water flow rate, the lower the maximum height of pumped water. This is because as the water flow rate increases, the pressure exerted on the water decreases, making it harder for the pump to lift the water to a high height.

Can the maximum height of pumped water be increased?

Yes, the maximum height of pumped water can be increased by using a larger and more powerful pump, reducing the diameter and length of the pipe, or by using a pump with a higher pressure rating. However, these changes may also affect the overall efficiency and cost of the pumping system.

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